# Assistant conversation 89BPW3 - Canonical URL: - Resource IRI: - Type: assistant conversation - Mode: chat ## Transcript ### 1. User Import the attached PDF documents. [Uploaded PDFs] - peatfield-minoan-peak-sanctuaries.pdf: Sheaf file #53RA8V ### 2. Assistant tool calls #### Tool call: `document_import` ```json { "action": "stage", "file_ids": [ "53RA8V" ], "name": "Import peatfield-minoan-peak-sanctuaries.pdf" } ``` ### 3. Tool result: document_import { "status": { "counts": { "pending": 1 }, "files": [ { "error": null, "status": "pending", "file_id": "53RA8V", "execution_id": null } ] }, "sources": [], "action": "stage", "run_id": "SXAKGL", "file_ids": [ "53RA8V" ], "run_iri": "https://m.sheaf.less.rest/SXAKGL" } ### 4. Assistant tool calls #### Tool call: `document_import` ```json { "action": "extract", "run_id": "SXAKGL" } ``` ### 5. 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Tool result: document_import { "next": "Resolve metadata, rebuild indexes, and validate reader pages.", "action": "import", "documents": [ { "status": "imported", "title": null, "file_id": "53RA8V", "document_id": "ARP5U7", "document_iri": "https://m.sheaf.less.rest/ARP5U7" } ], "run_id": "SXAKGL" } ### 10. Assistant tool calls #### Tool call: `document_import` ```json { "action": "metadata", "run_id": "SXAKGL" } ``` ### 11. Tool result: document_import { "action": "metadata", "documents": [ { "match": { "reason": "title match accepted for Crossref type journal-article", "source": "doi", "identifier": "10.1017/s0068245400019729", "score": 1.0, "doi": "10.1017/s0068245400019729", "accept?": true, "crossref_title": "The Topography of Minoan Peak Sanctuaries", "crossref_type": "journal-article" }, "metadata": { "title": "The Topography of Minoan Peak Sanctuaries", "usage": { "cost": { "total": 0.001468, "tokens": 0.001468, "tools": 0.0, "storage": 0.0, "images": 0.0, "input_cost": 0.001206, "output_cost": 2.62e-4, "reasoning_cost": 0.0, "line_items": [ { "count": 4824, "id": "token.input", "kind": "tokens", "component": "token.input", "cost": 0.001206, "quantity": 4824 }, { "count": 175, "id": "token.output", "kind": "tokens", "component": "token.output", "cost": 2.62e-4, "quantity": 175 } ] }, "output_tokens": 175, "input_tokens": 4824, "total_cost": 0.001468, "reasoning_tokens": 0, "input_cost": 0.001206, "output_cost": 2.62e-4, "reasoning_cost": 0.0, "cached_tokens": 0, "total_tokens": 4999, "tool_usage": {}, "image_usage": {}, "cache_creation_tokens": 0 }, "year": "1983", "model": "google:gemini-3.1-flash-lite-preview", "notes": "The document provides clear bibliographic metadata, including author, title, publication, volume, year, and pages. The DOI is explicitly stated.", "issue": null, "pages": "273-279", "authors": [ "A. A. D. Peatfield" ], "doi": "10.1017/s0068245400019729", "volume": "78", "isbn": null, "publication": "The Annual of the British School at Athens", "confidence": "high", "source_filename": null }, "document_id": "ARP5U7", "wrote": true } ], "run_id": "SXAKGL" } ### 12. Assistant tool calls #### Tool call: `document_import` ```json { "action": "validate", "run_id": "SXAKGL" } ``` ### 13. Tool result: document_import { "action": "validate", "documents": [ { "title": "The Topography of Minoan Peak Sanctuaries", "valid": true, "document_id": "ARP5U7", "readable_chunks": 82, "source_pages": 8, "reader_path": "/ARP5U7" } ], "run_id": "SXAKGL", "embedding_status": "completed", "search_rows": 3613, "embedding_errors": 0 } ### 14. Assistant Imported and validated: - **A. A. D. Peatfield, “The Topography of Minoan Peak Sanctuaries” (1983)** — #ARP5U7 - 8 pages, 82 readable chunks - DOI: `10.1017/S0068245400019729` - Extraction and search indexing completed successfully. ### 15. User thanks! i just accidentally rederived the principle of this paper while thinking about the dual of basins and stuff... can you read it and write a microabstract for it, and give it some beautiful cover art? ### 16. Assistant tool calls #### Tool call: `get_document` ```json { "id": "ARP5U7" } ``` ### 17. Tool result: get_document DOCUMENT #ARP5U7 Title: The Topography of Minoan Peak Sanctuaries Outline: - 1 #5Y4734 The Annual of the British School at Athens - 2 #9XNNAS The Topography of Minoan Peak Sanctuaries - 2.1 #8VUZRZ How to cite this article: - 3 #S9HW3P THE TOPOGRAPHY OF MINOAN PEAK SANCTUARIES ### 18. Assistant tool calls #### Tool call: `read` ```json { "blocks": [ "S9HW3P" ], "expand": true } ``` ### 19. Tool result: read DOCUMENT #ARP5U7 The Topography of Minoan Peak Sanctuaries SECTION #S9HW3P THE TOPOGRAPHY OF MINOAN PEAK SANCTUARIES EXCERPT #U6V3KU p. 1 MOUNTAINTOP shrines are common to the religions of many cultures, but in Bronze Age Greece they appear to be limited to Minoan Crete; none has yet been positively identified in Mycenaean Greece or the Cyclades. 1 The purpose of this paper is to examine the topographic position of Minoan peak sanctuaries, that is, their numbers, distribution, proximity to, and relationship with nearby settlements, and finally to consider the apparent change in these patterns that occurs after LM I. EXCERPT #LHHHF7 p. 1 More than fifty sites are presently claimed as peak sanctuaries all over Crete. 2 Included with this paper is a distribution map of fifty-two sites (FIG. 1). The sites listed are based on Faure's identifications and Rutkowski's own lists, 3 with some additions and deletions based on later research. 4 There is no reason to suppose that the work of identification is at an end; one day the gaps in the distribution map will be filled, and all major Minoan settlements will have their own peak sanctuaries. At present the map shows the greatest proportion of sites grouped in the mountainous region of east Crete. Both Faure and Rutkowski have suggested that it was in Sitias that peak sanctuaries originated. 5 Faure notes the presence of EM III sherds on these eastern peak sanctuaries. 6 Rutkowski, however, shows that almost all peak sanctuaries come within the altitude regions associated with the summer transhumance of sheep and goats. The link between peak sanctuary cult and pastoral farming is also strongly demonstrated by the vast numbers of votive clay figurines of domestic farm animals. East Crete is a predominantly pastoral region; so Rutkowski argues: 'peak sanctuaries came into existence mainly to relieve the fears and cares of the shepherds and cattle breeders'. 7 EXCERPT #U7KFZC p. 1 Faure's arguments from the EM III sherds should be treated with some caution; such pottery continued to be used in east Crete as MM I pottery was introduced and used elsewhere. The large number of peak sanctuaries in Sitias may have less to do with chronology and more EXCERPT #J3QF5Y p. 1 This paper is adapted from a dissertation submitted to the University of London in 1980 as partial fulfilment of an M.A. degree in Aegean Archaeology. The dissertation was a study of Minoan peak sanctuaries based primarily on the published sources. My research is continuing with a doctoral thesis examining all available evidence for Minoan rural shrines; that is, peak sanctuaries, sacred enclosures, and cave shrines. I wish to thank the many archaeologists who have helped me; particularly I am indebted to my supervisor, Professor J. N. Coldstream, and to Professor Bogdan Rutkowski for their advice and encouragement. In addition I am grateful to my fellow student Christine Morris for reading through my script and for help with the distribution map. EXCERPT #GKFZM7 p. 1 1 Possible sites such as the Mycenaean shrine at Apollo Maleatas near Epidaurus or Troilus on Kea may strictly be classed as hill shrines, but they do not reflect the same cult system as the Minoan peak sanctuaries that I argue for here. EXCERPT #MPRNRE p. 1 2 The first sites to be investigated and classed as peak sanctuaries were Petsopha and Iouktas, published respectively in BSA 9 (1902-3) 356-87 and PM 1 (1921) 153-9. Even Platon's general study in KrChron 5 (1951) 96-160 only identified eleven sites. Since 1956, however, Paul Faure's field-work has identified more than fifty possible peak EXCERPT #N7QW83 p. 1 sanctuaries. See BCH 80 (1956) 95-103; 82 (1958) 485-515; 84 (1960) 189-220; 86 (1962) 36-56; 87 (1963) 493-508; 89 (1965) 27-63; 91 (1967) 114-150; 93 (1969) 174-213; 96 (1972) 389-426; 102 (1978) 629-40. Faure's surveys have been followed up by the excavations of Davaras. The latter's excavations of many sites is complemented by Mrs. A. Karetsou's long-term excavation of Mt. Iouktas; see PAE (1974) onwards. Rutkowski's general study of peak sanctuaries, Cult Places in the Aegean World (1972) 152-88, came a little too early to include the work of Davaras and Karetsou. Nevertheless, his work provides a solid foundation for all future study of Minoan shrines; many of his conclusions have been confirmed by the later excavations. EXCERPT #YSMK63 p. 1 3 Rutkowski, op. cit. 321-3. EXCERPT #5GZU7B p. 1 4 In my thesis I shall reassess evidence for the claimed sites and from that produce a revised catalogue and distribution map. In the key to the map here I have asterisked the sites which I feel to be definite or probable peak sanctuaries. EXCERPT #8LSMR2 p. 1 5 Faure, BCH 93 (1969) 174-213, 96 (1972) 389-426 passim ; Rutkowski, op. cit. 184-5. EXCERPT #2SV9ZX p. 1 6 Faure, BCH 96 (1972) 402. EXCERPT #K6GKR3 p. 1 7 Rutkowski, op. cit. 185. EXCERPT #LSVGR7 p. 2 EXCERPT #7RNZ6Y p. 2 EXCERPT #K4CD6P p. 2 A map of the island of Zakros showing the locations of 51 peak sanctuaries. The sanctuaries are marked with numbers 1 through 51, often preceded by an asterisk (*). The map shows the island's coastline, major roads, and a scale bar from 0 to 40 km. The sanctuaries are distributed across the island, with a higher concentration in the central and eastern parts. EXCERPT #HJHCWC p. 2 Key. 1. Vigla, Ayia Triadha: Sitias. 2. Perivolakia: Sitias. 3. Etiani Kephala: Sitias.* 4. Ai Ilia: Sitias. 5. Xykephalo: Sitias.* 6. Vigla Zakrou: Sitias.* 7. Plagia: Sitias.* 8. Korphi tou Mare: Sitias.* 9. Ambelos: Sitias.* 10. Gorge of the Dead, Kato Zakro: Sitias. 11. Traostalos: Sitias.* 12. Zou/Prinias: Sitias.* 13. Modhi: Sitias.* 14. Petsophas: Sitias.* 15. Kalamaki: Sitias.* 16. Lastros: Sitias. 17. Volakas: Ierapetras. 18. Thylakas: Mirabello.* 19. Karphi: Lasithi.* 20. Kراسi: Pedhiadha. 21. Arkovouno: Mirabello. 22. Prophitis Elias, Mallia: Pedhiadha. 23. Entichti Mochos: Pedhiadha. 24. Maza: Pedhiadha.* 25. Smari: Pedhiadha.* 26. Roussos Dhetis: Viannos.* 27. Dhernati: Monophatsi. 28. Choudhetsi: Pedhiadha. 29. Iouktas: Temenos.* 30. Ai Lias: Monophatsi. 31. Koumasa: Monophatsi. 32. Linarou Selli: Monophatsi. 33. Kophinas: Monophatsi.* 34-8. Ayiopharango Valley: Kainourio. 39. Pobia: Kainourio.* 40. Krousonas: Malevisi. 41. Keria: Malevisi.* 42. Gonies: Malevisi.* 43. Pyrgos: Malevisi.* 44. Ayia Apakoe: Mylopotamos. 45. Grivigla: Mylopotamos. 46. Vrysinas: Rethymnon.* 47. Angouscliana: Ayios Vasilios. 48. Drapanokephalo: Apokoronas.* 49. Zourva (nr. Aptera): Apokoronas. 50. Sklokas: Kydonias.* 51. Onychas Rodhopou: Kissamos. 52. Chesmeni Gramvoussa: Kissamos. EXCERPT #G3B95A p. 2 to do with the development of the settlement pattern in that region. In simple terms, Sitias consists of a series of mountain ridges, which are separated by small valleys. These valley plains can be quite fertile, watered by the springs from the mountains that enclose them; settlements, therefore, ancient and modern, are scattered along them. These mountains can also give access to high upland plains suitable for summer pasturage. Consequently, we have a pattern of small communities, made up of one or more settlements within a small valley. Overlooking each valley is the highest peak of the enclosing mountain ridge. In short, the landscape, with its contrasting small valleys and dominating peaks, is particularly suited to the spread of mountain shrines. EXCERPT #65886B p. 2 The altitude of peak sanctuaries varies considerably. Generally, the lowest are around 200 m, e.g. Petsopha at 215 m. At the other end of the scale sanctuaries are also found at over 1000 m, e.g. Karphi at 1148 m, Kastellos at 1160 m, Keria at 1168 m. Despite this huge difference in altitudes Rutkowski has pointed out that all peak sanctuaries fall within certain vegetation zones. 8 Referring to the work of Philippon, 9 Rutkowski has shown that all peak sanctuaries, irrespective of height, are associated with altitude regions that allow for some sort of farming, arable or pastoral, often both. Therefore, today, routes up to the summit pass through vineyards and groves of olive and fruit trees; they climb past mountain meadows of fragrant herb bushes where bees gather nectar, and sheep and goats graze in summer. Indeed, it is striking just how many peak sanctuaries have a gentle slope on one side of the summit, or a high flat area below it, where flocks are still pastured today: e.g. Petsopha, Pyrgos, Vrysinas, Traostalos, Modhi, and Zou. EXCERPT #V45F4Q p. 2 The Minoans obviously made this association between goats and peak sanctuaries, as shown by the agrimia on the famous stone 'peak sanctuary' rhyton from Zakro. 10 Platon has suggested EXCERPT #J8RL4Q p. 2 8 Rutkowski, op. cit. 153-5. EXCERPT #9WYW7N p. 2 9 A. Philippon, Das Klima Griechenlands (1948) 157 ff. EXCERPT #URSWTF p. 2 10 Platon, Zakros (1971) 165. EXCERPT #NWW2TL p. 3 EXCERPT #YTZSZ3 p. 3 EXCERPT #4AWALF p. 3 an etymology for the name Traostalos, the peak sanctuary north of Zakro; he suggests that it means 'enclosure' or 'sanctuary of goats'. 11 EXCERPT #R7HRDE p. 3 Reference to the varying altitudes of peak sanctuaries can be misleading. It is better to speak of distance relative to the nearest settlements, as they display a remarkable consistency. Most peak sanctuaries are within reasonable walking distance even of modern villages. There is no reason to suppose that Minoan settlements and villages were further away; indeed, Faure's surveys make a point of noting Minoan remains which are usually closer than modern settlements. Throughout their work, Faure and Rutkowski state walking times from villages up to the sites. The average quoted time is about one hour. While most of these times are quite possible, it should be understood that these are the optimum times, given the most favourable circumstances—that is, reasonable fitness, knowledge of the quickest route, good weather (not too hot or too windy), etc. It is only our speed-obsessed society that measures time so precisely; so, to people for whom walking was the usual mode of transport, a leisurely climb of several hours would not have seemed a great hardship. For modern mountain chapel festivals (particularly those dedicated to Aphendis Christos on 6 August each year), many people from all over the district gather to make the pilgrimage up the mountain. Only the very old, the very young, and the sick exclude themselves, but even then few people are inclined to race up the mountain. So it seems that a more realistic definition of an average climb is one that takes several hours. EXCERPT #WZ2YSX p. 3 It appears then that the Minoans chose particular mountain summits for peak sanctuaries. Of the various factors which may have influenced that choice, Rutkowski has rightly emphasized accessibility and proximity to mountain pastures. Another factor appears to have been the general prominence and visibility of the chosen mountain. In the open plains height and reasonable access were most important—i.e. the highest mountain is the obvious one from which to worship the deity. For example, Vrysinas is a solitary mountain in the plain of Rethymnon; Kophinas is the highest mountain of the Asterousia range, and its peak is visible even from Phaistos at the far end of the Mesara plain. Iouktas, in turn, dominates the whole of the north central region of Crete, and its profile, like the face of a bearded man lying down (best seen from the west), can only have added to the Minoan belief in its sanctity. EXCERPT #QPEZUU p. 3 In some areas, however, it is not the highest point which is chosen. Minoan Palaikastro is sited in a small coastal plain, just north of the mountain Petsopha. This mountain is a ridge, which juts out from the encircling massif. The ridge has three peaks and the sanctuary is sited on the lowest of the three; it is this peak which most directly overlooks the town. From the other summits the view is obscured by lower platforms and cliffs. Faure notes a similar situation with the peak sanctuary at Etia. 12 The shrine is not on the highest peak of the massif, which is Skopeli at 715 m. Rather it is situated on an isolated butte to the north, 100 m lower down. From there, however, one can see the valley plains of Armeni and Chandra. A third example is observable at Zou. 13 The summit is 803 m high, but the peak sanctuary is on the rising edge of a small plateau, north-west of the summit, at an altitude of 725 m. It is only from this high point that the coastal plain of Sitia can be seen; moreover, from the plain this point looks like the summit. EXCERPT #N7XTK3 p. 3 It seems important then that the sanctuary should be seen from the region it served, and also that it should 'see' that region. The reason may simply have been that the most prominent mountain is the best landmark for worshippers to travel to. We do know, however, EXCERPT #DG93BD p. 3 11 Ibid. 167. EXCERPT #V6H8WE p. 3 12 Faure, BCH 91 (1967) 121. EXCERPT #E5CV7U p. 3 13 Davaras calls this site Prinias, but to avoid confusion with EXCERPT #3VPF89 p. 3 the Iron Age site in Central Crete, I shall follow Faure in referring to this site as Zou. EXCERPT #YF2AGK p. 4 EXCERPT #G6PCML p. 4 EXCERPT #RBPN5L p. 4 from the remains of greasy ashes on the peak sanctuaries, that sacrificial bonfires were lit; fires on mountain tops are lit to be seen, so it is pointless to place one where it could not be seen from the homes of the worshippers. In choosing a mountain with the best view, it seems that the Minoans did not attribute complete omniscience to their deities. For example, the votive figurines of humans and animals were in part, at least, intended as reminders of who and what needed to be protected; similarly, the model parts of the body showed precisely what needed to be cured. Thus, it was important also that the deity could see the area from which the faithful came. EXCERPT #GDV37F p. 4 Naturally, the view from each peak sanctuary is spectacular. As noted above, the peak sanctuaries of east Crete are clustered closely together; so close that one or more other peak sanctuaries are often visible from one another. The most outstanding example of this is Traostalos; from the summit at least six other peak sanctuaries can be seen: Petsopha to the north, Modhi to the north-west, Vigla Zakrou, the tip of Plagia, and Korphi tou Mare, all to the south-west, and Ambelos to the south. A similar situation is found a little further west in central Sitias. The peak sanctuary that dominates the north central plain of Sitias is Zou. South of this mountain are several other peak sanctuaries: Ai Ilia, Xykephalo, and Etia. From all of them Zou can be seen clearly, and the eye is drawn north towards it, as the highest peak on the horizon. In the Iraklion region the same is true, as there Mt. Iouktas is the major focal point for all the other peak sanctuaries as far west as Gonia, and as far east as Karphi. In all these cases it appears that one mountain dominates not only the settlements nearby, but also the other peak sanctuaries within view. EXCERPT #3NXXTZ p. 4 A recent survey of the Ayiopharango valley in south Crete has shown many of these topographic features on a smaller scale. 14 Within this small area the surveyors identified five small hills as peak sanctuaries: sites E4A, E12, E18, W11, MOW1. Each 'peak sanctuary' overlooks a small farmstead and associated tholos tomb. It is suggested that each of these hills was the local shrine of the family/clan who lived in the farmstead and buried their dead in the tholos. The hills are quite low and the surveyors suggested that the site E12, in the centre of the valley, may have been a focus for the whole valley community, not just the local farm. From this and other evidence Bintliff has developed the idea of a sacred hierarchy of peak sanctuaries and other shrines. 15 Furthermore, using a Mexican anthropological study as a model, he goes on to suggest a 'series of ritual pilgrimages' to these shrines 'which unite ever larger units of the regional community'. 16 That is to say, the people near Xykephalo and Etia would have visited not only their own peak sanctuary but also that of Zou, which dominated the whole region. EXCERPT #JRBSR6 p. 4 This idea of a hierarchy among the cult places is both attractive and plausible. 17 Unfortunately, not all the evidence can be said to support it, in particular that of the peak sanctuary shrines themselves. While the peak sanctuaries share certain characteristics—topographic position, votive offerings, etc.—the structural remains vary greatly. On a number of sites Faure has identified walls of stones limiting a temenos area; on some there are small elliptical enclosures, while others have more elaborate multi-roomed structures with large EXCERPT #RK4PYA p. 4 14 Blackman and Branigan, BSA 72 (1977) 13–84. EXCERPT #8LWFKG p. 4 15 Bintliff, Natural Environment and Human Settlement in Pre-historic Greece (British Archaeological Reports, Supplementary series 28, 1977) 145–70. EXCERPT #HE7DN7 p. 4 16 Ibid. 151. EXCERPT #6SJHA3 p. 4 17 The Ayiopharango model is an inspired idea. There is, however, reason to doubt the identification of the five hill sites as peak sanctuaries. My own arguments will be fully presented EXCERPT #HLF9X2 p. 4 in my thesis, but briefly: the sites are chronologically too early; they are too low in relation to the high mountain walls of the narrow valley; there are no figurine finds; none of the hills is visible from any other. In consultation Professor Branigan has agreed that they do not fit the proposed definitions of Minoan peak sanctuaries, but insists that they must be shrines, perhaps some form of EM sacred enclosure. EXCERPT #2NDW6U p. 5 EXCERPT #F6JKNS p. 5 EXCERPT #F2VBJL p. 5 stones incorporated as altars, etc. In contrast, most sites have no identifiable structural remains at all. This great variety seems to bear no relation at all to the suggested hierarchy of peak sanctuaries. For example, from its topographical position, Petsopha can only have been important to the town of Palaikastro. Yet it has a three-roomed structure with a cult bench and stone walls preserved up to a height of about two metres. 18 Modhi and Traostalos, however, have very crude two-roomed structures delineated only by lines of stones, even though from their topographic position they should be more important in the hierarchy. 19 It seems, therefore, that the individual peak sanctuaries were very local, serving only the settlements in the immediate area. Petsopha's comparative elaboration is explained by the nearness and prosperity of its town Palaikastro, whereas Modhi and Traostalos served poorer and smaller farming communities spread over larger areas. EXCERPT #JAHVNN p. 5 We know from the thick layers of ash on all peak sanctuaries that large bonfires must have been lit as part of the ceremonies. From the lines of view noted above, individual bonfires would have been visible from several other peak sanctuaries. The suggested hierarchy then may not have been for a series of ritual pilgrimages, but for a network of sacred beacons which would have united various regions on a single festival night. Perhaps when the gaps in the distribution map are filled, a network of peak sanctuaries may unite all the main inhabited areas of Minoan Crete. EXCERPT #LHVW5W p. 5 In whatever way a hierarchy exists, it must be assumed that Iouktas stands at the head of it. The magnificence of the architecture and quality of the finds are unparalleled at any other peak sanctuary. 20 The site was in use from MM I, as the earliest finds show. 21 But from MM III the shrine underwent a dramatic change; to that period are dated the first of the monumental structures and from then the votives become noticeably richer. 22 It should be noted that MM III is the suggested date for the shrine buildings on other peak sanctuaries which have them. 23 This date coincides with Knossos' increased control over the island and the setting up of the villa system. Rutkowski has suggested that from MM III the peak sanctuary cult became more institutionalized under Knossian royal authority, perhaps with permanent priests. 24 As the peak sanctuary cult was an apparently unifying factor on Minoan society, centralized control over it could have been used politically. As Knossos was the administrative focus for all Crete, so, perhaps, Iouktas became the focal point for the peak sanctuary cult. EXCERPT #ZVRKAG p. 5 Most peak sanctuaries seem to come to an abrupt end soon after the close of the Middle Bronze Age. All the reports date the greater proportion of the excavated material to the Middle Minoan period; Late Minoan finds seem to be few and apparently limited to LM I. Rutkowski suggested 25 that this apparent decline was due to the series of natural catastrophes that Crete suffered from MM III to LM I. The disastrous effects of the Thera eruption finally caused the people to turn from the powerless gods of the skies whence came the poisonous fall-out, and they abandoned the peak sanctuaries. As the following period sees an increase of cult activity in the caves, it is argued that the people turned to chthonic deities, who might be able to stop the earthquakes and protect the homes. Peak sanctuaries, however, were not irrevocably abandoned, as there was a small revival of the cult on a few sites late in LM III. EXCERPT #5G623Y p. 5 18 Myres, BSA 9 (1902-3). EXCERPT #CM9895 p. 5 19 Modhi: Adelt 27 (1972) B2 652; Traostalos: KrChron 17 (1963) 405-6. EXCERPT #AYHZ7Y p. 5 20 Karetsou, PAE (1974) 228-39, (1976) 408-18, (1977) 417-42, (1978) 232-58, (1979) 280-1. EXCERPT #V6MXR5 p. 5 21 Karetsou, PAE (1974) pl. 179c. EXCERPT #R8T4MT p. 5 22 Karetsou, PAE (1976) 408-18. EXCERPT #5BQN7T p. 5 23 Those best substantiated are Petsopha, Traostalos, Modhi, Pyrgos, Gonies, Kophinas, Vrysinas, and Iouktas. EXCERPT #KB3946 p. 5 24 Rutkowski, op. cit. 186. EXCERPT #G7VZW5 p. 5 25 Rutkowski, 'The Decline of the Minoan Peak Sanctuaries', Atti e Memorie del I Congresso Internazionale di Micenologia (Rome 1967) i. 163-8. EXCERPT #PEA9V7 p. 6 EXCERPT #LWFGL6 p. 6 EXCERPT #P6Y3WZ p. 6 The scientific papers of the Second Thera Congress 26 tended to minimize the destructive effects on Crete of the earthquakes, tidal waves, and poisonous ash. The general conclusion reached was that the area and level of ashfall on Crete was far less than previously argued, and the consequent destruction less. 27 This does not, however, deny that the effects were traumatic enough to elicit some religious response from the Minoans. Hood recalled votive deposits at Zakro, Palaikastro, and Nirou Chani which appear to have some connection with the Thera eruption in LM IA. 28 EXCERPT #JPQH23 p. 6 It seems, therefore, that the decline in the number of peak sanctuaries should be more closely associated with the general decline in the number of settlements after LM IB. That there was an abandonment of settlements in east Crete then is not disputed; the cause of that abandonment is more controversial. It may have been caused by the effects of the Thera volcanic ash, or by a Mycenaean invasion, or by a combination of both factors. It has already been shown above how the peak sanctuaries were closely connected with areas of settlement. Therefore, if those settlements were abandoned, obviously their associated peak sanctuaries were also deserted. EXCERPT #ZUX9UH p. 6 The question of the abandonment is linked with the suggested revival of the cult in LM III. Material from this period has been identified on Angouseliana, Drapanokephala, Iouktas, Karphi, Kastellos, Kophinas, Modhi, Pobia, Smari, and Vrysinas. Of these only Modhi (for which the evidence is dubious) is in east Crete; the other sites are in parts of Crete not generally affected either by Thera in LM IA or by the abandonments of LM IB. Even the idea of an LM II interval is partly illusory, as the absence of datable, fine pottery is not a valid criterion. For the period of certain occupation (MM I-LM I) fine decorated wares have not been found on any peak sanctuary except Iouktas (so far as can be judged from the reports). LM II pottery, anyway, appears to have a limited distribution; 29 it is still best known from Knossos, and the one peak sanctuary where LM II sherds have been identified is Iouktas. 30 EXCERPT #3W2EH9 p. 6 Therefore, I suggest an alternative interpretation of the decline of peak sanctuaries: the east Cretans' faith in the peak sanctuary cult was shaken, though not broken, by the natural catastrophes which hit them from MM III to LM I. The causes which led to the abandonment of their homes in LM IB naturally led to a desertion of their shrines. The decline in the numbers of peak sanctuaries did not mean a diminution of the importance of the cult. Where there was continuity of occupation, particularly at Knossos and in west and south Crete, the peak sanctuary cult also continued. EXCERPT #WN728U p. 6 While such a theory can only be proved by a full study of the material from all the peak sanctuaries, Iouktas and Knossos do give some evidence for this. First, LM II pottery is found on Iouktas. 31 Secondly, there may have been buildings in use then. 32 Thirdly, the so-called 'Mountain Mother' sealing from Knossos is also dated to LM II. This sealing shows a female figure on a hill, flanked by heraldic lions. She hands a staff to a larger male figure who holds one hand to his forehead (a gesture of worship). This scene is interpreted by Rutkowski 33 as the goddess of the peak sanctuaries endowing the king with her divine authority and power, to be her earthly representative. (The goddess's gesture recalls that of the authoritative figure EXCERPT #H48894 p. 6 26 Thera and the Aegean World (1978). In particular see the article by Cita and Ryan, 'The Deep-Sea Record of the Eastern Mediterranean in the Last 150,000 Years' 45-60. This amends the earlier arguments of Ninkovitch and Heezen, 'Santorini Tephra: Submarine Geology and Geophysics', Proc. of the 17th Symposium, Colston Research Society (1965) 413-53. EXCERPT #YATK36 p. 6 27 Popham, Antiquity (1974) 58. EXCERPT #TQUF5A p. 6 28 Hood, 'Traces of the Eruption Outside Thera', Thera and the Aegean World (1978) 681-90. EXCERPT #PT28GS p. 6 29 Popham, BSA 75 (1980) 163-8. EXCERPT #8NAZN8 p. 6 30 Karetsou, Ergon (1978) 62. EXCERPT #YR34BT p. 6 31 Ibid. EXCERPT #5HXM3A p. 6 32 Ibid. EXCERPT #5UYYEP p. 6 33 Rutkowski, op. cit. (1972) 173. EXCERPT #KHHZT3 p. 7 EXCERPT #33GJYG p. 7 EXCERPT #9RGV5F p. 7 on the 'Chieftain' cup from Ayia Triadha.) LM II is the period of Mycenae rule at Knossos, so it may be that this sealing was intended as a piece of religious propaganda to justify that rule. However fanciful this idea may seem, the date is still significant. After all, why should the goddess be endowing anyone with anything if she had been abandoned for more powerful deities? EXCERPT #94DSSV p. 7 A. A. D. PEATFIELD ### 20. Assistant tool calls #### Tool call: `generate_image` ```json { "prompt": "A beautiful, atmospheric editorial cover for an archaeology paper titled “The Topography of Minoan Peak Sanctuaries.” Portrait book-cover composition, no text and no typography. View from a Bronze Age Cretan valley at blue hour toward a rugged mountain ridge: a modest open-air sanctuary crowns the visually dominant peak overlooking scattered pale-stone Minoan farmsteads, while tiny sacrificial bonfires glow on several mutually visible summits receding across the island, suggesting a network of sacred beacons. A winding footpath rises through olive groves, vineyards, aromatic scrub, and a few grazing goats. The main summit is not necessarily the tallest but has a commanding reciprocal sightline with the inhabited valley. Distant Aegean Sea glimmers at the horizon. Evoke Minoan fresco pigments—deep lapis blue, mineral turquoise, terracotta red, saffron ochre, chalk white—with elegant flattened shapes, subtle archaeological-map contour lines embedded in the sky and terrain, and delicate gold illumination around the fires. Scholarly yet lyrical, refined museum-catalogue aesthetic, dramatic negative space, richly textured handmade gouache and fresco surface, historically suggestive rather than fantasy, no modern structures, no readable symbols, no people in close-up." } ``` ### 21. Tool result: generate_image GENERATED IMAGE #G6ANKU URL: /images/G6ANKU Model: gpt-image-2 Prompt: A beautiful, atmospheric editorial cover for an archaeology paper titled “The Topography of Minoan Peak Sanctuaries.” Portrait book-cover composition, no text and no typography. View from a Bronze Age Cretan valley at blue hour toward a rugged mountain ridge: a modest open-air sanctuary crowns the visually dominant peak overlooking scattered pale-stone Minoan farmsteads, while tiny sacrificial bonfires glow on several mutually visible summits receding across the island, suggesting a network of sacred beacons. A winding footpath rises through olive groves, vineyards, aromatic scrub, and a few grazing goats. The main summit is not necessarily the tallest but has a commanding reciprocal sightline with the inhabited valley. Distant Aegean Sea glimmers at the horizon. Evoke Minoan fresco pigments—deep lapis blue, mineral turquoise, terracotta red, saffron ochre, chalk white—with elegant flattened shapes, subtle archaeological-map contour lines embedded in the sky and terrain, and delicate gold illumination around the fires. Scholarly yet lyrical, refined museum-catalogue aesthetic, dramatic negative space, richly textured handmade gouache and fresco surface, historically suggestive rather than fantasy, no modern structures, no readable symbols, no people in close-up. ### 22. Assistant tool calls #### Tool call: `update_document_metadata` ```json { "cover_image_id": "G6ANKU", "document_id": "ARP5U7", "micro_abstract": "Argues that Minoan peak sanctuaries were chosen for visibility and proximity to local settlements, forming a beacon-like sacred network whose contraction tracked settlement abandonment rather than cultic collapse." } ``` ### 23. Tool result: update_document_metadata Updated metadata for #ARP5U7: cover_image_id, micro_abstract ### 24. Assistant Updated #ARP5U7 with: - **Microabstract:** “Argues that Minoan peak sanctuaries were chosen for visibility and proximity to local settlements, forming a beacon-like sacred network whose contraction tracked settlement abandonment rather than cultic collapse.” - **Cover art:** a fresco-inspired Cretan landscape of settlements and mutually visible summit fires — #G6ANKU. ### 25. User here's what i was rambling: "Well, I was thinking like, with the shrines, it's kind of natural to imagine that you have the shrines on some kind of summit or near summit. Maybe you don't want the shrine to be on top of the summit. You don't want the shrine to see the whole world. You want the shrine to be like near the summit, but on one side of the, you know, ridge, the catchment basin. It needs to belong to one catchment basin. But then like, the shrine's influence is somehow like similar to the fluvial downstream relation, but it's, it feels like it's kind of, you know, it could be about line of sight. I mean, I'm just making up some completely random ideas here." and then gpt-5.6 found this paper... look at how it relates to the other stuff in this workspace, for context! ### 26. Assistant tool calls #### Tool call: `list_documents` ```json {} ``` ### 27. Tool result: list_documents FOLDERS - Living Structure, Wholeness & Beauty - Procedural Generation & Co-Creation - Roads, Trails & Movement - Terrain, Hydrology & Erosion - Water Simulation & Rendering Living Structure, Wholeness & Beauty (8) - #MH5J8D Beautimeter: Harnessing GPT for Assessing Architectural and Urban Beauty Based on the 15 Properties of Living Structure - 2025 | Bin Jiang | AI | 12 pp. | doi:10.3390/ai6040074 Micro abstract: Presents Beautimeter, a GPT-based tool that scores buildings and urban scenes against Christopher Alexander’s 15 properties of living structure to assess their coherence and beauty. - #XW22YY Generative Codes: The Path to Building Welcoming, Beautiful, Sustainable Neighborhoods - 2005 | Brian Hanson, Christopher Alexander, Maggie Moore Alexander, Michael Mehaffy, Randall Schmidt | Center for Environmental Structure | 21 pp. Micro abstract: Argues that living neighborhoods arise from generative codes: ordered, participatory steps that let buildings and public spaces unfold from local people, land, and context. - #SKRF4C Geography as a Science of the Earth’s Surface Founded on the Third View of Space - 2022 | Bin Jiang | Annals of GIS | 14 pp. | doi:10.1080/19475683.2021.1966502 Micro abstract: Recasts geography around an organismic view of space, using scaling and spatial dependence to understand—and deliberately create—places with greater living structure. - #PXG56P Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole - 2009 | Christopher Alexander | Unpublished manuscript | 66 pp. Micro abstract: Proposes harmony-seeking computation as a creative process that repeatedly strengthens latent centers in a configuration while preserving and deepening the larger whole. - #MJKTBB Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space - 2023 | Bin Jiang, Chris de Rijke | Annals of the American Association of Geographers | 19 pp. | doi:10.1080/24694452.2023.2178376 Micro abstract: Measures an image’s structural beauty by recursively extracting its nested substructures, revealing a compact hierarchy that also captures visual saliency. - #3XSLTA Structural Beauty: A Structure-Based Computational Approach to Quantifying the Beauty of an Image - 2021 | Bin Jiang, Chris de Rijke | Journal of Imaging | 15 pp. | doi:10.3390/jimaging7050078 Micro abstract: Proposes a quantitative measure of structural beauty based on how many substructures an image contains and how strongly they form a hierarchy across scales. - #ZU8GZV Structure-Preserving Transformations - 2002 | Christopher Alexander | The Nature of Order, Book Two: The Process of Creating Life | 4 pp. | doi:10.2307/j.ctv27ftw6c.5 Micro abstract: Explains structure-preserving transformations: incremental changes that extend the centers and relationships already present in a place rather than weakening its wholeness. - #BYG3BQ Wholeness as a Hierarchical Graph to Capture the Nature of Space - 2015 | Bin Jiang | International Journal of Geographical Information Science | 14 pp. | doi:10.1080/13658816.2015.1038542 Micro abstract: Models spatial wholeness as a hierarchical graph of mutually reinforcing centers, using PageRank and scaling depth to quantify the life of parts and wholes. Procedural Generation & Co-Creation (6) - #4TH488 Explainable AI for Designers: A Human-Centered Perspective on Mixed-Initiative Co-Creation - 2018 | Antonios Liapis, G. Michael Youngblood, Jichen Zhu, Rafael Bidarra, Sebastian Risi | 2018 IEEE Conference on Computational Intelligence and Games (CIG) | 8 pp. | doi:10.1109/CIG.2018.8490433 Micro abstract: Defines explainable AI for game designers, mapping co-creative systems by their explainability, initiative, and domain overlap so explanations serve concrete design tasks. - #9NQ94D Extracting Physics from Blended Platformer Game Levels - 2020 | Adam Summerville, Anurag Sarkar, Joseph C. Osborn, Sam Snodgrass | Joint Proceedings of the AIIDE 2020 Workshops (CEUR Workshop Proceedings, Vol. 2862) | 7 pp. Micro abstract: Infers playable jump physics from generated platformer levels, including hybrid physics models for levels that blend the geometry and style of multiple games. - #7GR3AQ Procedural Content Generation through Quality Diversity - 2019 | Ahmed Khalifa, Antonios Liapis, Daniele Gravina, Georgios N. Yannakakis, Julian Togelius | 2019 IEEE Conference on Games (CoG) | 8 pp. | doi:10.1109/CIG.2019.8848053 Micro abstract: Argues for quality-diversity algorithms in procedural generation, producing broad collections of varied, playable content while exposing the design space for exploration and co-creation. - #CQBDX4 Procedural Content Generation via Machine Learning (PCGML) - 2018 | Aaron Isaksen, Adam Summerville, Amy K. Hoover, Andy Nealen, Christoffer Holmgård, Julian Togelius, Matthew Guzdial, Sam Snodgrass | IEEE Transactions on Games | 15 pp. | doi:10.1109/TG.2018.2846639 Micro abstract: Defines and surveys PCGML: generating functional game content directly from models trained on existing examples, with uses spanning creation, completion, repair, critique, and compression. - #WZ8DHP Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents - 2026 | Rishabh Kar | arXiv | 25 pp. | doi:10.48550/arXiv.2605.01783 Micro abstract: Integrates procedural generation and validation in an endless runner, using aerial and ground agents to detect blocked or unnavigable content before the player reaches it. - #NRBMD5 Towards Friendly Mixed Initiative Procedural Content Generation: Three Pillars of Industry - 2020 | Frederic Fol Leymarie, Gorm Lai, William Latham | Proceedings of the International Conference on the Foundations of Digital Games (FDG '20) | 4 pp. | doi:10.1145/3402942.3402946 Micro abstract: Distills three requirements for industry-friendly co-creative PCG tools: preserve designer control, keep feedback loops short, and fit into existing production pipelines. Roads, Trails & Movement (7) - #G3TBNG A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories - 2016 | J. Christian Gerdes, John Subosits, Nitin R. Kapania | Journal of Dynamic Systems, Measurement, and Control | 12 pp. | doi:10.1115/1.4033311 Micro abstract: Generates near-optimal racing trajectories quickly by alternating between a minimum-time speed profile and a convex path update that reduces curvature. - #B6P8L4 Active walker model for the formation of human and animal trail systems - 1997 | Dirk Helbing, Frank Schweitzer, Joachim Keltsch, Péter Molnár | Physical Review E | 34 pp. | doi:10.1103/physreve.56.2527 Micro abstract: Models trail systems as self-organization: walkers reinforce attractive routes while unused traces fade, producing dendritic ant trails and low-detour pedestrian networks. - #V4TQYB Interactive procedural street modeling - 2008 | Eugene Zhang, Gregory Esch, Guoning Chen, Pascal Müller, Peter Wonka | ACM Transactions on Graphics | 10 pp. | doi:10.1145/1360612.1360702 Micro abstract: Lets designers generate and edit large street networks through tensor fields, combining procedural speed with brush-like global and local control over street patterns. - #UYLTYJ Modelling the Evolution of Human Trail Systems - 1997 | Dirk Helbing, Joachim Keltsch, Péter Molnár | Nature | 11 pp. | doi:10.1038/40353 Micro abstract: Shows how pedestrian trails emerge through feedback between destination-seeking walkers, existing paths, and vegetation recovery, yielding a compromise between directness and shared infrastructure. - #GY93FG Mountain Trail Formation and the Active Walker Model - 2009 | J. P. Hague, S. J. Gilks | International Journal of Modern Physics C | 22 pp. | doi:10.1142/S0129183109014059 Micro abstract: Extends the active-walker model to steep terrain, explaining zigzag mountain trails through slope avoidance, directional persistence, and mutual reinforcement by ascending and descending walkers. - #LXV9AT Principles of Trail Layout and Design - 2019 | California State Parks | California State Parks Trails Handbook | 64 pp. Micro abstract: A field-oriented guide to durable trail design, emphasizing curvilinear alignment, natural drainage, sustainable grades, control points, and close reading of landform and soils. - #XDEFZS Procedural Generation of Roads - 2010 | A. Peytavie, E. Galin, E. Guérin, N. Maréchal | Computer Graphics Forum | 10 pp. | doi:10.1111/j.1467-8659.2009.01612.x Micro abstract: Automatically routes and constructs roads with an anisotropic shortest-path method that weighs slope and obstacles while treating surface segments, bridges, and tunnels consistently. Terrain, Hydrology & Erosion (6) - #NV2YRW FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation - 2024 | Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain | Computer Graphics Forum | 13 pp. | doi:10.1111/cgf.15243 Micro abstract: A GPU framework for routing surface flow through terrain and its depressions fast enough to make erosion, river, lake, and ecosystem simulations interactive. - #96ZMGK Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion - 2016 | Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin | Computer Graphics Forum | 11 pp. | doi:10.1111/cgf.12820 Micro abstract: Generates large, controllable mountain terrains by coupling user-painted tectonic uplift with fluvial erosion, then turning the resulting stream graph into detailed landforms. - #DWXKYQ Physically-based analytical erosion for fast terrain generation - 2024 | Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer | Computer Graphics Forum | 14 pp. | doi:10.1111/cgf.15033 Micro abstract: Turns the stream power law into an interactive terrain tool, replacing thousands of erosion time steps with analytical solutions and a direct control for landscape age. - #MTDKDE Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models - 2014 | Clarence Lehman, David Mulla, Richard Barnes | Computers & Geosciences | 17 pp. | doi:10.1016/j.cageo.2013.04.024 Micro abstract: Introduces Priority-Flood, a simple, optimal algorithm that removes drainage-blocking depressions from elevation models and can also derive watersheds and flow directions. - #AK7NGE Procedural Riverscapes - 2019 | A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial | Computer Graphics Forum | 12 pp. | doi:10.1111/cgf.13814 Micro abstract: Builds editable, animated riverscapes from bare terrain by carving hydrologically plausible channels and blending real-time procedural water primitives instead of simulating fluids. - #DMTA8Y Terrain Generation Using Procedural Models Based on Hydrology - 2013 | Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin | ACM Transactions on Graphics | 10 pp. | doi:10.1145/2461912.2461996 Micro abstract: Generates controllable, multiscale terrain from a sketched drainage network, representing rivers and landforms as an editable hierarchy of continuous procedural primitives. Water Simulation & Rendering (12) - #RBS5K6 A Layered Particle-Based Fluid Model for Real-Time Rendering of Water - 2010 | Daniel Scherzer, Florian Bagar, Michael Wimmer | Computer Graphics Forum | 7 pp. | doi:10.1111/j.1467-8659.2010.01734.x Micro abstract: Renders particle-based water and volumetric foam in real time using perspective-aware surface smoothing, physically guided foam formation, and layered depth compositing. - #C4AY2M A Survey of Ocean Simulation and Rendering Techniques in Computer Graphics - 2011 | B. Crespin, D. Ghazanfarpour, E. Darles, J.-C. Gonzato | Computer Graphics Forum | 17 pp. | doi:10.1111/j.1467-8659.2010.01828.x Micro abstract: Surveys ocean graphics from spectral deep-water models to near-shore fluid simulation, then covers the foam, spray, and light transport needed for convincing rendering. - #WZMZGY Advected river textures - 2009 | Dirk Arnold, Stephen Brooks, Tim Burrell | Computer Animation and Virtual Worlds | 11 pp. | doi:10.1002/cav.288 Micro abstract: Combines a 2D Navier–Stokes solver, hydrostatic pressure columns, and advected procedural textures to render detailed, terrain-responsive rivers at real-time frame rates. - #92XRH7 Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field - 2011 | Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch | IEEE Transactions on Visualization and Computer Graphics | 13 pp. | doi:10.1109/tvcg.2010.263 Micro abstract: Advects fluid textures with deformable particle grids, preserving both the input texture’s visual spectrum and exact motion along the velocity field without cumulative stretching. - #8SERGP Real-time Breaking Waves for Shallow Water Simulations - 2007 | Markus Gross, Matthias Müller-Fischer, Nils Thürey, Simon Schirm | 15th Pacific Conference on Computer Graphics and Applications (Pacific Graphics 2007) | 8 pp. | doi:10.1109/PG.2007.33 Micro abstract: Adds real-time overturning waves to shallow-water heightfields by detecting steep fronts and spawning connected particle sheets that collapse into splashes and foam. - #CWC7H9 Real-time Rendering of Enhanced Shallow Water Fluid Simulations - 2013 | Antonio Susín, Jesús Ojeda | Computers & Graphics | 9 pp. Micro abstract: Builds a real-time rendering pipeline for shallow-water simulations, adding fine surface detail, advected foam, photon-based caustics, and screen-space reflection and refraction. - #MVUJ8Z Real-time Rendering of River Networks - 2010 | Quintijn Hendrickx, Rafael Bidarra, Ruben M. Smelik | Proceedings of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games | 1 pp. Micro abstract: Renders branching river networks efficiently with quadratic Bézier curves, GPU distance fields, and streaming normal maps instead of dense geometry or particle simulation. - #5MGCZ5 Real-time River Representation by Dynamic Control of Data on Waves - 2008 | Makoto Kosugi, Nobuhiko Mukai, Yasuhiro Kato | 4 pp. | doi:10.3169/itej.62.2063 Micro abstract: Dynamically switches river-wave models by viewing distance, preserving nearby reflection and wave detail while retaining wind-driven motion across the full landscape. - #XDESU9 Scalable real‐time animation of rivers - 2009 | Eric Bruneton, Fabrice Neyret, Nicolas Holzschuch, Qizhi Yu | Computer Graphics Forum | 11 pp. | doi:10.1111/j.1467-8659.2009.01363.x Micro abstract: Animates rivers across vast terrains by computing steady flow locally and advecting fine surface detail only where visible, at a screen-space sampling density. - #869NHK Very Fast Real-Time Ocean Wave Foam Rendering Using Halftoning - 2011 | Ian Parberry, Jennifer R. Alford, Mary Yingst | Proceedings of the 6th International North American Conference on Intelligent Games and Simulation (GAMEON-NA) | 7 pp. Micro abstract: Uses a spectrally controlled halftone mask to make texture-based ocean foam dissipate as clumped bubbles that pop, rather than merely fading transparently. - #A2QB8L Water Flow in Portal 2 - 2010 | Alex Vlachos | ACM SIGGRAPH 2010 Course: Advances in Real-Time Rendering in 3D Graphics and Games | 54 pp. Micro abstract: Explains Portal 2’s production-friendly water shader: artist-painted flow maps advect layered normal maps, while offsets and noise suppress repetition and pulsing on limited hardware. - #PBM2TC Water surface wavelets - 2018 | Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan | ACM Transactions on Graphics | 13 pp. | doi:10.1145/3197517.3201336 Micro abstract: Represents water waves as spatially varying directional amplitudes, enabling vast interactive simulations with fine detail, moving obstacles, solid coupling, and direct artistic control. Unfiled (2) - #C8FHDZ On implication and negation in partition logic - 2025 | , David Ellerman | Open Journal of Mathematical Sciences | 9 pp. | doi:10.30538/oms2025.0250 Micro abstract: Develops implication as a refinement-sensitive operation on set partitions, showing how relative negation yields local Boolean cores within the non-distributive algebra of partitions. - #ARP5U7 The Topography of Minoan Peak Sanctuaries - 1983 | A. A. D. Peatfield | The Annual of the British School at Athens | 8 pp. | doi:10.1017/s0068245400019729 Micro abstract: Argues that Minoan peak sanctuaries were chosen for visibility and proximity to local settlements, forming a beacon-like sacred network whose contraction tracked settlement abandonment rather than cultic collapse. ### 28. Assistant tool calls #### Tool call: `search_text` ```json { "limit": 12, "query": "catchment basin watershed partition ridge drainage divide" } ``` #### Tool call: `search_text` ```json { "limit": 12, "query": "line of sight visibility viewshed landmark summit" } ``` #### Tool call: `search_text` ```json { "limit": 12, "query": "centers reinforce whole hierarchy local region" } ``` #### Tool call: `search_text` ```json { "limit": 12, "query": "dual graph basins downstream flow relation" } ``` ### 29. Tool result: search_text Exact matches 1. Source: On implication and negation in partition logic (#C8FHDZ), , David Ellerman, p. 1 Context: #L8JZAG On implication and negation in partition logic #7WB5RZ 2. The logic of partitions Matching excerpt #HTEQ5J: The indit set of a partition is the equivalence relation defined by the partition, and the ditset of a partition is the complementary partition relation defined by the partition. 2. Source: On implication and negation in partition logic (#C8FHDZ), , David Ellerman, p. 6 Context: #L8JZAG On implication and negation in partition logic #LEZCCF 6. Valid formulas Matching excerpt #XWG2AT: There is a simple way to see that all partition tautologies are also subset tautologies, i.e., valid formulas of subset logic. Consider the partition algebra \Pi(2) on the two-element set 2 = \{0, 1\} . It has only two partitions, the discrete partition \mathbf{1} = \{\{0\}, \{1\}\} where 0 and 1 are distinguished, and the indiscrete partition \mathbf{0} = \{\{0, 1\}\} where they are not distinguished. The partition operations, such as join, meet, and implication, applied to those two partitions could be described in "truth tables" since \mathbf{0} and \mathbf{1} are the only partitions on 2. And those truth tables are the same as the Boolean subset operations on the two subsets of the one-element set. Hence we have an isomorphism between the partition algebra \Pi(2) on 2 and the power-set Boolean algebra \wp(1) = 2 for 1 as the one-element set. 3 Now consider any formula that is a valid formula in partition logic. Since it evaluates to \mathbf{1} for all partitions on any U where |U| \geq 2 , it does that for U = 2 , but then the isomorphism \Pi(2) \cong \wp(1) means that the same formula will be a truth table tautology in \wp(1) and thus it is a valid formula for subset logic in general. Hence all partition tautologies are subset tautologies. But the inclusion is strict. For instance, the law of excluded middle \sigma \vee \neg\sigma = \sigma \vee (\sigma \Rightarrow \mathbf{0}) is not a partition tautology since for any \sigma \neq \mathbf{0}, \mathbf{1} , \sigma \Rightarrow \mathbf{0} = \mathbf{0} , and \sigma \vee \neg\sigma = \sigma \vee \mathbf{0} = \sigma \neq \mathbf{1} . 3. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 2 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #QW6CT7 3. Background and overview #MYA2EJ 3.1. Landscape dynamics in geology Matching excerpt #ESC38J: A first common modeling approximation is to consider surface evolution as a detachment-limited process (as opposed to transport-limited) where the evolution of surface elevation z is directly related to the competition between rock uplift and erosion rate, and not to the capacity of the rivers to transport or deposit sediments [How94]. In this setting, erosion is generally described using the stream power incision model [HK83, How94, WT99, Lag14], where erosion rate is a power law of the surface slope \|\nabla z\| , and drainage area A that acts as a proxy for the river discharge. The drainage area A(\mathbf{x}) is defined at a position \mathbf{x} as the area of the drainage basin - or catchment - upstream of \mathbf{x} . Coupled with the uplift u , the Stream Power Law expresses the rate of change of surface elevation: 4. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 8 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #97YQQD 6. Other erosion factors #C4WS38 6.1. Hillslope erosion Matching excerpt #FJ5WJ6: We integrate from s to the ridge r , where the slope vanishes; and use Hack's law [Hac57] to associate the distance to the ridge with the drainage A : r - s = CA(s)^h , where C is a constant in the range [1.4 – 2], and the exponent is usually set to h = 0.6 : 5. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 31 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #XSQ2CN 5.7.3. Maximum Sustainable Linear Grades #74WYLZ 5.7.3.3. Rainfall Intensity Matching excerpt #UG2WS4: The intensity of rainfall can affect the performance of a trail's surface, especially where the runoff coefficient is high due to up slope conditions, such as the amount of exposed bed rock in the watershed, a lack of vegetative cover, road building, grazing, or recent fire activity in the watershed. High rainfall intensity can generate a significant runoff response up slope, which can impact drainage structures and trail surfaces. Drainage structures need to be designed and constructed to accommodate this runoff and the linear grades need to be adjusted to reduce the possibility of rilling caused by increased sheet flow. 6. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 48 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #9WNHGK 5.7.5. Field Reconnaissance #XG25M6 5.7.5.2. Designed Control Points #UM24VH 5.7.5.2.4. Problematic Topography Matching excerpt #B5L73Y: Certain locations on the landform should be avoided by trail designers whenever possible. One of these locations is a ridge top. Trail designers often locate trails along the tops of ridges for the view and to minimize the amount of required brushing, clearing, and trail construction. If the ridge is comprised of very durable bedrock, this layout practice is acceptable. However, if the ridge top is comprised of soil, the construction of the trail tread (even light brushing and clearing) will result in the trail bed being lower than the surrounding soil horizon. With the trail bed lower than the terrain adjacent to it, surface runoff cannot flow off the trail, and it will begin to flow down the trail. The trail effectively becomes a ditch and the combination of water erosion and mechanical wear quickly incises the trail bed. This condition cannot be remedied with drainage structures such as water bars or grade reversals. (See Photo 5.32.) 7. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 24 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #M2FCT4 5.6. Maintaining Natural Drainage Matching excerpt #EZ5S8W: Natural flow is maintained by laying out trails on the contour of the land, which helps facilitate natural sheet drainage. This type of trail layout is called curvilinear alignment (crossing contour lines at nearly flat or oblique angles). Curvilinear layout keeps the trail alignment nearly perpendicular to natural sheet runoff, and requires following the landform, pulling in and out of swales and crenulations. Pulling in, dipping down, and pulling up and out of drain swales (even in the most subtle crenulations) ensures that the trail alignment cannot capture or divert flow. This technique effectively de-couples the trail from the watershed and eliminates or minimizes the need for drainage structures such as grade reversals and water bars that use the trail to capture water and drain it onto the slope below the trail where rills and gullies can form. Curvilinear alignment does not alter the flow of watercourses bisected by the trail, which is critical to plant and animal communities associated with wetland and riparian corridors. (See Figure 5.3.) Photo 5.19 illustrates how a trail gradually dips down and pulls out of an ephemeral watercourse (top) and contours up the hillslope (bottom). 8. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 48 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #9WNHGK 5.7.5. Field Reconnaissance #XG25M6 5.7.5.2. Designed Control Points #UM24VH 5.7.5.2.4. Problematic Topography Matching excerpt #DY8MQW: If a trail is to be located along a ridge, it is much better design practice to locate it just below the ridge top where hillside construction will facilitate sheet flow across the trail bed. The trail is close enough to the top of the ridge to offer good views yet facilitate natural surface runoff. This layout practice may also provide opportunities to have the trail cross the ridge top where a low point or saddle occurs. This design offers the trail user different views in a dramatic fashion rather than just seeing the same view for an extended period of time. (See Figure 5.9.) 9. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 32 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #XSQ2CN 5.7.3. Maximum Sustainable Linear Grades #SB9AAG 5.7.3.6. Location on the Hillslope Matching excerpt #EZKSLY: Generally, within a watershed, trail alignment at lower elevations will encounter more shallow groundwater and accumulate greater amounts of sheet flow than trails at higher elevations. The amount of sheet flow and shallow groundwater that accumulates on the trail is generally proportional to the watershed's surface area above the trail alignment. This concept is important to understand when designing trails on slopes because the more water the trail encounters, the lower the linear grade it can sustain. In addition, trails at the bottom of a watershed usually encounter less stable geology, as inner gorges undergo a more dynamic geomorphic process. Trail alignments at higher elevations in the watershed usually can sustain higher linear grades. 10. Source: Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models (#MTDKDE), Clarence Lehman, David Mulla, Richard Barnes, p. 2 Context: #XJ3LVD Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models #C5TMDU 3. The Priority-Flood Algorithm #CUHFR9 3.1. History Matching excerpt #ZZD5A8: The most accurate method for determining watershed boundaries involves placing a person familiar with the nuances of contour maps at a drafting table to manually interpret drainage basins. 11. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 3 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #SD69QC 3. Overview #CPNMBK 3.2. Depression routing Matching excerpt #A6G5PJ: We are now in a position to define what a depression means in our context. As a preliminary, we use the term basin for the set of terrain cells that share the same stream tree, effectively all belonging to the same catchment area and channeling water to a single root cell. If this root cell is an outflow, then the basin is classified as an outflow basin, otherwise, it constitutes a depression (Figure 2 (c)). 12. Source: Partition lens across the corpus (#TUCFMG) Matching note #TUCFMG: Ellerman’s partition logic suggests a useful cross-corpus lens, but only where blocks are mutually exclusive and jointly exhaustive (#ZBQE96). The clearest exact case is hydrological catchments: terrain cells are equivalent when they drain to the same outlet, and watershed labeling assigns one common label to every such equivalence class (#NNC37P, #477DMT). FastFlow similarly defines a basin as cells sharing a stream tree/root (#A6G5PJ) and propagates basin identifiers upstream (#C9XNSJ); saddle crossings then connect or merge basin blocks (#L94DMG), suggesting dynamic coarsening of a catchment partition. Hydrological terrain generation also constructs Voronoi cells and hierarchical watersheds/subwatersheds (#KAMGFF, #WL3SCW), giving nested partitions at multiple scales. Other exact or near-exact corpus examples include planar regions cut by major streets/topographic boundaries (#PUZXXV); recursive figure/ground and connected-pixel segmentation (#FXLSNG); head/tail classes (#WQW77N); MAP-Elites bins that partition behavior/search space (#DJQRBX, #964T2S); fluid particles classified into rendering layers (#48RCD2); and walker populations grouped by entry–destination pair (#RRJ2BJ). Alexanderian centers should not be treated as a partition without qualification because their local symmetries and centers overlap across scales (#LNKPPL). Conceptually, a deterministic map from each terrain cell to its terminal outlet realizes Ellerman’s function-to-partition idea (#BLF82B): catchments are the inverse-image fibers of the outlet map. Approximate matches 1. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 3 Context: #JJE8HN Procedural Riverscapes #Z6DVCN 4. River Network Graph Score: 0.023 Related excerpt #TRPJZX: Figure 5). One complication is that the drainage calculation assumes that there are no depressions (local minima) in the digital elevation model, since these have no outlet to neighboring cells. To prevent disconnected river graphs we apply an optimal depression filling algorithm [BLM14], which leaves the surface slightly proud with an available flow channel. 2. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 5 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #T6FSBF 5 River Classification #TRR58W 5.1 Segmentation and Elevation of Crests Score: 0.029 Related excerpt #WL3SCW: Watersheds are associated with each water outlet s of a cell V_j and are defined as the set of upstream connected cells V_k \in V . 3. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 5 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #T6FSBF 5 River Classification #TRR58W 5.1 Segmentation and Elevation of Crests Score: 0.024 Related excerpt #XA9BE4: Ridges. The computation of ridge elevation is important to guarantee a coherent flow. Each Voronoi cell has two types of edges: those that do not intersect the river graph and that define ridge lines, and those that carry a river entry e_k or outlet s . 4. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 4 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #T6FSBF 5 River Classification #TRR58W 5.1 Segmentation and Elevation of Crests Score: 0.023 Related excerpt #Q4MUQB: The domain \Omega is decomposed into a set of cells \mathcal{V} = \{V_i\} computed from the Voronoi diagram of node locations \mathbf{p}_i . Some Voronoi cell boundaries correspond to the ridges that define the edges of the watersheds. Each cell vertex has an elevation assigned, and each cell V is represented as a polygon composed of crest points \mathbf{q}_i . Water entries are denoted \mathbf{e}_0, \dots, \mathbf{e}_{n-1} , and the water outlet is denoted s (see Fig. 10). 5. Source: Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models (#MTDKDE), Clarence Lehman, David Mulla, Richard Barnes, p. 2 Context: #XJ3LVD Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models #C5TMDU 3. The Priority-Flood Algorithm #CUHFR9 3.1. History Score: 0.022 Related excerpt #ZZD5A8: The most accurate method for determining watershed boundaries involves placing a person familiar with the nuances of contour maps at a drafting table to manually interpret drainage basins. 6. Source: Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models (#MTDKDE), Clarence Lehman, David Mulla, Richard Barnes, p. 12 Context: #XJ3LVD Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models #4K4XN3 7. Variants #LFYVTV 7.3. Watershed Labeling Score: 0.021 Related excerpt #NNC37P: Watershed labeling applies a common label—such as an integer number—to all cells which drain to a given outlet. The algorithm (Alg. 5) for this works in much the same way as the improved Priority-Flood (Alg. 2). The DEM is flooded inwards from its edges with the lowest cell always being processed first. Rather than filling cells in depressions, this algorithm merely prioritizes them to the level of their outlet. 7. Source: Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models (#MTDKDE), Clarence Lehman, David Mulla, Richard Barnes, p. 12 Context: #XJ3LVD Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models #4K4XN3 7. Variants #LFYVTV 7.3. Watershed Labeling Score: 0.021 Related excerpt #L6E5XU: Following execution, watershed boundaries may be identified by locating adjacent cells with differing labels. To mark the border cells, consistently choose either the cell with the lower label, the cell with the higher label, or both. 8. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 3 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #SD69QC 3. Overview #CPNMBK 3.2. Depression routing Score: 0.029 Related excerpt #A6G5PJ: We are now in a position to define what a depression means in our context. As a preliminary, we use the term basin for the set of terrain cells that share the same stream tree, effectively all belonging to the same catchment area and channeling water to a single root cell. If this root cell is an outflow, then the basin is classified as an outflow basin, otherwise, it constitutes a depression (Figure 2 (c)). 9. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 5 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #J5PECC 5. Depression routing #UJCLXC Algorithm 2: Propagation of basin identifiers Score: 0.029 Related excerpt #C9XNSJ: Basin identification. Our algorithm begins by segmenting out each stream tree and associating with its cells a unique basin identifier (hereafter referred to as a basin-id , or bid in the pseudo-code of Algorithm 2). To this end, we assign to each non-outflow local minima a unique identifier – leaving a common outflow identifier for all outflow basins – and use pointer jumping to copy this identifier in parallel to all upstream nodes of its stream tree (Algorithm 2). 10. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 9 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #M2TBHA 7. Results #HTXQDQ 7.2. Interactive landscape simulation Score: 0.021 Related excerpt #NEL8YN: Rivers and lakes In Figure 9, we demonstrate how our algorithms can be used on complex large-scale terrains to demarcate lakes and rivers that are registered correctly with existing erosion lines and depressions. On the left in Figure 9, a mountainous region in the Alps transitions into an urbanized flat glacial valley. On the right, a tidal estuary around Mont Saint-Michel, France, leads into the sea. They contain 383,918 and 8,445,644 basins, respectively. In both cases, the elevation data was obtained from the IGN RGE ALTI Digital Elevation 1m dataset [IGN22]. 11. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 6 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #J5PECC 5. Depression routing #2HKXNP Algorithm 3: Finding saddles and outlets Score: 0.021 Related excerpt #L94DMG: Input : Terrain cells \mathcal{T} with elevation z , set of depression basins \mathcal{D} Output : Per-depression saddle and outlet 1 // Compute border cells and store the border altitude in z' 2 foreach cell c \in \mathcal{T} in parallel do 3 if bid_c \neq bid_n of any 4-neighbour n of c ( n \in \mathcal{N}_c ) then 4 tag c as a border cell 5 znb \leftarrow \min(z_n \text{ for } n \in \mathcal{N}_c \text{ such that } bid_c \neq bid_n) 6 z'_c \leftarrow \max(z_c, znb) 7 end 8 end 9 // Saddles and outlets (with atomic lexicographic argmin) 10 foreach basin d \in \mathcal{D} in parallel do 11 saddle of d \leftarrow \text{argmin}((z'_c, bid_n) for each border cell c 12 and n \in \mathcal{N}_c such that bid_c = d and bid_n \neq d ) 13 outlet of d \leftarrow \text{argmin}(z_n for each neighbor n of the 14 saddle such that bid_n \neq d ) 15 end 16 // Remove cycles 17 foreach basin d \in \mathcal{D} in parallel do 18 d' \leftarrow basin of outlet of d 19 if bid of outlet of d' = bid of saddle of d then 20 if bid of outlet of d < bid of saddle of d then 21 Delete the saddle and outlet of d 22 end 23 end 24 end 12. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 7 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #34USBX 6. Application to landscape simulation #BTBPNF Algorithm 6: Extracting a depression-free water surface Score: 0.02 Related excerpt #6ADZ5Q: River and lake modeling. To identify the surface of rivers and lakes we begin by filling depressions in the terrain. This is sometimes referred to as pit removal and has value as an algorithm in its own right. Our input is the terrain elevation grid, and a set of recipients identified during depression routing to provide the flow path with minimum energy cost. We call the water surface the elevations obtained after filling the identified depressions. This surface should obey two conditions: it should be as close as possible to the terrain, and at the same time be monotonically non-decreasing along all stream trees, which we intuitively expect since water flows downhill. To achieve this, in Algorithm 6 we introduce a variant of the basin identification algorithm. We follow the water path of each stream tree upwards from destination to sources, retaining as the water surface the maximum elevation previously reached. For completeness, we optionally allow a small slope \epsilon on the water surface as this is sometimes required in hydrology applications. Note that this variant is only possible with the depression carving strategy, as it requires a continuous path. Next, cells with water discharge above a specified threshold can be tagged as belonging to bodies of water, as illustrated in Figure 9 where the water surface and its discharge are highlighted. ### 30. Tool result: search_text Exact matches 1. Source: Explainable AI for Designers: A Human-Centered Perspective on Mixed-Initiative Co-Creation (#4TH488), Antonios Liapis, G. Michael Youngblood, Jichen Zhu, Rafael Bidarra, Sebastian Risi, p. 6 Context: #TS8HQQ Explainable AI for Designers: A Human-Centered Perspective on Mixed-Initiative Co-Creation #L7TGN5 VI. THREE USE CASES #AK3WD7 C. Use Case 3: Black-box NPC Behavior System Matching excerpt #4YQ2JP: Given the large number of possible actions and/or situations, similar to highlights in white-box PCG systems, a good design guideline for XAID is to highlight the unexpected and reduce the visibility of the common ones. A key open challenge to providing both types of information to a human designer is how to design the reward function for the NPC. 2. Source: Real-time Breaking Waves for Shallow Water Simulations (#8SERGP), Markus Gross, Matthias Müller-Fischer, Nils Thürey, Simon Schirm, p. 3 Context: #FA7BE4 Real-time Breaking Waves for Shallow Water Simulations #JL4FVP 5 Wave Patch Generation: Matching excerpt #ESTKYQ: The fluid sheet of an overturning wave is represented with a wave patch that is built from connected particles generated at the wave line. In time intervals t_g a set of particles along the wave line is spawned for each point of the line, adding another layer of quads to the patch. Amongst each other, the particles have the same connectivity as the wave line. If a previous set of particles exists, the new set is connected to the previous one. If the same point on the line existed at the generation time of both particle sets, this is trivial. From these one-to-one connections, quads can be easily generated to form a closed surface of the wave patch. If points were added or removed from the wave line, these are marked, and corresponding connection shapes are inserted to guarantee a closed surface, as shown in Figure 5. To ensure that these three cases are sufficient, we only allow a single merging or insertion for a point within the time interval t_g . 3. Source: Real-time Breaking Waves for Shallow Water Simulations (#8SERGP), Markus Gross, Matthias Müller-Fischer, Nils Thürey, Simon Schirm, p. 3 Context: #FA7BE4 Real-time Breaking Waves for Shallow Water Simulations #PHN7AY 4 Wave Simulation Matching excerpt #WH7SNE: Here the line \mathcal{L}_g = \mathbf{x}'_n + t\nabla H(\mathbf{x}'_n) consists of all points along the height field gradient at \mathbf{x}'_n that are in \mathcal{P}_b . The point \mathbf{x}_{n+1} is added to \mathcal{L} and connected to \mathbf{x}_n . These steps are repeated until \mathbf{x}_{n+1} is not part of \mathcal{P}_b . In this case, the process of the line construction is restarted with the second tangent direction if t = t_1 , or the line is complete for t = t_2 . Likewise, if \mathbf{x}_{n+1} has a distance less than p_d to the first point of the line, the line is completed by connecting the two points, resulting in a closed loop. 4. Source: Real-time Breaking Waves for Shallow Water Simulations (#8SERGP), Markus Gross, Matthias Müller-Fischer, Nils Thürey, Simon Schirm, p. 4 Context: #FA7BE4 Real-time Breaking Waves for Shallow Water Simulations #JL4FVP 5 Wave Patch Generation: Matching excerpt #WFFDGJ: Here, p_o is a parameter to control the strength of the height influence. As the wave line tracks the steepest point of the wave front, the generated particles have to be positioned at the wave crest to correctly give the impression of an overturning wave. The particle generation would be simplified if the crest of the wave was tracked instead of the front, as is done in our approach. However, the line of the wave crest is not as clearly defined, e.g., for saddle points and saddle lines of the height field. Thus, upon creation, the particles of the wave patch are moved to the crest along the inverted wave line velocity -\mathbf{u}_l . We furthermore subtract t_g \mathbf{u}_s from the particle position at the top of the wave, to ensure an overlap of the wave patch and the shallow water surface. This allows a smooth transition from the height field values to the wave mesh, as explained below in more detail. 5. Source: Real-time Breaking Waves for Shallow Water Simulations (#8SERGP), Markus Gross, Matthias Müller-Fischer, Nils Thürey, Simon Schirm, p. 3 Context: #FA7BE4 Real-time Breaking Waves for Shallow Water Simulations #PHN7AY 4 Wave Simulation Matching excerpt #723HGZ: During its movement, the length of the wave front can change significantly. We thus adaptively resample the wave line by introducing new points when the distance between two neighbors is larger than 2\Delta x . Similarly, points with a distance of less than \Delta x/2 are merged. A folding of the line can also be prevented by merging segments where (\mathbf{p}_{n+1} - \mathbf{p}_n) \cdot (\mathbf{p}_{n-1} - \mathbf{p}_n) > 0 holds. In both cases the new points are initialized by averaging the properties of the neighboring points. Hence, the resulting wave line consists of segments that have a similar scale as the grid size of the simulation throughout its lifetime. 6. Source: The Topography of Minoan Peak Sanctuaries (#ARP5U7), A. A. D. Peatfield, p. 3 Context: #S9HW3P THE TOPOGRAPHY OF MINOAN PEAK SANCTUARIES Matching excerpt #QPEZUU: In some areas, however, it is not the highest point which is chosen. Minoan Palaikastro is sited in a small coastal plain, just north of the mountain Petsopha. This mountain is a ridge, which juts out from the encircling massif. The ridge has three peaks and the sanctuary is sited on the lowest of the three; it is this peak which most directly overlooks the town. From the other summits the view is obscured by lower platforms and cliffs. Faure notes a similar situation with the peak sanctuary at Etia. 12 The shrine is not on the highest peak of the massif, which is Skopeli at 715 m. Rather it is situated on an isolated butte to the north, 100 m lower down. From there, however, one can see the valley plains of Armeni and Chandra. A third example is observable at Zou. 13 The summit is 803 m high, but the peak sanctuary is on the rising edge of a small plateau, north-west of the summit, at an altitude of 725 m. It is only from this high point that the coastal plain of Sitia can be seen; moreover, from the plain this point looks like the summit. 7. Source: The Topography of Minoan Peak Sanctuaries (#ARP5U7), A. A. D. Peatfield, p. 2 Context: #S9HW3P THE TOPOGRAPHY OF MINOAN PEAK SANCTUARIES Matching excerpt #65886B: The altitude of peak sanctuaries varies considerably. Generally, the lowest are around 200 m, e.g. Petsopha at 215 m. At the other end of the scale sanctuaries are also found at over 1000 m, e.g. Karphi at 1148 m, Kastellos at 1160 m, Keria at 1168 m. Despite this huge difference in altitudes Rutkowski has pointed out that all peak sanctuaries fall within certain vegetation zones. 8 Referring to the work of Philippon, 9 Rutkowski has shown that all peak sanctuaries, irrespective of height, are associated with altitude regions that allow for some sort of farming, arable or pastoral, often both. Therefore, today, routes up to the summit pass through vineyards and groves of olive and fruit trees; they climb past mountain meadows of fragrant herb bushes where bees gather nectar, and sheep and goats graze in summer. Indeed, it is striking just how many peak sanctuaries have a gentle slope on one side of the summit, or a high flat area below it, where flocks are still pastured today: e.g. Petsopha, Pyrgos, Vrysinas, Traostalos, Modhi, and Zou. 8. Source: Active walker model for the formation of human and animal trail systems (#B6P8L4), Dirk Helbing, Frank Schweitzer, Joachim Keltsch, Péter Molnár, p. 13 Context: #E9C9Y2 Active Walker Model for the Formation of Human and Animal Trail Systems #3WQXTG IV. HUMAN TRAIL FORMATION Matching excerpt #MZP8G3: where \sigma(\mathbf{r}_\alpha) characterizes the sight, i.e. the range of visibility. In analogy to (10), this formula could be easily generalized to include conceivable effects of a pedestrian's angle of sight. However, we will not do this here, since we would have to calculate different trail potentials V_{tr}^\alpha for all walkers \alpha , then. This would make the model much more complicated. 9. Source: Active walker model for the formation of human and animal trail systems (#B6P8L4), Dirk Helbing, Frank Schweitzer, Joachim Keltsch, Péter Molnár, p. 14 Context: #E9C9Y2 Active Walker Model for the Formation of Human and Animal Trail Systems #3WQXTG IV. HUMAN TRAIL FORMATION #FG65J6 A. Scaling to dimensionless equations Matching excerpt #C93YHS: The use of existing trails depends on the visibility, as given by Eq. (20). Assuming that the sight parameter \sigma is approximately space-independent, an additional simplification of the equations of trail formation can be reached by introducing dimensionless variables 10. Source: Active walker model for the formation of human and animal trail systems (#B6P8L4), Dirk Helbing, Frank Schweitzer, Joachim Keltsch, Péter Molnár, p. 7 Context: #E9C9Y2 Active Walker Model for the Formation of Human and Animal Trail Systems #P3AR99 III. TRUNK TRAIL FORMATION BY ANTS Matching excerpt #NWNBH2: Before we present our model, we would like to mention some differences between active walkers and ants. The latter are rather complex biological creatures which are capable of using additional information (e.g. landmark use) or egocentric navigation [55] for their food searching and homing. Moreover, they can store information in an individual memory and communicate with nest mates in a very complex manner [56]. 11. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 54 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #8BZAPC 5.7.7. Flagging the Trail Alignment #AGRR47 5.7.7.1. Initial Flagging Process Matching excerpt #74BTZF: Normally, two people are sufficient for flagging a trail alignment. They use clinometers or Abney hand levels to sight linear grades. Prior to starting, they stand on level ground and use their instruments to obtain a horizontal reference point on each other's bodies. They look through their instruments at 0% (level to eye height) and locate where that horizontal line is on the body part of the other person. People of similar height are usually partnered, so their reference points are on each other's faces. If one person is substantially taller than the other, the taller person will sight over the shorter person's head, and they will not have a horizontal reference point. When shooting grades in the field, both members of the flagging team must be able to sight on each other to validate the linear grade. The flagging team's linear grade measurements should be within 1% of each other, which cannot be accomplished if one partner is unable to sight on the other. If there is a significant difference in height between the two flaggers, the shorter person can carry a rod or pole that is long enough for the taller person to obtain a horizontal reference point. That location on the rod is then marked with colored tape and flagging for future reference. (See Figure 5.12 and Photo 5.36.) 12. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 46 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #9WNHGK 5.7.5. Field Reconnaissance #XG25M6 5.7.5.2. Designed Control Points #9EED3X 5.7.5.2.2. Turns Matching excerpt #ZT9RRA: Another important location criterion for these structures is a break in slope. By locating the corner of the turn where there is a distinct change or break in the slope of the hillside, one leg can be located above the break and one leg can be located below the break. This break in slope can be used to obscure the lower leg from the field of vision of a trail user coming down the upper leg. The trail user coming down the upper leg will not see the lower leg until they reach the turn, which is a very effective method of preventing users from cutting between the two legs of a turn. This technique can be further enhanced by taking advantage of natural barriers such as trees, large rocks, or dense brush. The turn is placed where these barriers are located between the two legs. Natural barriers also obscure the lower leg from the trail user's line of sight and can prevent cutting between the two legs of the turn. Approximate matches 1. Source: The Topography of Minoan Peak Sanctuaries (#ARP5U7), A. A. D. Peatfield, p. 3 Context: #S9HW3P THE TOPOGRAPHY OF MINOAN PEAK SANCTUARIES Score: 0.029 Related excerpt #N7XTK3: It seems important then that the sanctuary should be seen from the region it served, and also that it should 'see' that region. The reason may simply have been that the most prominent mountain is the best landmark for worshippers to travel to. We do know, however, 2. Source: The Topography of Minoan Peak Sanctuaries (#ARP5U7), A. A. D. Peatfield, p. 4 Context: #S9HW3P THE TOPOGRAPHY OF MINOAN PEAK SANCTUARIES Score: 0.027 Related excerpt #GDV37F: Naturally, the view from each peak sanctuary is spectacular. As noted above, the peak sanctuaries of east Crete are clustered closely together; so close that one or more other peak sanctuaries are often visible from one another. The most outstanding example of this is Traostalos; from the summit at least six other peak sanctuaries can be seen: Petsopha to the north, Modhi to the north-west, Vigla Zakrou, the tip of Plagia, and Korphi tou Mare, all to the south-west, and Ambelos to the south. A similar situation is found a little further west in central Sitias. The peak sanctuary that dominates the north central plain of Sitias is Zou. South of this mountain are several other peak sanctuaries: Ai Ilia, Xykephalo, and Etia. From all of them Zou can be seen clearly, and the eye is drawn north towards it, as the highest peak on the horizon. In the Iraklion region the same is true, as there Mt. Iouktas is the major focal point for all the other peak sanctuaries as far west as Gonia, and as far east as Karphi. In all these cases it appears that one mountain dominates not only the settlements nearby, but also the other peak sanctuaries within view. 3. Source: The Topography of Minoan Peak Sanctuaries (#ARP5U7), A. A. D. Peatfield, p. 3 Context: #S9HW3P THE TOPOGRAPHY OF MINOAN PEAK SANCTUARIES Score: 0.026 Related excerpt #WZ2YSX: It appears then that the Minoans chose particular mountain summits for peak sanctuaries. Of the various factors which may have influenced that choice, Rutkowski has rightly emphasized accessibility and proximity to mountain pastures. Another factor appears to have been the general prominence and visibility of the chosen mountain. In the open plains height and reasonable access were most important—i.e. the highest mountain is the obvious one from which to worship the deity. For example, Vrysinas is a solitary mountain in the plain of Rethymnon; Kophinas is the highest mountain of the Asterousia range, and its peak is visible even from Phaistos at the far end of the Mesara plain. Iouktas, in turn, dominates the whole of the north central region of Crete, and its profile, like the face of a bearded man lying down (best seen from the west), can only have added to the Minoan belief in its sanctity. 4. Source: The Topography of Minoan Peak Sanctuaries (#ARP5U7), A. A. D. Peatfield, p. 3 Context: #S9HW3P THE TOPOGRAPHY OF MINOAN PEAK SANCTUARIES Score: 0.022 Related excerpt #QPEZUU: In some areas, however, it is not the highest point which is chosen. Minoan Palaikastro is sited in a small coastal plain, just north of the mountain Petsopha. This mountain is a ridge, which juts out from the encircling massif. The ridge has three peaks and the sanctuary is sited on the lowest of the three; it is this peak which most directly overlooks the town. From the other summits the view is obscured by lower platforms and cliffs. Faure notes a similar situation with the peak sanctuary at Etia. 12 The shrine is not on the highest peak of the massif, which is Skopeli at 715 m. Rather it is situated on an isolated butte to the north, 100 m lower down. From there, however, one can see the valley plains of Armeni and Chandra. A third example is observable at Zou. 13 The summit is 803 m high, but the peak sanctuary is on the rising edge of a small plateau, north-west of the summit, at an altitude of 725 m. It is only from this high point that the coastal plain of Sitia can be seen; moreover, from the plain this point looks like the summit. 5. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 34 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #9WNHGK 5.7.5. Field Reconnaissance Score: 0.03 Related excerpt #ZQLAER: This “big picture view” also helps to understand the spatial relationships of topographic features, such as ridges, watercourses, hilltops, rock outcrops, and flat benches of land. If an overhead flight is not possible, viewing the area from a prominent elevation such as a mountain top or ridge is the next best option. Computer programs that render a 3 dimensional representation of the earth also provide the designer with a view of the landform. These programs map the earth by superimposing satellite images, aerial photography, and GIS data onto a 3D globe, allowing users to see landscapes from various angles. They provide a virtual flight over the landform with a variety of views. The quality of the view depends on the aerial photographic coverage and how recently the photographs and satellite images were taken. On the ground, this kind of overview is more difficult and time-consuming to obtain. 6. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 35 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #9WNHGK 5.7.5. Field Reconnaissance Score: 0.028 Related excerpt #HWVANA: In Photo 5.21 below, the top view identifies vegetation, escarpments, stream valleys, and talus slopes. The bottom view identifies watercourses, vegetation, and unstable geomorphic areas. 7. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 34 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #9WNHGK 5.7.5. Field Reconnaissance Score: 0.026 Related excerpt #FDY266: Prior to setting foot on the landform, it may be desirable to use a helicopter or fixed wing aircraft to fly above the proposed alignment to give the designer a “bird’s eye” view of the landform. An overhead view provides an image of the land and helps locate potential problems, such as landslides, unstable inner gorges, cliffs, and steep slopes. It also provides the designer with a view of the vegetation types growing within the trail corridor. Vegetation is often a good indicator of soil type. Some plants prefer saturated soils while others prefer rocky well drained soils. Identifying vegetation and the soil types they prefer gives the designer a good indication of the soil types they will encounter once they perform on the ground reconnaissance. 8. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 48 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #9WNHGK 5.7.5. Field Reconnaissance #XG25M6 5.7.5.2. Designed Control Points #UM24VH 5.7.5.2.4. Problematic Topography Score: 0.024 Related excerpt #DY8MQW: If a trail is to be located along a ridge, it is much better design practice to locate it just below the ridge top where hillside construction will facilitate sheet flow across the trail bed. The trail is close enough to the top of the ridge to offer good views yet facilitate natural surface runoff. This layout practice may also provide opportunities to have the trail cross the ridge top where a low point or saddle occurs. This design offers the trail user different views in a dramatic fashion rather than just seeing the same view for an extended period of time. (See Figure 5.9.) 9. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 47 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #9WNHGK 5.7.5. Field Reconnaissance #XG25M6 5.7.5.2. Designed Control Points #W2A9QZ 5.7.5.2.3. Topographic Control Points Score: 0.023 Related excerpt #NQEQL9: Sometimes there are topographic features on the landform that can serve as control points. The most common of these features is a low point or saddle on an extended ridge. These locations control the elevation of a potential trail alignment simply by being the lowest point of land that a trail can pass through. Recognizing these control points early in the layout and reconnaissance process can expedite the determination of the trail corridor, the location of control points, and the grades between those control points. Photo 5.31 demonstrates how for a trail alignment with a starting location (A) and an ending location (B), the saddle on the ridge between those two locations (arrow) can serve as an elevation control. 10. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 36 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #9WNHGK 5.7.5. Field Reconnaissance #7JBFFE 5.7.5.1. Minor Control Point Identification Score: 0.022 Related excerpt #BQ5JNU: Often, these control points are obvious, though occasionally they are not, and careful observation of the landform is required. Conditions such as the presence of wetland obligate plants, pistol grip or tilted trees, ponding water, or old landslide rotations overgrown with vegetation indicate unstable or problematic terrain. These areas require additional investigation and thorough assessment by an appropriate specialist. All of these features are potential control points that may influence the trail alignment. Unique features such as view sheds, waterfalls, flowering plants, specimen trees, or access to water should also be considered minor control points that designers integrate into the alignment. 11. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 57 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #8BZAPC 5.7.7. Flagging the Trail Alignment #AGRR47 5.7.7.1. Initial Flagging Process #SKHQPC SIGHTING FOR GRADE WITH CLINOMETER Score: 0.022 Related excerpt #FXYT4A: In Figure 5.39, two flaggers shoot across a small rounded ridge (yellow lines) that does not follow curvilinear alignment, resulting in an alignment close to the fall line. An intermediate station (pink flag) at the center of the ridge would produce an alignment slightly longer (green line) but closer to the contour of the landform. 12. Source: Modelling the Evolution of Human Trail Systems (#UYLTYJ), Dirk Helbing, Joachim Keltsch, Péter Molnár, p. 1 Context: #BSSYS2 Modelling the Evolution of Human Trail Systems Score: 0.022 Related excerpt #XDF23G: The attractiveness of a trail segment at place \vec{r} from the perspective of place \vec{r}_\alpha decreases with its distance \|\vec{r} - \vec{r}_\alpha(t)\| and depends on the visibility \sigma(\vec{r}_\alpha) . Considering this by a factor \exp(-\|\vec{r} - \vec{r}_\alpha\|/\sigma(\vec{r}_\alpha)) and taking the spatial average by integration of the weighted ground structure over the green area, we obtain ### 31. Tool result: search_text Exact matches 1. Source: The Topography of Minoan Peak Sanctuaries (#ARP5U7), A. A. D. Peatfield, p. 4 Context: #S9HW3P THE TOPOGRAPHY OF MINOAN PEAK SANCTUARIES Matching excerpt #3NXXTZ: A recent survey of the Ayiopharango valley in south Crete has shown many of these topographic features on a smaller scale. 14 Within this small area the surveyors identified five small hills as peak sanctuaries: sites E4A, E12, E18, W11, MOW1. Each 'peak sanctuary' overlooks a small farmstead and associated tholos tomb. It is suggested that each of these hills was the local shrine of the family/clan who lived in the farmstead and buried their dead in the tholos. The hills are quite low and the surveyors suggested that the site E12, in the centre of the valley, may have been a focus for the whole valley community, not just the local farm. From this and other evidence Bintliff has developed the idea of a sacred hierarchy of peak sanctuaries and other shrines. 15 Furthermore, using a Mexican anthropological study as a model, he goes on to suggest a 'series of ritual pilgrimages' to these shrines 'which unite ever larger units of the regional community'. 16 That is to say, the people near Xykephalo and Etia would have visited not only their own peak sanctuary but also that of Zou, which dominated the whole region. 2. Source: Wholeness as a Hierarchical Graph to Capture the Nature of Space (#BYG3BQ), Bin Jiang, p. 5 Context: #V2MHRV Wholeness as a Hierarchical Graph to Capture the Nature of Space #9FK8U9 3. Wholeness as a hierarchical graph Matching excerpt #25Z8H8: The idea of wholeness has been discussed in a variety of sciences such as physics, biology, neurophysiology, medicine, cosmology, and ecology (e.g., Bohm 1980), but no one prior to Alexander (2002-2005) has ever formulated and defined it in precise mathematical language. Following Alexander's definition of wholeness, some previous efforts have been made (e.g., Salinas 1997) to quantify the degree of life of architecture. The proposed measure L does indicate approximately the degrees of life, but it lacks of the recursive property. We represent a whole as a graph, in which the nodes and links represent identified centers and their relationships within the whole (Figure 3). With the graph, we can compute the degrees of life for the individual centers and the whole. What is unique for our model is that it captures fairly well the recursive nature of wholeness as defined by Alexander. This section presents the two measures, the PR scores and ht-index, and argues why they can be a good proxy of degrees of life or beauty. In the next section, we further illustrate through case studies that a living structure demonstrates a scaling hierarchy of far more low-degree-of-life centers than high-degree-of-life centers; and the degree of the scaling hierarchy can be characterized by the ht-index: the higher the ht-index, the higher degree of life or wholeness. 3. Source: Wholeness as a Hierarchical Graph to Capture the Nature of Space (#BYG3BQ), Bin Jiang, p. 0 Context: #V2MHRV Wholeness as a Hierarchical Graph to Capture the Nature of Space #QT5RF7 Abstract Matching excerpt #HDXQZV: According to Christopher Alexander's theory of centers, a whole comprises numerous, recursively defined centers for things or spaces surrounding us. Wholeness is a type of global structure or life-giving order emerging from the whole as a field of the centers. The wholeness is an essential part of any complex system and exists, to some degree or other, in spaces. This paper defines wholeness as a hierarchical graph, in which individual centers are represented as the nodes and their relationships as the directed links. The hierarchical graph gets its name from the inherent scaling hierarchy revealed by the head/tail breaks, which is a classification scheme and visualization tool for data with a heavy-tailed distribution. We suggest that (1) the degrees of wholeness for individual centers should be measured by PageRank (PR) scores based on the notion that high-degree-of-life centers are those to which many high-degree-of-life centers point, and (2) that the hierarchical levels, or the ht-index of the PR scores induced by the head/tail breaks can characterize the degree of wholeness for the whole: the higher the ht-index, the more life or wholeness in the whole. Three case studies applied to the Alhambra building complex and the street networks of Manhattan and Sweden illustrate that the defined wholeness captures fairly well human intuitions on the degree of life for the geographic spaces. We further suggest that the mathematical model of wholeness be an important model of geographic representation, because it is topological oriented that enables us to see the underlying scaling structure. The model can guide geodesign, which should be considered as the wholeness-extending transformations that are essentially like the unfolding processes of seeds or embryos, for creating beautiful built and natural environments or with a high degree of wholeness. 4. Source: Wholeness as a Hierarchical Graph to Capture the Nature of Space (#BYG3BQ), Bin Jiang, p. 1 Context: #V2MHRV Wholeness as a Hierarchical Graph to Capture the Nature of Space #3KT2GU 1. Introduction Matching excerpt #EHDJCS: This paper develops a mathematical model of wholeness by defining it as a hierarchical graph, in which the nodes and links respectively represent individual centers and their relationships. The graph provides a powerful means for computing the degree of wholeness or life. First, the graph can be easily perceived as a whole of interconnected centers, enabling a recursive definition of wholeness or centers. Second, spaces with a living structure demonstrate a scaling hierarchy of far more low-degree-of-life centers than high-degree-of-life ones. The life or beauty of individual centers can be measured by PageRank (PR) scores (Page and Brin 1998), which are based on a recursive definition that high-degree-of-life centers are those to which many high-degree-of-life centers point. For the graph as a whole, its degree of life can be characterized by the ht-index derived from the PR scores; the higher the ht-index, the higher degree of life in the whole. The ht-index (Jiang and Yin 2014) was initially developed to measure the complexity of fractals or geographic features in particular, and it was actually induced by head/tail breaks as a classification scheme (Jiang 2013a), and a visualization tool (Jiang 2015a). Things of different sizes can be ranked in decreasing order and broken down around the average or mean into two unbalanced parts. Those above the mean, essentially a minority, constitute the head, and those below the mean, a majority, are the tail. This breaking process continues recursively for the head (or the large things) until the notion of far more small things than large ones is violated. 5. Source: Wholeness as a Hierarchical Graph to Capture the Nature of Space (#BYG3BQ), Bin Jiang, p. 5 Context: #V2MHRV Wholeness as a Hierarchical Graph to Capture the Nature of Space #LWK7XQ 2. The 15 properties #FGVYNH Not-separateness Matching excerpt #7U7YF9: A center is not separable from its surrounding centers. This property has several other meanings. All scales, from the smallest to the largest, are essential and not separable in forming a scaling hierarchy. A whole connects to the nearby wholes to recursively form even larger wholes, toward the entire universe. A whole connects to human beings in their deep psyche, evoking a sense of beauty. That is why both the snowflake (Figure 2a) and axial map (Figure 2f) look beautiful. 6. Source: Wholeness as a Hierarchical Graph to Capture the Nature of Space (#BYG3BQ), Bin Jiang, p. 10 Context: #V2MHRV Wholeness as a Hierarchical Graph to Capture the Nature of Space #7HNVWB 5. Further discussions on the mathematical model of wholeness Matching excerpt #GPK35V: Wholeness emerges from recursively defined centers, so it can be considered as an emergence of complex structures. To sense or appreciate the wholeness, we must develop both figural and analytical perception, or see things holistically and sequentially. However, a majority of people tend to see things analytically rather than figuratively (Alexander 2005). These two kinds of perception help us see a whole and its building-block centers, and perceive the degree of life or wholeness through the interacting and reinforcing centers. These perception processes are manifested in the mathematical model of wholeness. In other words, this model enables us to see things in their wholeness from their fragmented, yet interconnected, parts. The wholeness, or life, or beauty is something real, rather than a matter of opinion (Alexander 2002–2005). This kind of beauty exists in geographic space, arising from the underlying scaling hierarchy, or the notion of far more small geographic features than large ones (Jiang and Sui 2014). Large amounts of geographic information harvested from social media and the Internet enable us to illustrate striking scaling patterns (Jiang and Miao 2014, Jiang 2015a) and assess the goodness of geographic space. 7. Source: Wholeness as a Hierarchical Graph to Capture the Nature of Space (#BYG3BQ), Bin Jiang, p. 3 Context: #V2MHRV Wholeness as a Hierarchical Graph to Capture the Nature of Space #LWK7XQ 2. The 15 properties #VKHKZE Strong centers Matching excerpt #GHEACQ: A strong center is supported by other surrounding centers in a configuration as a whole. Centers are not separable in forming a coherent whole. The strongest center of the snowflake is in the middle of the pattern (Figure 2b), and it is supported by six, 18, and 54 other centers in a recursive manner. The strongest center of the axial map is the red line, and it is recursively supported by yellow, green, cyan, and blue lines (Figure 2f). 8. Source: Wholeness as a Hierarchical Graph to Capture the Nature of Space (#BYG3BQ), Bin Jiang, p. 8 Context: #V2MHRV Wholeness as a Hierarchical Graph to Capture the Nature of Space #TXBKLJ 4. Case studies: Computing the degrees of life #B54GRW 4.1 The plan of Alhambra Matching excerpt #7SQMAC: Note: There are 725 convex spaces, or centers, and 880 relationships between the centers. The centers are divided into three parts (left, right, and middle) or subparts, indicated by red lines. The degrees of life for the individual centers are indicated by dot sizes, while the plan as a whole has a degree of life 6. 9. Source: Beautimeter: Harnessing GPT for Assessing Architectural and Urban Beauty Based on the 15 Properties of Living Structure (#MH5J8D), Bin Jiang, p. 2 Context: #HAZYNL Beautimeter: Harnessing GPT for Assessing Architectural and Urban Beauty based on the 15 Properties of Living Structure #6XBA45 2. Theoretical Framework #NQ4QUT 2.1 Living Structure and the 15 Fundamental Properties Matching excerpt #SFQXRA: The 15 properties can be distilled into two overarching laws – the scaling law (Jiang 2015) and Tobler’s law (Tobler 1971) – that are foundational for understanding and characterizing living structure. Firstly, the scaling law is essentially the levels of scale property, asserting that, across any given structure, a hierarchy exists in which there are far more small substructures (or centers) than large ones. This distribution is seen across several levels of scale, from the smallest components within a system to the most significant elements. Having many small centers contributes to the overall structure’s richness, complexity, and coherence, enabling it to exhibit the qualities of life and vibrancy that are characteristics of a living structure. The scaling law shows the importance of having a fine-grained hierarchy in order to create environments that resonate with human experience, and many of the 15 properties (e.g., alternating repetition, contrast, roughness, positive space, and local symmetries) recur at different levels of scale. 10. Source: Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole (#PXG56P), Christopher Alexander, p. 12 Context: #Q94AYK IV HARMONY-SEEKING COMPUTATIONS #XE4TCT What Are The Underlying Qualities Common to Different Examples of Harmony-Seeking Steps in Different Systems? #QJLGS4 Example 4: Hayricks in a Field Matching excerpt #4Q8VNF: The people who built and placed these ricks, were, consciously or unconsciously, performing a harmony-seeking computation. There are ECHOES of shape and size between land and hayricks, ECHOES of a certain kind of curve, LOCAL SYMMETRIES in the ricks themselves, and the placing of the ricks emphasizes naturally occurring STRONG CENTERS that are generated by shelves and flattened places, bounded so that the hayricks nestle in the land, are subdued and congruent, and inside the structure which exists. The hayricks are kindly to the land, but they are placed with enormous care. They follow the wholeness. And if I were to move them slightly, to different positions, the placement and the whole then created, the ensemble, would be less profound and less harmonious. 11. Source: Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole (#PXG56P), Christopher Alexander, p. 61 Context: #A6ZZPA XI CONCLUSIONS #MRNGTP Structure-Preserving Transformations #2K9BAZ A Few Randomly Chosen Examples of Harmony-Seeking Computations Matching excerpt #A9ET32: → STRONG CENTERS, LEVELS OF SCALE → LOCAL SYMMETRIES → 12. Source: Boom box on the terrace: an Alexanderian violation test (#VZHR9P) Matching note #VZHR9P: Thought experiment: a family quietly inhabits an oak-and-bench setting or Ravello terrace; an intruder plays clipping loud music and scribbles on the columns. The wrongness is relational, not intrinsic to rock music or marker strokes. In another context either could be good. Here they overwrite existing centers—conversation, play, repose, columns, view and acoustic enclosure—without helping the larger whole. This exemplifies Alexander’s SP criterion: a transformation should elaborate existing/latent centers rather than introduce centers that violate or cut across them (#XZ4XQ3), and should improve a larger whole (#GXVBDU). The intrusion is also ethically wrong because it coercively monopolizes a shared sensory field and irreversibly damages a common artifact. The case helps distinguish objective/intersubjective structural badness from mere disliked style: observers could potentially identify loss of affordances, interrupted coordination, distress, damage, and reduced mutual support even without sharing the participants’ musical or decorative preferences. Approximate matches 1. Source: Wholeness as a Hierarchical Graph to Capture the Nature of Space (#BYG3BQ), Bin Jiang, p. 3 Context: #V2MHRV Wholeness as a Hierarchical Graph to Capture the Nature of Space #LWK7XQ 2. The 15 properties #VKHKZE Strong centers Score: 0.03 Related excerpt #GHEACQ: A strong center is supported by other surrounding centers in a configuration as a whole. Centers are not separable in forming a coherent whole. The strongest center of the snowflake is in the middle of the pattern (Figure 2b), and it is supported by six, 18, and 54 other centers in a recursive manner. The strongest center of the axial map is the red line, and it is recursively supported by yellow, green, cyan, and blue lines (Figure 2f). 2. Source: Wholeness as a Hierarchical Graph to Capture the Nature of Space (#BYG3BQ), Bin Jiang, p. 4 Context: #V2MHRV Wholeness as a Hierarchical Graph to Capture the Nature of Space #LWK7XQ 2. The 15 properties #ZBHUGU Gradients Score: 0.029 Related excerpt #54527U: The centers gradually strengthen from the smallest to the largest scale, from the shortest to the longest line, from blue to red (Figure 2f), from the smallest to biggest dots (Figure 2b), and from the least-connected to the most-connected lines. This property of gradients can also be referred to as the scaling hierarchy ranging from the smallest to the largest. 3. Source: Wholeness as a Hierarchical Graph to Capture the Nature of Space (#BYG3BQ), Bin Jiang, p. 3 Context: #V2MHRV Wholeness as a Hierarchical Graph to Capture the Nature of Space #LWK7XQ 2. The 15 properties #3ZAA2T Alternating repetition Score: 0.027 Related excerpt #3K57DA: Centers are strengthened if they are repeated by the property of alternating repetition. This property exists in the snowflake with the surrounding alternations of indents and outcrops of the edge, as well as in the axial map. The shortest lines (blue) bearing this property of alternating repetition are strengthened to form the lowest hierarchical level as a center, which supports other hierarchical levels or centers (Figure 2f). The notion of far more short lines than long ones recurs four times, also indicating an alternating repetition, or repeating the head/tail contrast statistically rather than strictly. 4. Source: Wholeness as a Hierarchical Graph to Capture the Nature of Space (#BYG3BQ), Bin Jiang, p. 3 Context: #V2MHRV Wholeness as a Hierarchical Graph to Capture the Nature of Space #LWK7XQ 2. The 15 properties #ZEFTKL Thick boundaries Score: 0.026 Related excerpt #THP9B9: Centers are often differentiated by thick boundaries. For example, the different triangle sizes in the snowflake (Figure 2a) and the convex spaces of the urban layout have thick boundaries (Figure 2d). The five hierarchical levels of the axial map can be perceived as centers, represented by five different colors (Figure 2f), which apparently lack thick boundaries. In this regard, the different means used for the head/tail breaks process might be considered thin boundaries. 5. Source: Wholeness as a Hierarchical Graph to Capture the Nature of Space (#BYG3BQ), Bin Jiang, p. 5 Context: #V2MHRV Wholeness as a Hierarchical Graph to Capture the Nature of Space #LWK7XQ 2. The 15 properties #FGVYNH Not-separateness Score: 0.026 Related excerpt #7U7YF9: A center is not separable from its surrounding centers. This property has several other meanings. All scales, from the smallest to the largest, are essential and not separable in forming a scaling hierarchy. A whole connects to the nearby wholes to recursively form even larger wholes, toward the entire universe. A whole connects to human beings in their deep psyche, evoking a sense of beauty. That is why both the snowflake (Figure 2a) and axial map (Figure 2f) look beautiful. 6. Source: Wholeness as a Hierarchical Graph to Capture the Nature of Space (#BYG3BQ), Bin Jiang, p. 2 Context: #V2MHRV Wholeness as a Hierarchical Graph to Capture the Nature of Space #LWK7XQ 2. The 15 properties #7DFB5R Levels of scale Score: 0.025 Related excerpt #TAB4VD: As the building blocks of a whole, centers are defined at different levels of scale. For example, the snowflake has four scales: 1, 1/3 , 1/9 , and 1/27 (Figures 2a, 2b), while the axial map has five scales based on head/tail breaks (Figure 2f). In general, the levels of scale can be characterized by the ht-index (Jiang and Yin 2014), or the number of times that the scaling pattern of far more small things than large ones recurs. 7. Source: Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole (#PXG56P), Christopher Alexander, p. 60 Context: #A6ZZPA XI CONCLUSIONS #MRNGTP Structure-Preserving Transformations #HWWGSL Models Of The Wholeness In A Given Configuration? Score: 0.024 Related excerpt #KJBJ2D: Postulate A4. Certain centers may be very low saliency, almost invisible, but are nevertheless coherent configurations in their own right, which are created by others in the configuration. These will be referred to as latent centers. 8. Source: Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole (#PXG56P), Christopher Alexander, p. 35 Context: #567Q7Z VII HARMONY-SEEKING RATHER THAN MERELY “EMERGENCE” #S4HQZJ A Whole-Based, Harmony-Seeking Process Which Works By Continually Strengthening Latent Centers. #WE6WWG In Detail, What Exactly Does It Mean For A System To Help The Larger System It Is Embedded In? Score: 0.024 Related excerpt #D53VF2: Let us return to the example of St Mark's Square. At each cycle the process identifies a latent center in the larger configuration. This latent center is an area or potential center which is weak, and which – if strengthened -- would improve the coherence of the whole. The area immediately around that latent center is healed or made more whole by the injection of the repaired latent center. 9. Source: Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole (#PXG56P), Christopher Alexander, p. 60 Context: #A6ZZPA XI CONCLUSIONS #MRNGTP Structure-Preserving Transformations #HWWGSL Models Of The Wholeness In A Given Configuration? Score: 0.024 Related excerpt #KAKBB9: Postulate B2. The best latent center to work on, is the latent center whose improvement or repair, will (probably) do the most to increase the coherence of the whole configuration. 10. Source: Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole (#PXG56P), Christopher Alexander, p. 59 Context: #A6ZZPA XI CONCLUSIONS #B6DWSV A Single Conclusion From These Studies Score: 0.023 Related excerpt #EU44Z5: The issue is recursive. It is not only large-scale configurations that need to benefit from this insight. The idea that every configuration, at every level, is working to help the coherence of some larger configuration in which it is embedded, runs up and down the ladder of scales, and must do so in any living world. A successful computation will emulate this upwards- and downwards-reaching process. Purely bottom-up forms of calculation, not invoking this principle, will always remain too sterile to be real or profound. 11. Source: Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole (#PXG56P), Christopher Alexander, p. 36 Context: #567Q7Z VII HARMONY-SEEKING RATHER THAN MERELY “EMERGENCE” #S4HQZJ A Whole-Based, Harmony-Seeking Process Which Works By Continually Strengthening Latent Centers. #WE6WWG In Detail, What Exactly Does It Mean For A System To Help The Larger System It Is Embedded In? Score: 0.021 Related excerpt #V7GAR8: Abstractly we may express this concept through the following diagram. The red area is a latent center, a weak center which has the capacity to heal the blue area beyond it: and it is able to do so by creation of the smaller white centers -- they are built to create coherence in the red center. However, the key point is that the healing will not take place, unless the red center then also helps to heal the larger blue center beyond it. 12. Source: Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole (#PXG56P), Christopher Alexander, p. 33 Context: #QUCRWC VI STRUCTURE-PRESERVING TRANSFORMATIONS: HELPING A LARGER WHOLE TO FORM #FSRDPE The SP-Postulate: Always Helping A Larger Whole To Form #T3NUBP The SP-Transformations Of St Mark's Square, Previously Discussed. Score: 0.021 Related excerpt #RRPPUH: Here, for example, the red ellipse, is \mathcal{L} , the latent center formed by the three buildings around it. To confirm and strengthen \mathcal{L} , the blue building mass is built, thus forming a stronger rectangular space, by enclosure, and establishing continuity with the buildings on the right of the latent configuration. ### 32. Tool result: search_text Exact matches 1. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 2 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #ZRSZUM 3. Background and Overview #DH5T8U 3.2. Algorithm Overview Matching excerpt #A8CFAJ: Our algorithm proceeds in two main steps: erosion simulation computed on planar graph \mathcal{G} embedding elevation and flow information, called the stream graph , and conversion of this graph into an elevation model \mathcal{M} representing the terrain. 2. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 5 Context: #JJE8HN Procedural Riverscapes #TFD8TX 5. River Network Amplification #U4VCJG 5.3. Seeding Riverflow Primitives Matching excerpt #5NJY7V: In terms of the impact of Rosgen type on the choice of water primitives, for type A we assign near constant height over each basin and then add fall primitives where basins intersect. Next, we place downstream turbulence primitives based on the waterfall drop and average flow velocity. These decrease in amplitude and frequency with increasing distance from the waterfall. For type C , the bends have high turbulence and velocity in deeper areas with calmer primitives placed in the shallows. The straights are seeded with high turbulence primitives to emulate rapids. For type D , the velocity and turbulence parameters of water primitives are keyed to channel depth and distance from the center of the nearest channel. 3. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 3 Context: #JJE8HN Procedural Riverscapes #TFD8TX 5. River Network Amplification Matching excerpt #8RD8MD: Amplification proceeds by first refining the trajectories of edges \mathcal{E} in the river graph \mathcal{G} , based on their Rosgen type (see Section 5.1). The result is a revised geometric graph \hat{\mathcal{G}} = \{\mathcal{N}, \hat{\mathcal{E}}\} . Importantly, this process not only adjusts the planar (x, y) course of the river, but also its longitudinal profile ( z elevation values along the river spine) so as to create appropriate basins, pools and cascades. Then, the geometry of the riverbed is realised, by selecting, scaling and assigning Rosgen cross-sectional templates along the river, and carved into the terrain \mathcal{T} , which results in a modified terrain \hat{\mathcal{T}} (Section 5.2). Finally, we distribute riverflow primitives (Section 5.3), in readiness for their assembly into a blend-flow tree that defines the animated water surface. 4. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 7 Context: #JJE8HN Procedural Riverscapes #9ZYJP2 6. Animated Procedural River Model #U6BTCY 6.1. Riverflow Primitives Matching excerpt #GC73J3: Cascade and wave primitives are defined by blending upstream f_u and downstream f_d functions. The relative positioning of upstream and downstream is expressed according to the prescribed direction of the flow \mathbf{u} . The functions are parameterized by the relative height h of the wave or fall. Downstream we use a turbulent water function, and upstream calm water. Let g : \mathbf{R} \rightarrow [0, 1] denote the C^2 smooth step function, and \epsilon the size of the blending region between upstream and downstream water heights. We define the blending function as: 5. Source: On implication and negation in partition logic (#C8FHDZ), , David Ellerman, p. 0 Context: #L8JZAG On implication and negation in partition logic #ZZPBEJ 1. Introduction: The Boolean logic of subsets and the logic of partitions Matching excerpt #BLF82B: T oday, the ‘classical’ form of logic is seen as the Boolean logic of subsets usually presented as the special case of propositional logic (i.e., the logic of subsets 0 and 1 of the one element set 1). Other related logics, such as intuitionistic logic (e.g., the logic of the open subsets of a topological space) are considered as non-classical. But there is another recently developed and little-known logic that is at the same mathematical level of fundamentality as subset logic and is thus ‘classical’ in that nontemporal sense. Since the development of category theory starting in the middle of the twentieth century, it has been known that the concept of a subset has a category-theoretic dual in the notion of a quotient set (or, equivalently, a partition or equivalence relation). F. William Lawvere calls the generalization of a subset a “part” and “The dual notion (obtained by reversing the arrows) of ‘part’ is the notion of partition.” [1, p. 85] The simplest illustration of this is the fact that given a set function f : X \rightarrow Y , the image of f is a subset f(X) \subseteq Y of the codomain Y and the inverse-image \{f^{-1}(y) \neq \emptyset : y \in Y\} is a partition on the domain X . Hence, it should be expected that there is a logic of partitions ([2,3]) dual to the Boolean logic of subsets. And since subsets and quotient sets are at the same basic level from the mathematical point of view, partition logic is more of a dual sibling to subset logic rather than being another ‘non-classical’ off-shoot of the classical subset logic. 6. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 4 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #T6FSBF 5 River Classification Matching excerpt #U7AJ7K: The river graph divides the domain \Omega into nonoverlapping cells that allow us to build a set of watersheds and to construct a dual graph that stores crests (Section 5.1). The water flow is extracted from the river graphs, and each water-course is labeled with respect to the Rosgen classification (Section 5.2). 7. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 4 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #J5PECC 5. Depression routing Matching excerpt #98BGB6: Broadly speaking, this involves connecting depression basins with outflow basins through saddle points and then re-orienting a path of edges within each depression to flow uphill and link to the corresponding outlet. The challenge lies in preventing the formation of cycles as this will lead to highly unnatural flow behavior. Once all stream trees have been corrected, we only need to run flow routing once to calculate discharge volumes. 8. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 3 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #7UZAMN 4. Flow routing Matching excerpt #RB2V29: Water flows downstream from donor cells to recipients, and therefore the flow routing problem consists of accumulating all of the upstream precipitation: 9. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 4 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #J5PECC 5. Depression routing Matching excerpt #KLSYT3: Depression routing consists of building a depression graph, in which the depression and outflow basins represent nodes, and edges are formed by the adjacent cells between different basins. It is likely that there will be multiple potential candidates between any two basin nodes formed by cells paired along their common border. We choose the one with the lowest maximum altitude and call this the saddle (see Figure 4). The saddle altitude is the weight assigned to the new edge in the depression graph. From a physical perspective, choosing the path with the lowest altitude ensures that the potential energy cost of water routed out of the basin is kept to a minimum. 10. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 8 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #34USBX 6. Application to landscape simulation #53AQ2N Algorithm 7: Implicit fluvial erosion Matching excerpt #VU6KLE: where k_d is the sediment deposition coefficient and Q_s is sediment flux, obtained by accumulating the negative elevation balance -\Delta x^2 \frac{\partial z}{\partial t} downstream with flow routing. While Yuan et 11. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 3 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #SD69QC 3. Overview #CPNMBK 3.2. Depression routing Matching excerpt #B2XLDW: Two families of solutions have been proposed to tackle this issue. One option is to progressively flood the terrain from the outflow cells towards the interior, keeping track of cells to be processed through a priority queue [BLM14]. While this enables a simple and efficient single-threaded solution, it is not suited to parallelization on the GPU, because it imposes a sequential order, with each processed cell potentially changing the subsequent state of the queue. The other option is to build a depression graph by representing depressions as nodes and their adjacency relationships as edges. There are two subtleties. First, all outflow basins are grouped into a single node marked as the start. Second, edges are weighted according to the lowest altitude along their shared boundary. The path out of all depressions is then given by the Minimum Spanning Tree (MST) of the depression graph, which connects all depressions to the collection of outflow basins. 12. Source: Scalable real‐time animation of rivers (#XDESU9), Eric Bruneton, Fabrice Neyret, Nicolas Holzschuch, Qizhi Yu, p. 4 Context: #B9LYTR Scalable real-time animation of rivers #S3P9T2 4. Computing flow velocities #89NKTG 4.1. Finding the volumetric flow rate from the hydro geometry Matching excerpt #GBD3PY: For an acyclic graph, these two conditions are sufficient to get the volumetric flow rate values for each edge of the graph in a single traversal, up to a multiplicative constant: we select an edge of the graph, for example one where the volumetric flow rate, Q_0 is known. All flow rate values for the edges of the graph will be proportional to Q_0 . If we don't know Q for any edge, we simply pick an edge that is convenient for the user interface in controlling the flow rate, for example at the mouth of the river. Approximate matches 1. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 3 Context: #JJE8HN Procedural Riverscapes #TFD8TX 5. River Network Amplification Score: 0.026 Related excerpt #EWA69A: The river graph \mathcal{G} has nodes \mathcal{N}_i that correspond to river junctions and edges \mathcal{E}_{ij} that represent the intervening trajectory of the river. The graph nodes store geomorphological data; in particular, the average slope s_i in the local neighborhood of the node and the flow of the river \phi_i . Graph edges, meanwhile, store their Rosgen type t_{ij} (see Figure 3) and encode the river trajectory as a piecewise-cubic curve. 2. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 3 Context: #JJE8HN Procedural Riverscapes #Z6DVCN 4. River Network Graph Score: 0.023 Related excerpt #HS22AT: Next, graph nodes are labeled with the terrain slope s and river flow \phi values at their cell position. The latter is a measure of the volumetric rate at which water is carried down the river and an accurate estimation is problematic, since it depends on parameters such as rainfall and soil composition. Instead, we apply a simplified model based on an empirical power law observed in geomorphology [Dun78]: from drainage area A_{ij} [ m^2 ], the flow \phi_{ij} of the river [ m^3 s^{-1} ] is approximated by \phi_{ij} = 0.42A_{ij}^{0.69} . This equation takes into account evaporation and infiltration, which is why the volume of flow is not preserved. 3. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 3 Context: #JJE8HN Procedural Riverscapes #Z6DVCN 4. River Network Graph Score: 0.021 Related excerpt #TRPJZX: Figure 5). One complication is that the drainage calculation assumes that there are no depressions (local minima) in the digital elevation model, since these have no outlet to neighboring cells. To prevent disconnected river graphs we apply an optimal depression filling algorithm [BLM14], which leaves the surface slightly proud with an available flow channel. 4. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 4 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #T6FSBF 5 River Classification Score: 0.024 Related excerpt #U7AJ7K: The river graph divides the domain \Omega into nonoverlapping cells that allow us to build a set of watersheds and to construct a dual graph that stores crests (Section 5.1). The water flow is extracted from the river graphs, and each water-course is labeled with respect to the Rosgen classification (Section 5.2). 5. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 6 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #J5PECC 5. Depression routing #V69QNF Algorithm 5: Depression Routing Score: 0.028 Related excerpt #CJMQ7G: Implementation. As with flow routing, we prevent read-after-write hazards while minimizing the extent of copying. For basin identification, we store the basin-id only for the local minima and not for all cells, and we use the updated recipients at the end of Algorithm 2 as a per-cell pointer to the downstream local minima, which we interrogate to obtain the basin-id. This change relaxes the need for any copy during basin identification, as read-after-write no longer prevents the correct convergence of the algorithm. Furthermore, we observe that this operation is required only for the first iteration. In subsequent iterations, we need only update the pointers to reflect the new connections out of the local minima, yielding an overall complexity of \mathcal{O}(\log(n) + \log^2(L)) . 6. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 5 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #J5PECC 5. Depression routing #UJCLXC Algorithm 2: Propagation of basin identifiers Score: 0.025 Related excerpt #FHU2AM: Close-coupled loops can occur when two basins have saddle edges pointing at each other. We resolve this by simply deleting the edge with the higher saddle basin-id. We also apply a similar strategy to choose among saddles of identical elevation, which could lead to larger cycles. This is prevented by selecting saddles in lexicographic order (elevation concatenated with the basin-id of the outlet). This algorithm is summarized in Algorithm 3. 7. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 5 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #J5PECC 5. Depression routing #UJCLXC Algorithm 2: Propagation of basin identifiers Score: 0.024 Related excerpt #C9XNSJ: Basin identification. Our algorithm begins by segmenting out each stream tree and associating with its cells a unique basin identifier (hereafter referred to as a basin-id , or bid in the pseudo-code of Algorithm 2). To this end, we assign to each non-outflow local minima a unique identifier – leaving a common outflow identifier for all outflow basins – and use pointer jumping to copy this identifier in parallel to all upstream nodes of its stream tree (Algorithm 2). 8. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 4 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #J5PECC 5. Depression routing Score: 0.023 Related excerpt #98BGB6: Broadly speaking, this involves connecting depression basins with outflow basins through saddle points and then re-orienting a path of edges within each depression to flow uphill and link to the corresponding outlet. The challenge lies in preventing the formation of cycles as this will lead to highly unnatural flow behavior. Once all stream trees have been corrected, we only need to run flow routing once to calculate discharge volumes. 9. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 6 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #J5PECC 5. Depression routing #2HKXNP Algorithm 3: Finding saddles and outlets Score: 0.022 Related excerpt #L94DMG: Input : Terrain cells \mathcal{T} with elevation z , set of depression basins \mathcal{D} Output : Per-depression saddle and outlet 1 // Compute border cells and store the border altitude in z' 2 foreach cell c \in \mathcal{T} in parallel do 3 if bid_c \neq bid_n of any 4-neighbour n of c ( n \in \mathcal{N}_c ) then 4 tag c as a border cell 5 znb \leftarrow \min(z_n \text{ for } n \in \mathcal{N}_c \text{ such that } bid_c \neq bid_n) 6 z'_c \leftarrow \max(z_c, znb) 7 end 8 end 9 // Saddles and outlets (with atomic lexicographic argmin) 10 foreach basin d \in \mathcal{D} in parallel do 11 saddle of d \leftarrow \text{argmin}((z'_c, bid_n) for each border cell c 12 and n \in \mathcal{N}_c such that bid_c = d and bid_n \neq d ) 13 outlet of d \leftarrow \text{argmin}(z_n for each neighbor n of the 14 saddle such that bid_n \neq d ) 15 end 16 // Remove cycles 17 foreach basin d \in \mathcal{D} in parallel do 18 d' \leftarrow basin of outlet of d 19 if bid of outlet of d' = bid of saddle of d then 20 if bid of outlet of d < bid of saddle of d then 21 Delete the saddle and outlet of d 22 end 23 end 24 end 10. Source: Scalable real‐time animation of rivers (#XDESU9), Eric Bruneton, Fabrice Neyret, Nicolas Holzschuch, Qizhi Yu, p. 3 Context: #B9LYTR Scalable real-time animation of rivers #S3P9T2 4. Computing flow velocities Score: 0.026 Related excerpt #GQ3S48: Given a connected graph for the hydrographic network, the values of the volumetric flow rate Q_i for each branch of the graph yields directly the values of the stream function \psi on each of the channel boundaries, up to a constant. The constant is meaningless since we are only interested in the curl of \psi . 11. Source: Scalable real‐time animation of rivers (#XDESU9), Eric Bruneton, Fabrice Neyret, Nicolas Holzschuch, Qizhi Yu, p. 3 Context: #B9LYTR Scalable real-time animation of rivers #S3P9T2 4. Computing flow velocities Score: 0.024 Related excerpt #WR3N89: The stream function is related to the volumetric flow rate inside each branch of the hydrographic network: \psi must be constant along every connected boundary of the system, and the volumetric flow rate Q inside a given channel is equal to the difference between the values of \psi on each bank (see Figure 3): 12. Source: Scalable real‐time animation of rivers (#XDESU9), Eric Bruneton, Fabrice Neyret, Nicolas Holzschuch, Qizhi Yu, p. 3 Context: #B9LYTR Scalable real-time animation of rivers #S3P9T2 4. Computing flow velocities #89NKTG 4.1. Finding the volumetric flow rate from the hydro geometry Score: 0.024 Related excerpt #QXKFZQ: The hydrographic network is a directed graph, expressing the connections between channels, and flowing from the source to the ocean. In the case of streams joining into rivers, themselves joining into larger rivers, the graph is a tree. At the delta of a river, the graph is an inverted tree. If there are no islands, we have an acyclic graph; each obstacle or island results in a cycle in the graph. Islands and obstacles can either be treated at this level, or be treated as a special case in the interpolation method. ### 33. Assistant tool calls #### Tool call: `search_text` ```json { "document_id": "GY93FG", "limit": 8, "query": "mountain trails slope destination visibility zigzag least effort" } ``` #### Tool call: `search_text` ```json { "document_id": "B6P8L4", "limit": 8, "query": "trail attraction visibility destination path formation" } ``` #### Tool call: `search_text` ```json { "document_id": "PXG56P", "limit": 8, "query": "land placement latent center whole terrain landscape" } ``` #### Tool call: `search_text` ```json { "document_id": "DMTA8Y", "limit": 8, "query": "dual graph crests watersheds hierarchy" } ``` ### 34. Tool result: search_text Exact matches 1. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 13 Context: #G4BEE9 Mountain trail formation and the active walker model #NBFQAN 5. Results #TPVRFV 5.1. Algorithm one Matching excerpt #EDDBRC: As the minimum safe angle is increased to 15^\circ , we note that the minimum values of \alpha which are needed to generate zig-zag patterns decreases slightly. In Fig. 5(a) where \alpha = 0.4 , we observe that a single zigzag emerges in the path. As walkers get closer to their destination, the rate at which they change their walking direction increases. Fig. 5(b) shows a similar path for \alpha = 0.45 . In Fig. 5(c) we observe that when \alpha = 0.5 walkers take larger detours away from the direct path between entry and exit, with several changes of direction along the trail. Similar results were found when \theta = 25^\circ (Fig. 6). While zigzag forms develop during the simulations, the rather diffuse paths are not satisfactory representations of mountain trails. 2. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 0 Context: #G4BEE9 Mountain trail formation and the active walker model Matching excerpt #2QALPN: We extend the active walker model to address the formation of paths on gradients, which have been observed to have a zigzag form. Our extension includes a new rule which prohibits direct descent or ascent on steep inclines, simulating aversion to falling. Further augmentation of the model stops walkers from changing direction very rapidly as that would likely lead to a fall. The extended model predicts paths with qualitatively similar forms to the observed trails, but only if the terms suppressing sudden direction changes are included. The need to include terms into the model that stop rapid direction change when simulating mountain trails indicates that a similar rule should also be included in the standard active walker model. 3. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 12 Context: #G4BEE9 Mountain trail formation and the active walker model #NBFQAN 5. Results #TPVRFV 5.1. Algorithm one Matching excerpt #WUZ6YE: In this section, results from the mountain walker extension to the active walker model are shown. We begin by considering only walkers traveling down the slope. The following parameters were used for the simulations: the maximum ground potential was set to G_{\max} = 200\text{m}^{-1} (the units of G are set by Eq. 3 and Eq. 4) while the minimum ground potential was set to G_0 = 0 . Larger values of G_{\max} lead to larger attraction to the path. A new walker descended the inclined area as soon as the existing walker reached the destination (tests showed that there was little difference between this scheme and starting a walker every 100s). The visibility, \sigma of the paths was set to 10m and the intensity, I was set to l^2 G_{\max}/N , where N is the number of footprints needed to wear the ground condition to 1/e of its maximum value. N was set to 50 footfalls and the weathering parameter was initially set to T = 1000\text{s} . The values of N and T are smaller than in a real trail system, where N would be of the order of several hundred footfalls and T would be of the order of a few days. This still leads to realistic simulations since Helbing et al. have found that a combination of several parameters of the active walker model could be represented by the single parameter \kappa = IT/\sigma = G_{\max}T/N\sigma 7 . Individual walkers were assigned a random speed between 0.5m/s and 1.5m/s. In the simulation, walkers were given the starting position \mathbf{r}_{\text{initial}} = (0\text{m}, 5\text{m}) and a destination of \mathbf{r}_{\text{final}} = (25\text{m}, 5\text{m}) with the x -direction being the distance down the incline and y -direction the distance across the incline. Initially, 25000 walkers traversed the incline in each simulation. 4. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 0 Context: #G4BEE9 Mountain trail formation and the active walker model Matching excerpt #7K9TW3: Keywords: Active walker model; Mountain trails 5. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 0 Context: #G4BEE9 Mountain trail formation and the active walker model #2F9V87 1. Introduction Matching excerpt #NDVFZG: In principle, there are a huge number of possible routes to be explored when choosing a path, and walkers could take any course between a starting point and a destination. A first approximation to the most probable path is a straight line between the initial and destination points (unless there are obstacles in the way). However, studies of trails using the active walker model have shown that the detailed patterns of paths form from a counterpoint between the desire to walk on well trodden paths, and the shortest route to be found by traveling directly between the origin and destination 7,9 . Well-trodden paths are likely to be favored by pedestrians because of reduced energy usage when compared, for example, to walking through long grass. This preference may be largely psychological, as internet based experiments in a virtual environment have also shown that 'walkers' tend to favor well-used 'paths' 4,5 . The preference to walk on regularly used paths leads to an effective interaction between past and present walkers, indicating that there is interesting physics involved in the formation of such trails. 6. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 16 Context: #G4BEE9 Mountain trail formation and the active walker model #NBFQAN 5. Results #TPVRFV 5.1. Algorithm one Matching excerpt #WJQCMK: combined effect of walkers moving in both directions are trails with zig-zag patterns that have a similar angle to the largest of the two forbidden angles. The walkers with a smaller forbidden angle round off the sharp turns in the paths that were found on the zig-zags formed when walkers are only permitted to move in a single direction. This rounding is a direct consequence of the attraction term in the active walker model and may explain the curved nature of spontaneously formed mountain trails. Moreover, the inclusion of walkers with different minimum safe angles leads to well defined trails (rather than the diffuse trails found previously). This is probably because the walkers with smaller forbidden angles have more freedom to change direction, allowing the active walker rules to function effectively. 7. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 16 Context: #G4BEE9 Mountain trail formation and the active walker model #HX4K49 6. Summary Matching excerpt #S2VCY4: We have developed an extension to the active walker model to handle the formation of trails on inclines. Our simulations are in qualitative agreement with empirical observations of mountain path formations. Such trails are characterized by a zig-zag pattern. Our extension took account of the inability of walkers to walk directly up or down very steep gradients. We have shown that some supplementary rules need to be included in the active walker model to achieve features consistent with mountain trails. Those additional rules are that (a) the consecutive steps of walkers tend to be in the same direction and that (b) there is a maximum permitted angle of motion down an incline to avoid falling and (c) there is a maximum angle of ascent for physiological reasons such as limited ankle flexibility. When rules to encourage consecutive steps are not present, we find that walkers travel in an unusual manner, only taking a single step before changing direction. We also found that the presence of walkers moving both uphill and downhill (with different forbidden angles) is important for forming well defined zig-zag paths. Walkers traveling downhill with a larger forbidden angle are constrained to form zigzags but create rather diffuse paths unless those paths are complemented by walkers traveling uphill. This happens because the walkers with more angular freedom become attracted to and reinforce the paths. 8. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 6 Context: #G4BEE9 Mountain trail formation and the active walker model #MKLE5Y 4. A model of mountain walkers #U98348 4.1. New rules for mountain walking Matching excerpt #ZHYXRP: It is our aim extend the active walker model to construct a “mountain walker model”. As we have discussed in section 3, our model should take account of the inability of walkers on steep inclines to walk directly up or down a slope if the gradient becomes too great, and avoid sudden changes of direction that can cause instability. Approximate matches 1. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 1 Context: #G4BEE9 Mountain trail formation and the active walker model #2F9V87 1. Introduction Score: 0.029 Related excerpt #JWYPGD: On inclines, there is a third influence. Walkers may ascend slopes diagonally if the gradient of the incline becomes too steep to ascend directly. Walking at an angle to the line of fastest ascent has the effect of decreasing the effective gradient of the incline, permitting travel up steeper slopes. On descent, it may not be possible to walk directly down a very steep slope without becoming unbalanced, again leading walkers to take a diagonal path. Our aim in this article is to determine if the walkers' desire to avoid steep gradients, in combination with the rules of the active walker model, can be used to simulate the zigzag paths that can be observed in mountainous regions. 2. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 13 Context: #G4BEE9 Mountain trail formation and the active walker model #NBFQAN 5. Results #TPVRFV 5.1. Algorithm one Score: 0.029 Related excerpt #EDDBRC: As the minimum safe angle is increased to 15^\circ , we note that the minimum values of \alpha which are needed to generate zig-zag patterns decreases slightly. In Fig. 5(a) where \alpha = 0.4 , we observe that a single zigzag emerges in the path. As walkers get closer to their destination, the rate at which they change their walking direction increases. Fig. 5(b) shows a similar path for \alpha = 0.45 . In Fig. 5(c) we observe that when \alpha = 0.5 walkers take larger detours away from the direct path between entry and exit, with several changes of direction along the trail. Similar results were found when \theta = 25^\circ (Fig. 6). While zigzag forms develop during the simulations, the rather diffuse paths are not satisfactory representations of mountain trails. 3. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 1 Context: #G4BEE9 Mountain trail formation and the active walker model #2F9V87 1. Introduction Score: 0.029 Related excerpt #GNDKEV: To demonstrate some examples of paths on inclines, we took photographs in the Lake District in Cumbria, England, which can be seen in Fig. 1. The upper panels Fig. 1(A1,A2) show spontaneously formed zig-zag paths on Wansfell. Two paths can be seen to the left and right hand sides of the picture, as highlighted in the figure on the right (A2). The left hand path has been augmented with rock since its formation, but still shows the characteristic zig-zag. To remove doubt on the origin of the zig-zags (for example, the stones might have been laid according to a plan) a second path can be seen to the right of the picture. The right hand path is spontaneously formed in the grass. Both have similar path angle and regularity of direction change. An example from further up the trail can be seen in panels B1 and B2. Here, there is additional wear to the side of the trail, indicating that the trail is still evolving. The paths are on inclines of around 1:8. The bottom path (C1 and C2) is on an incline of around 1:2, and was observed near Low Sweden Bridge which is close to the village of Ambleside. Trails of this type are not unique to England, and such paths can be seen in other locations, such as Smith Rock in the USA, where the bends in the paths are large enough to appear on trail maps 4. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 16 Context: #G4BEE9 Mountain trail formation and the active walker model #HX4K49 6. Summary Score: 0.027 Related excerpt #S2VCY4: We have developed an extension to the active walker model to handle the formation of trails on inclines. Our simulations are in qualitative agreement with empirical observations of mountain path formations. Such trails are characterized by a zig-zag pattern. Our extension took account of the inability of walkers to walk directly up or down very steep gradients. We have shown that some supplementary rules need to be included in the active walker model to achieve features consistent with mountain trails. Those additional rules are that (a) the consecutive steps of walkers tend to be in the same direction and that (b) there is a maximum permitted angle of motion down an incline to avoid falling and (c) there is a maximum angle of ascent for physiological reasons such as limited ankle flexibility. When rules to encourage consecutive steps are not present, we find that walkers travel in an unusual manner, only taking a single step before changing direction. We also found that the presence of walkers moving both uphill and downhill (with different forbidden angles) is important for forming well defined zig-zag paths. Walkers traveling downhill with a larger forbidden angle are constrained to form zigzags but create rather diffuse paths unless those paths are complemented by walkers traveling uphill. This happens because the walkers with more angular freedom become attracted to and reinforce the paths. 5. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 0 Context: #G4BEE9 Mountain trail formation and the active walker model Score: 0.027 Related excerpt #2QALPN: We extend the active walker model to address the formation of paths on gradients, which have been observed to have a zigzag form. Our extension includes a new rule which prohibits direct descent or ascent on steep inclines, simulating aversion to falling. Further augmentation of the model stops walkers from changing direction very rapidly as that would likely lead to a fall. The extended model predicts paths with qualitatively similar forms to the observed trails, but only if the terms suppressing sudden direction changes are included. The need to include terms into the model that stop rapid direction change when simulating mountain trails indicates that a similar rule should also be included in the standard active walker model. 6. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 1 Context: #G4BEE9 Mountain trail formation and the active walker model #2F9V87 1. Introduction Score: 0.026 Related excerpt #364B8H: The energetics of walking on an incline have been discussed by Alexander in a simple model of bipedal locomotion 1 . From energy considerations, walkers aim to change the angle of ascent from the vertical if a hill reaches a steep enough gradient. In Ref. 1, human walkers are omniscient, and are able to assess the energetic outlay for an entire route. In this way, they can assess if more energy would be expended taking a shallower and longer route, or if a quick hike up a steep route would be more favorable. We consider that it is unlikely that the information about all possible routes is available for global decisions to influence route and planning, and expect that decisions are more likely to be local. Moreover, modeling has concluded that humans choose well trodden paths in a more local manner 8 . We therefore consider that insight into mountain trail formation could be gained from active walker simulations of inclined planes. 7. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 16 Context: #G4BEE9 Mountain trail formation and the active walker model #NBFQAN 5. Results #TPVRFV 5.1. Algorithm one Score: 0.026 Related excerpt #WJQCMK: combined effect of walkers moving in both directions are trails with zig-zag patterns that have a similar angle to the largest of the two forbidden angles. The walkers with a smaller forbidden angle round off the sharp turns in the paths that were found on the zig-zags formed when walkers are only permitted to move in a single direction. This rounding is a direct consequence of the attraction term in the active walker model and may explain the curved nature of spontaneously formed mountain trails. Moreover, the inclusion of walkers with different minimum safe angles leads to well defined trails (rather than the diffuse trails found previously). This is probably because the walkers with smaller forbidden angles have more freedom to change direction, allowing the active walker rules to function effectively. 8. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 13 Context: #G4BEE9 Mountain trail formation and the active walker model #NBFQAN 5. Results #TPVRFV 5.1. Algorithm one Score: 0.024 Related excerpt #AJSDD6: We complete our simulations using algorithm one, by examining walkers that travel consecutively up and down the incline. Results of the simulations can be seen in figure 7. A slightly different weathering time of T = 1500s was used. There is no requirement that the forbidden angles are the same for hikers moving up and down the incline. In general, we expect that the different mechanisms for walking up and down inclines lead to different forbidden angles. In this set of simulations, we choose a forbidden angle of \theta_1 = 25^\circ for walkers moving up the diagram (down the gradient). Those moving down the diagram (up the gradient) have a minimum safe angle of \theta_2 = 10^\circ . We run simulations for a range of \alpha . Some zig-zag patterns can be seen for low alpha, but patterns of decent size do not appear until \alpha \gtrsim 0.45 (panel d). Again, the sizes of the bends in the path increase in size with \alpha . The ### 35. Tool result: search_text Exact matches 1. Source: Active walker model for the formation of human and animal trail systems (#B6P8L4), Dirk Helbing, Frank Schweitzer, Joachim Keltsch, Péter Molnár, p. 14 Context: #E9C9Y2 Active Walker Model for the Formation of Human and Animal Trail Systems #3WQXTG IV. HUMAN TRAIL FORMATION #FG65J6 A. Scaling to dimensionless equations Matching excerpt #C93YHS: The use of existing trails depends on the visibility, as given by Eq. (20). Assuming that the sight parameter \sigma is approximately space-independent, an additional simplification of the equations of trail formation can be reached by introducing dimensionless variables 2. Source: Active walker model for the formation of human and animal trail systems (#B6P8L4), Dirk Helbing, Frank Schweitzer, Joachim Keltsch, Péter Molnár, p. 11 Context: #E9C9Y2 Active Walker Model for the Formation of Human and Animal Trail Systems #3WQXTG IV. HUMAN TRAIL FORMATION Matching excerpt #JN4H6B: Trail formation by pedestrians has been investigated only very recently [60]. It can be interpreted as a complex interplay between pedestrian motion, human orientation, and environmental changes: On the one hand, pedestrians tend to take the shortest way to their destination. On the other hand, they avoid to walk on bumpy ground, since this is uncomfortable. Therefore, they prefer to use existing trails, but they build a new shortcut, if the relative detour would be too large. In the latter case they generate a new trail, since footprints clear some vegetation. Examples of the resulting trail systems can be found in green areas, like public parks (cf. Fig. 3). 3. Source: Active walker model for the formation of human and animal trail systems (#B6P8L4), Dirk Helbing, Frank Schweitzer, Joachim Keltsch, Péter Molnár, p. 15 Context: #E9C9Y2 Active Walker Model for the Formation of Human and Animal Trail Systems #3WQXTG IV. HUMAN TRAIL FORMATION #CAN22D B. Macroscopic formulation of trail formation Matching excerpt #RRJ2BJ: From the above ‘microscopic’ model of trail formation we will now derive the related ‘macroscopic’ equations. For this purpose we need to distinguish different subpopulations a of individuals \alpha . By a(\tau) we denote the time-dependent set of individuals \alpha who have started from the same entry point \mathbf{p}_a with the same destination \mathbf{d}_a . Therefore, the different sets a correspond to the possible (directed) combinations between existing entry points and destinations. 4. Source: Active walker model for the formation of human and animal trail systems (#B6P8L4), Dirk Helbing, Frank Schweitzer, Joachim Keltsch, Péter Molnár, p. 1 Context: #E9C9Y2 Active Walker Model for the Formation of Human and Animal Trail Systems #4PR2LM Abstract Matching excerpt #LFS7S4: Whereas pedestrians leave footprints on the ground, ants produce chemical markings for their orientation. Nevertheless, it is more important that pedestrians steer towards a certain destination, while ants usually find their food sources by chance, i.e. they reach their destination in a stochastic way. As a consequence, the typical structure of the evolving trail systems depends on the respective species. Some ant species produce a dendritic trail system, whereas pedestrians generate a minimal detour system. 5. Source: Active walker model for the formation of human and animal trail systems (#B6P8L4), Dirk Helbing, Frank Schweitzer, Joachim Keltsch, Péter Molnár, p. 3 Context: #E9C9Y2 Active Walker Model for the Formation of Human and Animal Trail Systems #TTL9MC I. INTRODUCTION Matching excerpt #T9CE9W: In Section II, the active walker model for trail formation is formulated in terms of a Langevin equation for the movement of the walkers, an equation for environmental changes, and a relation describing the orientation of the walkers with respect to existing trails. As one application of the model, Section III describes the formation of trunk trails in ant colonies, which are commonly used to exploit food sources. As a second application, in Section IV the evolution of pedestrian trail systems is modelled. Both Sections III and IV present a comparison of computational results with real trail systems, indicating a good agreement between model and empirical facts. In Section IV.A, the equations for pedestrian trail systems are scaled to dimensionless equations, in order to demonstrate that the evolving trail systems are (apart from the boundary conditions) only determined by two parameters. In Section IV.B, a macroscopic formulation of human trail formation is derived from the microscopic equations, allowing analytical investigations and an efficient calculation of the stationary solution by a self-consistent field method. Our conclusions and an outlook, which suggests an application of the model to the optimization of trail systems, are presented in Section V. 6. Source: Active walker model for the formation of human and animal trail systems (#B6P8L4), Dirk Helbing, Frank Schweitzer, Joachim Keltsch, Péter Molnár, p. 2 Context: #E9C9Y2 Active Walker Model for the Formation of Human and Animal Trail Systems #TTL9MC I. INTRODUCTION Matching excerpt #RF3SZN: In this paper, we draw the attention to the specific collective phenomenon of trail formation [33,34], which is widely spread in the world of animals and humans. Regarding their shape, duration and extension, trail systems of different animal species and humans differ, of course. However, more striking is the question, whether there is a common underlying dynamics which allows for a generalized description of the formation and evolution of trail systems. 7. Source: Active walker model for the formation of human and animal trail systems (#B6P8L4), Dirk Helbing, Frank Schweitzer, Joachim Keltsch, Péter Molnár, p. 6 Context: #E9C9Y2 Active Walker Model for the Formation of Human and Animal Trail Systems #YEVN37 II. ACTIVE WALKER MODEL OF TRAIL FORMATION Matching excerpt #TAPA6C: To complete our trail formation model, we must finally specify the orientation relation 8. Source: Active walker model for the formation of human and animal trail systems (#B6P8L4), Dirk Helbing, Frank Schweitzer, Joachim Keltsch, Péter Molnár, p. 3 Context: #E9C9Y2 Active Walker Model for the Formation of Human and Animal Trail Systems #TTL9MC I. INTRODUCTION Matching excerpt #8TZ5BY: Active walker models have proved their versatility in a variety of applications, such as formation of complex structures [36–42], pattern formation in physico-chemical systems [43–46], aggregation in biological [47,48] or urban [49] systems, and generation of directed motion [50,51]. The approach provides a quite stable and fast numerical algorithm for simulating processes involving large density gradients, and it is applicable also in cases where only small particle numbers govern the structure formation. In particular, the active walker model is applicable to processes of pattern formation which are intrinsically determined by the history of their creation, such as the formation of trail systems, discussed in this paper. Approximate matches 1. Source: Active walker model for the formation of human and animal trail systems (#B6P8L4), Dirk Helbing, Frank Schweitzer, Joachim Keltsch, Péter Molnár, p. 14 Context: #E9C9Y2 Active Walker Model for the Formation of Human and Animal Trail Systems #3WQXTG IV. HUMAN TRAIL FORMATION #FG65J6 A. Scaling to dimensionless equations Score: 0.03 Related excerpt #C93YHS: The use of existing trails depends on the visibility, as given by Eq. (20). Assuming that the sight parameter \sigma is approximately space-independent, an additional simplification of the equations of trail formation can be reached by introducing dimensionless variables 2. Source: Active walker model for the formation of human and animal trail systems (#B6P8L4), Dirk Helbing, Frank Schweitzer, Joachim Keltsch, Péter Molnár, p. 9 Context: #E9C9Y2 Active Walker Model for the Formation of Human and Animal Trail Systems #P3AR99 III. TRUNK TRAIL FORMATION BY ANTS Score: 0.029 Related excerpt #96FW7W: The perception of already existing trails will have an attractive effect \mathbf{f}_{tr}(\mathbf{r}_\alpha, \mathbf{v}_\alpha, t) to the active walkers. This has been defined by the gradients of the trail potentials, 3. Source: Active walker model for the formation of human and animal trail systems (#B6P8L4), Dirk Helbing, Frank Schweitzer, Joachim Keltsch, Péter Molnár, p. 12 Context: #E9C9Y2 Active Walker Model for the Formation of Human and Animal Trail Systems #3WQXTG IV. HUMAN TRAIL FORMATION Score: 0.028 Related excerpt #3BLFQL: However, the perception of already existing trails will have an attractive effect \mathbf{f}_{tr}(\mathbf{r}, t) on the walker, which will again be defined by the gradient of the trail potential V_{tr}(\mathbf{r}, t) , specified later on: 4. Source: Active walker model for the formation of human and animal trail systems (#B6P8L4), Dirk Helbing, Frank Schweitzer, Joachim Keltsch, Péter Molnár, p. 11 Context: #E9C9Y2 Active Walker Model for the Formation of Human and Animal Trail Systems #3WQXTG IV. HUMAN TRAIL FORMATION Score: 0.027 Related excerpt #JN4H6B: Trail formation by pedestrians has been investigated only very recently [60]. It can be interpreted as a complex interplay between pedestrian motion, human orientation, and environmental changes: On the one hand, pedestrians tend to take the shortest way to their destination. On the other hand, they avoid to walk on bumpy ground, since this is uncomfortable. Therefore, they prefer to use existing trails, but they build a new shortcut, if the relative detour would be too large. In the latter case they generate a new trail, since footprints clear some vegetation. Examples of the resulting trail systems can be found in green areas, like public parks (cf. Fig. 3). 5. Source: Active walker model for the formation of human and animal trail systems (#B6P8L4), Dirk Helbing, Frank Schweitzer, Joachim Keltsch, Péter Molnár, p. 13 Context: #E9C9Y2 Active Walker Model for the Formation of Human and Animal Trail Systems #3WQXTG IV. HUMAN TRAIL FORMATION Score: 0.027 Related excerpt #C4GYR3: Finally, we need to specify the trail potential V_{tr} for pedestrians. Obviously a trail must be recognized by the walkers and near enough in order to be used. Whereas the ground potential G(\mathbf{r}, t) describes the existence of a trail segment at position \mathbf{r} , the trail potential V_{tr}(\mathbf{r}_\alpha, t) reflects the attractiveness of a trail from the actual position \mathbf{r}_\alpha(t) of the walker. Since this will decrease with the distance \|\mathbf{r} - \mathbf{r}_\alpha\| , we have applied the relation 6. Source: Active walker model for the formation of human and animal trail systems (#B6P8L4), Dirk Helbing, Frank Schweitzer, Joachim Keltsch, Péter Molnár, p. 13 Context: #E9C9Y2 Active Walker Model for the Formation of Human and Animal Trail Systems #3WQXTG IV. HUMAN TRAIL FORMATION Score: 0.025 Related excerpt #JAAMW3: At the beginning, pedestrians take the direct ways to their respective destinations. However, after some time pedestrians begin to use already existing trails, since this is more comfortable than to clear new ways. The frequency of usage decides which trails are reinforced and which ones vanish in the course of time. If the attractiveness of the forming trails is large, the final trail system is a minimal way system (which is the shortest way system that connects all entry points and destinations). However, because of the pedestrians' dislike of taking detours the evolution of the trail system normally stops before this state is reached. In other words, a so-called minimal detour system develops if the model parameters are chosen realistically (cf. Fig. 5). The resulting trails can considerably differ from the direct ways which the pedestrians would use if these were equally comfortable. 7. Source: Active walker model for the formation of human and animal trail systems (#B6P8L4), Dirk Helbing, Frank Schweitzer, Joachim Keltsch, Péter Molnár, p. 2 Context: #E9C9Y2 Active Walker Model for the Formation of Human and Animal Trail Systems #TTL9MC I. INTRODUCTION Score: 0.024 Related excerpt #KXXUJY: As our experience tells us, trails are adapted to the requirements of their users. In the course of time, frequently used trails become more developed, making them more attractive, whereas rarely used trails vanish again. Trails with large detours become optimized by creating shortcuts. New destinations or entry points are connected to an existing trail system. These dynamical processes occur basically without any common planning or direct communication among the users. Instead, the adaptation process can be understood as a self-organization phenomenon, resulting from the non-linear feedback between the users and the trails [35]. 8. Source: Active walker model for the formation of human and animal trail systems (#B6P8L4), Dirk Helbing, Frank Schweitzer, Joachim Keltsch, Péter Molnár, p. 20 Context: #E9C9Y2 Active Walker Model for the Formation of Human and Animal Trail Systems #T6PSLK V. SUMMARY AND OUTLOOK Score: 0.024 Related excerpt #YZ2YVF: The structure of the resulting trail system can considerably vary with the species. This depends decisively on the main effect which counteracts the trail attraction. Whereas our model ants find their destinations (the food sources) by chance, pedestrians can directly orient towards their destinations, so that fluctuations are no necessary model component in this case. Thus, for certain ant species a dendritic trail system is found, the detailed form of which depends on random events, i.e. the concrete history of its evolution. Pedestrians, however, produce a minimal detour system, i.e. an optimal compromise between a direct way system and a minimal way system. ### 36. Tool result: search_text Exact matches 1. Source: Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole (#PXG56P), Christopher Alexander, p. 35 Context: #567Q7Z VII HARMONY-SEEKING RATHER THAN MERELY “EMERGENCE” #S4HQZJ A Whole-Based, Harmony-Seeking Process Which Works By Continually Strengthening Latent Centers. #WE6WWG In Detail, What Exactly Does It Mean For A System To Help The Larger System It Is Embedded In? Matching excerpt #D53VF2: Let us return to the example of St Mark's Square. At each cycle the process identifies a latent center in the larger configuration. This latent center is an area or potential center which is weak, and which – if strengthened -- would improve the coherence of the whole. The area immediately around that latent center is healed or made more whole by the injection of the repaired latent center. 2. Source: Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole (#PXG56P), Christopher Alexander, p. 32 Context: #QUCRWC VI STRUCTURE-PRESERVING TRANSFORMATIONS: HELPING A LARGER WHOLE TO FORM #FSRDPE The SP-Postulate: Always Helping A Larger Whole To Form Matching excerpt #S3MN33: In each case there is a whole, \mathcal{W} , and within the whole a latent center which is being modified, transformed, shaped, or reshaped, by a certain step. This latent center is the focus of the transformation, and the latent center sets the boundary of the geometrical and physical transformations that are then actively being undertaken. Let's call this focal latent center \mathcal{L} . 3. Source: Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole (#PXG56P), Christopher Alexander, p. 60 Context: #A6ZZPA XI CONCLUSIONS #MRNGTP Structure-Preserving Transformations #HWWGSL Models Of The Wholeness In A Given Configuration? Matching excerpt #KAKBB9: Postulate B2. The best latent center to work on, is the latent center whose improvement or repair, will (probably) do the most to increase the coherence of the whole configuration. 4. Source: Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole (#PXG56P), Christopher Alexander, p. 25 Context: #EAB6Y7 V EXAMPLES OF HARMONY-SEEKING COMPUTATIONS FROM DIFFERENT FIELDS #A8GDQA Example 11. Historical evolution of St Mark's Square – 10 cycles Matching excerpt #7NGJCE: The procedure goes like this: Find the latent center which is most salient, seems most likely to strengthen the wholeness of the larger configuration. Act locally, in such a way that this latent center gets strengthened, and so that this strengthening helps, also, to strengthen the largest whole. Repeat this cycle ten times over a period of about 1000 years, (roughly once per century), and the result was St Mark's Square as we know it today. This rule, then, explains (or generates), the ten actual cycles of construction and improvement which occurred around St. Mark's in Venice from 600 AD to 1600 AD. 5. Source: Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole (#PXG56P), Christopher Alexander, p. 12 Context: #Q94AYK IV HARMONY-SEEKING COMPUTATIONS #XE4TCT What Are The Underlying Qualities Common to Different Examples of Harmony-Seeking Steps in Different Systems? #QJLGS4 Example 4: Hayricks in a Field Matching excerpt #4Q8VNF: The people who built and placed these ricks, were, consciously or unconsciously, performing a harmony-seeking computation. There are ECHOES of shape and size between land and hayricks, ECHOES of a certain kind of curve, LOCAL SYMMETRIES in the ricks themselves, and the placing of the ricks emphasizes naturally occurring STRONG CENTERS that are generated by shelves and flattened places, bounded so that the hayricks nestle in the land, are subdued and congruent, and inside the structure which exists. The hayricks are kindly to the land, but they are placed with enormous care. They follow the wholeness. And if I were to move them slightly, to different positions, the placement and the whole then created, the ensemble, would be less profound and less harmonious. 6. Source: Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole (#PXG56P), Christopher Alexander, p. 32 Context: #QUCRWC VI STRUCTURE-PRESERVING TRANSFORMATIONS: HELPING A LARGER WHOLE TO FORM #FSRDPE The SP-Postulate: Always Helping A Larger Whole To Form #T3NUBP The SP-Transformations Of St Mark's Square, Previously Discussed. Matching excerpt #MKUQJP: Please look back at pages 24-26. Here, in each cycle, the next building to be built is occurring in \mathcal{L} , and the larger context of the whole St. Mark's area is \mathcal{W} . However, there is now a subtlety. In a particular step, we know what \mathcal{L} is, because we are looking back in time and see what the step was. But the people who actually did the step were not, at the time, so clear. They could not know what \mathcal{L} was to be, until examination of the context and the larger whole revealed it to them. And there is a further subtlety. The context \mathcal{W} is not something so vague and general as the whole St. Mark's area. It is, rather, a particular area within St. Mark's square, where a latent center has been identified as being in need of improvement, or presenting itself for elaboration and strengthening. This latent center, which plays a crucial role in the structure-preserving transformations, we are calling \mathcal{L} , and the detailed effects are created (as discussed in my text) by the fifteen transformations acting together. So it is actually the immediate local context of \mathcal{L} that then gives rise to the step that transforms \mathcal{L} . 7. Source: Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole (#PXG56P), Christopher Alexander, p. 11 Context: #Q94AYK IV HARMONY-SEEKING COMPUTATIONS #XE4TCT What Are The Underlying Qualities Common to Different Examples of Harmony-Seeking Steps in Different Systems? #QJLGS4 Example 4: Hayricks in a Field Matching excerpt #U5JLND: In this photograph above, even simpler than a well-placed farmhouse, two modest hayricks are placed in a rolling field. The placement is done in such a way as to complement the land, to enrich the land, it is humble, self effacing, there is no ego visible, only concern that the land and its harmony should be enlarged. 8. Source: Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole (#PXG56P), Christopher Alexander, p. 36 Context: #567Q7Z VII HARMONY-SEEKING RATHER THAN MERELY “EMERGENCE” #S4HQZJ A Whole-Based, Harmony-Seeking Process Which Works By Continually Strengthening Latent Centers. #WE6WWG In Detail, What Exactly Does It Mean For A System To Help The Larger System It Is Embedded In? Matching excerpt #V7GAR8: Abstractly we may express this concept through the following diagram. The red area is a latent center, a weak center which has the capacity to heal the blue area beyond it: and it is able to do so by creation of the smaller white centers -- they are built to create coherence in the red center. However, the key point is that the healing will not take place, unless the red center then also helps to heal the larger blue center beyond it. Approximate matches 1. Source: Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole (#PXG56P), Christopher Alexander, p. 33 Context: #QUCRWC VI STRUCTURE-PRESERVING TRANSFORMATIONS: HELPING A LARGER WHOLE TO FORM #FSRDPE The SP-Postulate: Always Helping A Larger Whole To Form #T3NUBP The SP-Transformations Of St Mark's Square, Previously Discussed. Score: 0.029 Related excerpt #RRPPUH: Here, for example, the red ellipse, is \mathcal{L} , the latent center formed by the three buildings around it. To confirm and strengthen \mathcal{L} , the blue building mass is built, thus forming a stronger rectangular space, by enclosure, and establishing continuity with the buildings on the right of the latent configuration. 2. Source: Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole (#PXG56P), Christopher Alexander, p. 55 Context: #8MPFPH X ECOLOGY OF THE ORDINARY #TFM623 Example 20. The Ecology Of The Ordinary Score: 0.028 Related excerpt #ANS7MY: Cycle 2. latent centers in the site: the bike path, along the south side, Warwick avenue along the west, and Lowell Street in the south east corner. → The computation then identifies a connection and pedestrian precinct generates a curved line, more or less a median through the triangle of the site, but curving slightly and leading to stairs at the east end where there is a 20 foot rise to Lowell street. 3. Source: Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole (#PXG56P), Christopher Alexander, p. 55 Context: #8MPFPH X ECOLOGY OF THE ORDINARY #TFM623 Example 20. The Ecology Of The Ordinary Score: 0.028 Related excerpt #4B4QNJ: Cycle 1. The process starts with a triangular brown-field site in Somerville, 5.5 acres in area, between a railroad line, a bike path, and an existing neighborhood → The computation then identifies latent centers in the site: the bike path, along the south side, Warwick avenue along the west, and Lowell Street in the south east corner. 4. Source: Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole (#PXG56P), Christopher Alexander, p. 19 Context: #EAB6Y7 V EXAMPLES OF HARMONY-SEEKING COMPUTATIONS FROM DIFFERENT FIELDS #334A7K Example 8. Two possible plans for a five-story apartment building in Tokyo Score: 0.026 Related excerpt #SAHSN3: The fact that the right hand plan (as built) complements and intensifies the wholeness of the site, is intuitively clear -- just looking at the ground plan alone. However, to emphasize what this really means, and to illustrate the deeper structures that are involved, I will describe some specific features of the global structure which existed in that place, and which were then solidified and complemented by the building that was placed there. Here are some of the structural features of the original site: The center formed by the Y-configuration of the fork; The curving nature of the two branches; The space between the forks, and its specific V-shape; The southern spot hit by the sun. 5. Source: Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole (#PXG56P), Christopher Alexander, p. 19 Context: #EAB6Y7 V EXAMPLES OF HARMONY-SEEKING COMPUTATIONS FROM DIFFERENT FIELDS #334A7K Example 8. Two possible plans for a five-story apartment building in Tokyo Score: 0.024 Related excerpt #STQZME: The plan for a new building, when injected into this site, does the following things which help to accentuate and strengthen these structural features of the place: 6. Source: Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole (#PXG56P), Christopher Alexander, p. 32 Context: #QUCRWC VI STRUCTURE-PRESERVING TRANSFORMATIONS: HELPING A LARGER WHOLE TO FORM #FSRDPE The SP-Postulate: Always Helping A Larger Whole To Form Score: 0.016 Related excerpt #S3MN33: In each case there is a whole, \mathcal{W} , and within the whole a latent center which is being modified, transformed, shaped, or reshaped, by a certain step. This latent center is the focus of the transformation, and the latent center sets the boundary of the geometrical and physical transformations that are then actively being undertaken. Let's call this focal latent center \mathcal{L} . 7. Source: Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole (#PXG56P), Christopher Alexander, p. 12 Context: #Q94AYK IV HARMONY-SEEKING COMPUTATIONS #XE4TCT What Are The Underlying Qualities Common to Different Examples of Harmony-Seeking Steps in Different Systems? #QJLGS4 Example 4: Hayricks in a Field Score: 0.015 Related excerpt #WMWA8S: Below, I show a sketch, which in very broad-brush terms, approximates the wholeness present in that place. The wholeness includes the sinuous curves, the kinds of shapes which are present in the field, the dips and hollows, the surrounding trees, the trees along the ridge, and the fallen down enclosing fence below. 8. Source: Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole (#PXG56P), Christopher Alexander, p. 35 Context: #567Q7Z VII HARMONY-SEEKING RATHER THAN MERELY “EMERGENCE” #S4HQZJ A Whole-Based, Harmony-Seeking Process Which Works By Continually Strengthening Latent Centers. #WE6WWG In Detail, What Exactly Does It Mean For A System To Help The Larger System It Is Embedded In? Score: 0.015 Related excerpt #D53VF2: Let us return to the example of St Mark's Square. At each cycle the process identifies a latent center in the larger configuration. This latent center is an area or potential center which is weak, and which – if strengthened -- would improve the coherence of the whole. The area immediately around that latent center is healed or made more whole by the injection of the repaired latent center. ### 37. Tool result: search_text Exact matches 1. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 4 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #T6FSBF 5 River Classification Matching excerpt #U7AJ7K: The river graph divides the domain \Omega into nonoverlapping cells that allow us to build a set of watersheds and to construct a dual graph that stores crests (Section 5.1). The water flow is extracted from the river graphs, and each water-course is labeled with respect to the Rosgen classification (Section 5.2). 2. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 2 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #3G9YBV 3 Algorithm Overview Matching excerpt #KAMGFF: Once the river network is defined, the algorithm extracts the graph topology and geometry that is used for the terrain generation in the next step. We decompose the terrain into a set of patches by computing the Voronoi cells corresponding to the nodes of the river graph. The algorithm then generates the hierarchical watershed structure by traversing the geometric graph and gathering information of the Voronoi cells. This step enables us to compute the area of the watersheds and subwatersheds and to evaluate the flow of the water-courses at every node in the graph. 3. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 4 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #WWSSDJ 4 River Network Generation #DBN56J 4.2 River Network Generation #VTGN6K 4.2.2 Node Expansion Matching excerpt #5VRAH5: The effect of varying parameters on the generated river network is depicted in Fig. 8. The parameter set ( P_c = 0.2, P_s = 0.7, P_a = 0.1 ) produced highly curved watersheds (left). There are only a few main streams, but many ( > 75\% ) small streams with a Horton-Strahler numbers equal to 1 (Fig. 8 left). In contrast, the parameter set ( P_c = 0.2, P_s = 0.1, P_a = 0.7 ) produced drainage networks with watersheds of comparable sizes (Fig. 8 right). In the second case, the main rivers are longer because their priority indices were statistically kept longer in the queue during the graph generation, and the watersheds are structured around this main river. 4. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 0 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #F9QBNZ Abstract Matching excerpt #7CSK9U: We present a framework that allows quick and intuitive modeling of terrains using concepts inspired by hydrology. The terrain is generated from a simple initial sketch, and its generation is controlled by a few parameters. Our terrain representation is both analytic and continuous and can be rendered by using varying levels of detail. The terrain data are stored in a novel data structure: a construction tree whose internal nodes define a combination of operations, and whose leaves represent terrain features. The framework uses rivers as modeling elements, and it first creates a hierarchical drainage network that is represented as a geometric graph over a given input domain. The network is then analyzed to construct watersheds and to characterize the different types and trajectories of rivers. The terrain is finally generated by combining procedural terrain and river patches with blending and carving operators. 5. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 5 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #T6FSBF 5 River Classification #TRR58W 5.1 Segmentation and Elevation of Crests Matching excerpt #WL3SCW: Watersheds are associated with each water outlet s of a cell V_j and are defined as the set of upstream connected cells V_k \in V . 6. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 1 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #CZMG8P 2 Related Work Matching excerpt #898MUB: The above-mentioned algorithms provide river networks and watersheds that are not coherent, and the river paths are created with stochastic techniques that do not conform to the characteristics of rivers as observed in geomorphology. Moreover, these algorithms allow a user control limited to setting a few abstract parameters. 7. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 6 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #UAYDMD 6 Terrain Model Generation #FWT7FF 6.2 Terrain Primitives Generation Matching excerpt #Q42MDN: The shape of the terrain is modulated by a random noise. The noise attributes (amplitude, frequency) associated with the primitives are calculated with respect to the distance to the river d_a and the elevation differences between the river a_z and crests b_z . This modulation produces more roughness for the mountains than for the valleys. Using noise can produce small local minima, but they remain negligible in the context of large-scale hydrology. 8. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 2 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #WWSSDJ 4 River Network Generation #DBN56J 4.2 River Network Generation Matching excerpt #S2XAKJ: The graph \mathcal{G} is also updated to take into account the new nodes \{N\} . If any new node is not compatible with the previously created nodes, it is removed from the graph. Approximate matches 1. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 4 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #T6FSBF 5 River Classification Score: 0.03 Related excerpt #U7AJ7K: The river graph divides the domain \Omega into nonoverlapping cells that allow us to build a set of watersheds and to construct a dual graph that stores crests (Section 5.1). The water flow is extracted from the river graphs, and each water-course is labeled with respect to the Rosgen classification (Section 5.2). 2. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 5 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #T6FSBF 5 River Classification #TRR58W 5.1 Segmentation and Elevation of Crests Score: 0.016 Related excerpt #XA9BE4: Ridges. The computation of ridge elevation is important to guarantee a coherent flow. Each Voronoi cell has two types of edges: those that do not intersect the river graph and that define ridge lines, and those that carry a river entry e_k or outlet s . 3. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 1 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #3G9YBV 3 Algorithm Overview Score: 0.016 Related excerpt #EL3FAM: From this input, the system first generates the drainage river network. The network is created inside the domain formed by the contour and is represented as a geometric graph. The graph is generated by a progressive growth from the seeds placed on the domain contour and the input rivers already sketched by the user. The expansion algorithm is inspired by Horton-Strahler's ordering [Horton 1945], which quantifies the complexity of a tree structure. 4. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 2 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #WWSSDJ 4 River Network Generation Score: 0.015 Related excerpt #YYHJW8: Notations. Let \Omega denote the input domain and \Gamma its contour (defined as a 2-D polyline). The algorithm creates a coverage of \Omega by a set of trees denoted as \mathcal{G} . A tree is defined by its set of nodes \mathcal{N}_j and a set of edges \mathcal{E}_j . Every node N_i = (\mathbf{p}_i, s_i, \rho_i, \phi_i) has the position \mathbf{p}_i , the priority index s_i , the river type \rho_i according to Rosgen classification [Rosgen 1994], and the flow \phi_i . Every edge has a constant length e that is defined by the user. We will refer to the set of all nodes and edges \mathcal{N} = \cup_j \mathcal{N}_j and \mathcal{E} = \cup_j \mathcal{E}_j , respectively. 5. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 4 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #T6FSBF 5 River Classification #TRR58W 5.1 Segmentation and Elevation of Crests Score: 0.015 Related excerpt #Q4MUQB: The domain \Omega is decomposed into a set of cells \mathcal{V} = \{V_i\} computed from the Voronoi diagram of node locations \mathbf{p}_i . Some Voronoi cell boundaries correspond to the ridges that define the edges of the watersheds. Each cell vertex has an elevation assigned, and each cell V is represented as a polygon composed of crest points \mathbf{q}_i . Water entries are denoted \mathbf{e}_0, \dots, \mathbf{e}_{n-1} , and the water outlet is denoted s (see Fig. 10). 6. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 2 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #WWSSDJ 4 River Network Generation Score: 0.015 Related excerpt #QRZTYS: The river network covering the input domain is a geometric graph that is generated in two steps. First, the seed nodes are distributed on the boundary of the input contour and at the initial user-defined rivers (Section 4.1). The rivers are then generated by a progressive growth inside the domain (Section 4.2). 7. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 2 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #3G9YBV 3 Algorithm Overview Score: 0.015 Related excerpt #KAMGFF: Once the river network is defined, the algorithm extracts the graph topology and geometry that is used for the terrain generation in the next step. We decompose the terrain into a set of patches by computing the Voronoi cells corresponding to the nodes of the river graph. The algorithm then generates the hierarchical watershed structure by traversing the geometric graph and gathering information of the Voronoi cells. This step enables us to compute the area of the watersheds and subwatersheds and to evaluate the flow of the water-courses at every node in the graph. 8. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 2 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #WWSSDJ 4 River Network Generation #YQ7VH4 4.1 Initial Candidate Nodes Score: 0.014 Related excerpt #WJF6JY: The first step consists of creating the set of initial candidate nodes that will be expanded later. The candidate nodes are located at the river mouths on the contour \Gamma . Alternatively, if the user specified input sketches representing some parts of the rivers, the initial nodes are placed on their extremities and on regularly jittered sample locations along their paths as shown in Fig. 3. Each node has been assigned a priority index that defines its importance. Both the position and the priority index define the overall appearance of the resulting river network hierarchy. ### 38. Assistant tool calls #### Tool call: `write_note` ```json { "block_ids": [ "QPEZUU", "N7XTK3", "RBPN5L", "GDV37F", "F2VBJL", "JAHVNN", "U7AJ7K", "WL3SCW", "A6G5PJ", "BLF82B", "GHEACQ", "25Z8H8", "MZP8G3", "2QALPN" ], "text": "Peatfield’s evidence supports a precise version of the “dual of basins” intuition. Hydrologically, a watershed collects terrain cells toward a common outlet: watersheds are upstream-connected cells associated with an outlet (#WL3SCW), and FastFlow defines a basin by a shared stream-tree root (#A6G5PJ). The terrain-generation paper explicitly constructs a dual graph on the crests between watershed cells (#U7AJ7K). A sanctuary can be modeled as a culturally selected point on or just inside that crest system: not necessarily the highest summit, but the point that most directly overlooks—and is visible from—a particular inhabited plain (#QPEZUU, #N7XTK3). Its relation reverses downstream collection: settlement paths, attention, and offerings converge uphill, while sight, fire, and divine protection project back down (#RBPN5L). The local service regions suggested by Peatfield (#F2VBJL) are therefore analogous to catchments, while intervisible sanctuaries form a second, crest-level network (#GDV37F, #JAHVNN). Formally, assigning each inhabited cell to one shrine would induce a partition analogous to the inverse-image partition of a function (#BLF82B), but raw viewsheds overlap, so without a unique service assignment the better object is a cover, bipartite graph, or weighted field rather than a strict partition. Alexander’s language adds a complementary reading: each shrine is a strong center supported by its surrounding settlements and landscape (#GHEACQ), while dominant sanctuaries create a recursive hierarchy of centers (#25Z8H8). Movement closes the loop: visibility affects trail attraction (#MZP8G3), and slope-constrained walkers generate mountain paths (#2QALPN). This suggests a generative model coupling hydrological basin labels, one-sided viewsheds, accessibility/trail evolution, and shrine-to-shrine intervisibility.", "title": "Peak sanctuaries as an inhabited dual of drainage basins" } ``` ### 39. Tool result: write_note NOTE SAVED #79XGSQ IRI: https://m.sheaf.less.rest/79XGSQ ### 40. Assistant This is **not random at all**—your ramble nearly reconstructs Peatfield’s central topographic argument. ### The uncanny match You said the shrine might be **near a summit but displaced onto one side of the ridge**, so that it belongs to one catchment rather than “seeing the whole world.” Peatfield’s strongest examples say almost exactly this: - At Petsopha, the sanctuary occupies the **lowest of three peaks**, because that peak most directly overlooks Palaikastro. - At Etia, it is on an isolated butte **100 m below** the massif’s summit, positioned to see the Armeni and Chandra plains. - At Zou, it lies below the true summit on the particular edge from which the Sitia plain becomes visible—and from the plain, that point *appears* to be the summit (#QPEZUU). Peatfield’s formulation is that the shrine must be seen by the region it serves and must also “see” that region (#N7XTK3). The bonfire and votive evidence makes that reciprocity meaningful: inhabitants look upward toward the fire, while the deity looks downward toward the people, animals, and bodies placed under its protection (#RBPN5L). So the relevant criterion is not globally maximal elevation. It is something closer to **regional visual ownership**. ### The dual-of-basins idea The hydrology material gives your intuition a remarkably clean formal counterpart. A hydrological basin consists of cells sharing a stream tree or terminal root (#A6G5PJ); watersheds are upstream-connected cells associated with a common outlet (#WL3SCW). The terrain-generation paper then explicitly constructs a **dual graph on the crests** separating those watersheds (#U7AJ7K). A sanctuary can be understood as a culturally selected point on—or slightly inside—this crest structure: | Fluvial system | Ritual/visual dual | |---|---| | Water moves downhill | Worshippers and offerings move uphill | | Basin converges on an outlet | Community converges on a shrine | | Outlet receives flow | Shrine receives paths, attention, and offerings | | Watershed boundary separates drainage | Ridge controls visual and communal affiliation | | Discharge propagates downstream | Fire, visibility, and protection project downward | In symbols, hydrology gives a map $$ d:T\rightarrow O, $$ assigning every terrain cell to an outlet. Each catchment is an inverse-image fiber $d^{-1}(o)$. Your analogous ritual map would be $$ s:H\rightarrow P, $$ assigning inhabited locations $H$ to serving shrines $P$; each shrine’s “ritual catchment” is $s^{-1}(p)$. This is exactly the function-to-partition construction discussed in the partition-logic paper (#BLF82B). The important qualification is that **visibility itself is not generally a partition**. A settlement may see several shrines, and a shrine may see several valleys. Raw viewsheds therefore form an overlapping cover or bipartite visibility graph. They become basin-like only when ecological proximity, walking cost, settlement affiliation, or ritual practice selects one shrine as primary. Peatfield ultimately favors such strongly local service relations: shrine elaboration tracks the prosperity of its nearby community more closely than its rank in an island-wide hierarchy (#F2VBJL). ### The second network above the local basins The paper then adds another layer that your analogy makes especially legible. Local shrine-regions may be basin-like, but the shrines themselves form a **crest-level intervisibility network**. Traostalos can see at least six other sanctuaries, while Zou and Iouktas act as regional visual foci (#GDV37F). Peatfield proposes that simultaneous bonfires could have joined otherwise local shrines into a network of sacred beacons (#JAHVNN). So there are really two coupled graphs: 1. **Settlement $\rightarrow$ shrine:** local, uphill, catchment-like affiliation. 2. **Shrine $\leftrightarrow$ shrine:** ridge-level intervisibility and regional integration. That resembles the corpus’s distinction between a drainage graph in the basin interiors and its crest-based dual graph. ### Connections to the rest of the workspace - **Trail formation:** visibility affects which existing trails attract walkers (#MZP8G3), while slope constraints and repeated uphill/downhill travel generate reinforced zigzag mountain paths (#2QALPN). Shrine location and pilgrimage route could therefore co-evolve rather than being solved independently. - **Alexanderian centers:** a shrine is a strong center supported by its valley, settlements, paths, pastures, profile, and lines of sight—the surrounding centers that make *this particular point* stronger than the geometrically highest point (#GHEACQ). The larger sanctuaries then produce a recursive hierarchy of many local centers and a few regional ones (#25Z8H8). - **Harmony-seeking placement:** Alexander’s hayricks “nestle” into shelves and flattened places, strengthening latent centers already present in the land (#4Q8VNF). Peatfield’s off-summit shrines are an archaeological example of the same principle: placement discovers and intensifies a relational center rather than imposing the most obvious geometric extremum. A useful procedural formulation would therefore choose shrine sites by combining **one-sided viewshed coverage, apparent prominence from below, walking accessibility, pasture proximity, basin affiliation, and inter-shrine visibility**—not by maximizing elevation alone. I saved this cross-corpus connection as research note #79XGSQ. ### 41. User the crest network is very profound i think... i mean like in the return of the king hehe ### 42. Assistant Exactly—**the lighting of the beacons of Gondor** is almost a perfect dramatization of Peatfield’s proposed sacred network. Each beacon has two simultaneous orientations: - **Downward/inward:** it belongs to a particular inhabited valley or polity, which approaches it and reads its signal. - **Across/outward:** it participates in a chain of mutually visible high places, transmitting a signal over distances no valley settlement could span alone. That makes the crest network more than the boundary between basins. It is a **second geography laid over the drainage geography**: - valleys partition and gather; - ridges distinguish yet connect; - rivers carry matter downward; - beacons carry information laterally; - paths carry people upward. Peatfield’s striking suggestion is that Minoan sacrificial fires might have united local sanctuary communities on a single festival night (#JAHVNN). Tolkien gives the same structure narrative form: isolated mountain centers suddenly become one system as each fire awakens the next. It also explains why the shrine must not simply “see the whole world.” Its power comes from being a **hinge between scales**: legible from its own valley, but connected across the ridge network to larger centers. That is very Alexanderian—many local centers remaining genuinely local while helping constitute a larger whole (#GHEACQ, #7U7YF9). In graph terms, the valleys give you something tree-like and convergent; the crests give you a lateral communication graph. The shrine is where those two topologies touch.