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work has demonstrated consistent trends in preference for and complexity estimates of fractal patterns. However, limited information has been gathered on the impact of other visual judgments. Here we examine the aesthetic and perceptual experience of fractal âglobal-forestâ designs already installed in humanmade spaces and demonstrate how fractal pattern components are associated with positive psychological experiences that can be utilized to promote occupant wellbeing. These designs are composite fractal patterns consisting of individual fractal âtree-seedsâ which combine to create a âglobal fractal forest.â The local âtree-seedâ patterns, global configuration of tree-seed locations, and overall resulting âglobal-forestâ patterns have fractal qualities. These designs span multiple mediums yet are all intended to lower occupant stress without detracting from the function and overall design of the space. In this series of studies, we first establish divergent relationships between various visual attributes, with pattern complexity, preference, and engagement ratings increasing with fractal complexity compared to ratings of refreshment and relaxation which stay the same or decrease with complexity. Subsequently, we determine that the local constituent fractal (âtree-seedâ) patterns contribute to the perception of the overall fractal design, and address how to balance aesthetic and psychological effects (such as individual experiences of perceived engagement and relaxation) in fractal design installations. This set of studies demonstrates that fractal preference is driven by a balance between increased arousal (desire for engagement and complexity) and decreased tension (desire for relaxation or refreshment). Installations of these composite mid-high complexity âglobal-forestâ patterns consisting of âtree-seedâ components balance these contrasting needs, and can serve as a practical implementation of biophilic patterns in human-made environments to promote occupant wellbeing.
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422:, there are events and patterns in nature that never exactly repeat because extremely small differences in starting conditions can lead to widely differing outcomes. The patterns in nature tend to be static due to dissipation on the emergence process, but when there is interplay between injection of energy and dissipation there can arise a complex dynamic. Many natural patterns are shaped by this complexity, including
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A recent study from
Aesthetics and Psychological Effects of Fractal Based Design suggested that fractal patterns possess self-similar components that repeat at varying size scales. The perceptual experience of human-made environments can be impacted with inclusion of these natural patterns. Previous
556:
form in materials to relieve stress: with 120 degree joints in elastic materials, but at 90 degrees in inelastic materials. Thus the pattern of cracks indicates whether the material is elastic or not. Cracking patterns are widespread in nature, for example in rocks, mud, tree bark and the glazes of
1842:
The author attributes Eugene Wigner for the claim for the "unreasonable effectiveness of mathematics," a partial quote which continues "he miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor
852:, discussed in his 1991 paper of the same name, provides an ontological framework aiming to discern the reality of patterns beyond mere human interpretation, by examining their predictive utility and the efficiency they provide in compressing information. For example,
877:
is found in fractals. Examples of natural fractals are coast lines and tree shapes, which repeat their shape regardless of what magnification you view at. While self-similar patterns can appear indefinitely complex, the rules needed to describe or produce their
856:
is a real pattern because it allows us to predict the movements of a bodies such as the earth around the sun, and it compresses all the information about all the particles in the sun and the earth that allows us to make those predictions.
1936:
Robles, Kelly E.; Roberts, Michelle; Viengkham, Catherine; Smith, Julian H.; Rowland, Conor; Moslehi, Saba; Stadlober, Sabrina; Lesjak, Anastasija; Lesjak, Martin; Taylor, Richard P.; Spehar, Branka; Sereno, Margaret E. (2021).
753:
are repeated in various ways to form patterns. Most simply, structures such as windows can be repeated horizontally and vertically (see leading picture). Architects can use and repeat decorative and structural elements such as
728:
211:
structure; indeed, mathematics can be seen as the search for regularities, and the output of any function is a mathematical pattern. Similarly in the sciences, theories explain and predict regularities in the world.
670:
In visual art, pattern consists in regularity which in some way "organizes surfaces or structures in a consistent, regular manner." At its simplest, a pattern in art may be a geometric or other repeating shape in a
1815:
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is a source of ubiquitous scientific patterns or patterns of observation. The sun rising and falling pattern each day results from the rotation of the earth while in orbit around the sun. Likewise, the
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path through the sky is due to its orbit of the earth. These examples, while perhaps trivial, are examples of the "unreasonable effectiveness of mathematics" which obtain due to the
91:
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practice with the purposeful drawing of repetitive patterns or artistic tangles) has been copyrighted by Rick
Roberts and Maria Thomas. The process, using patterns such as
478:
that create the chaotic patterns of the sea. As they pass over sand, such waves create patterns of ripples; similarly, as the wind passes over sand, it creates patterns of
1402:
3235:
618:
and other scientists, described a mechanism that spontaneously creates spotted or striped patterns, for example in the skin of mammals or the plumage of birds: a
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In the broadest sense, any regularity that can be explained by a scientific theory is a pattern. As in mathematics, science can be taught as a set of patterns.
42:
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system involving two counter-acting chemical mechanisms, one that activates and one that inhibits a development, such as of dark pigment in the skin. These
3230:
223:, "pattern" is used for an ornamental design that is manufactured, perhaps for many different shapes of object. In art and architecture, decorations or
1622:
1162:
Clerc, Marcel G.; Gonzålez-Cortés, Gregorio; Odent, Vincent; Wilson, Mario (29 June 2016). "Optical textures: characterizing spatiotemporal chaos".
159:
may be observable only by analysis. Direct observation in practice means seeing visual patterns, which are widespread in nature and in art. Visual
766:. Repetitions need not be identical; for example, temples in South India have a roughly pyramidal form, where elements of the pattern repeat in a
901:, mathematicians attempt to describe the world in terms of patterns. The goal is to lay out the world in a more computationally friendly manner.
1788:
1253:
691:, but a pattern need not necessarily repeat exactly as long as it provides some form or organizing "skeleton" in the artwork. In mathematics, a
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of numbers that may be modeled by a mathematical function can be considered a pattern. Mathematics can be taught as a collection of patterns.
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are mathematical patterns that are scale invariant. This means that the shape of the pattern does not depend on how closely you look at it.
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333:: each flake is unique, its structure recording the varying conditions during its crystallisation similarly on each of its six arms.
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719:, be used as a therapeutic device to help to relieve stress, anxiety and depressive symptoms in children, adults and older adults.
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is the tiling of a plane using one or more geometric shapes (which mathematicians call tiles), with no overlaps and no gaps.
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2715:
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1667:"Effects of the original zentangle method on older adults with depressive symptoms a randomized waitlist-controlled trial"
806:
is sometimes called the "Science of
Pattern", in the sense of rules that can be applied wherever needed. For example, any
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of many plants, both of leaves spiralling around stems, and in the multiple spirals found in flowerheads such as the
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Resnik, Michael D. (November 1981). "Mathematics as a
Science of Patterns: Ontology and Reference".
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Crutchfield, James P; Farmer, J Doyne; Packard, Norman H; Shaw, Robert S (December 1986). "Chaos".
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may be combined and repeated to form patterns designed to have a chosen effect on the viewer.
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1567:"Effects of Zentangle art workplace health promotion activities on rural healthcare workers"
1419:
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Scroggie, A.J; Firth, W.J; McDonald, G.S; Tlidi, M; Lefever, R; Lugiato, L.A (August 1994).
1261:
Lecture Notes in
Incompressible Fluid Dynamics: Phenomenology, Concepts and Analytical Tools
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Some mathematical rule-patterns can be visualised, and among these are those that explain
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Symmetry is widespread in living things. Animals that move usually have bilateral or
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slowly drift, the animals' appearance changing imperceptibly as Turing predicted.
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ideas. As such, the elements of a pattern repeat in a predictable manner. A
1982:
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511:, which require films to be smooth and continuous, and to have a constant
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including the mathematics of symmetry, waves, meanders, and fractals.
703:
The materials and teaching tools of
ZentangleÂź (a blend of meditative
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515:. Foam and bubble patterns occur widely in nature, for example in
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CBMS Conference
Proceedings on Water Waves: Theory and Experiment
372:
Spiral patterns are found in the body plans of animals including
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2438:
1618:"The effects of Zentangles on affective well-being among adults"
1347:. Howard University, USA, 13â18 May 2008. World Scientific Publ.
887:
818:
777:
Patterns in
Architecture: the columns of Zeus's temple in Athens
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may directly observe patterns. Conversely, abstract patterns in
2174:
1739:
Heaven's
Fractal Net: Retrieving Lost Visions in the Humanities
731:
Patterns in architecture: the
Virupaksha temple at Hampi has a
2170:
1939:"Aesthetics and Psychological Effects of Fractal Based Design"
704:
3055:
Concluding Unscientific Postscript to Philosophical Fragments
2135:
Mathematics in Nature: Modeling Patterns in the Natural World
2005:
Mathematics in Nature: Modeling Patterns in the Natural World
1400:
Turing, A. M. (1952). "The Chemical Basis of Morphogenesis".
241:
Nature provides examples of many kinds of pattern, including
1451:. Springer Science & Business Media. pp. 436â450.
121:
is a regularity in the world, in human-made design, or in
1541:
1665:
Chan, Henri Chun-Yiu; Lo, Herman Hay-Ming (2023-05-05).
2995:
A Treatise Concerning the Principles of Human Knowledge
1381:, Scientific American, vol. 235, pp. 82â93, July 1976.
298:
as this favours movement. Plants often have radial or
466:
propagate through a medium â air or water, making it
2055:
What Shape is a Snowflake? Magical Numbers in Nature
3097:
2896:
2636:
2364:
2208:
2014:
The Self-made Tapestry: Pattern Formation in Nature
1263:. Syracuse, NY: Syracuse University. Archived from
735:-like structure where the parts resemble the whole.
455:
Dune ripples and boards form a symmetrical pattern.
430:in rivers. or nonlinear interaction of the system
2093:A Pattern Language: Towns, Buildings, Construction
1513:
715:clusters, or shaded or coloured in, can, like the
1403:Philosophical Transactions of the Royal Society B
1254:"Flow Separation and Secondary Flow: Section 9.1"
462:are disturbances that carry energy as they move.
2154:Gamma, E., Helm, R., Johnson, R., Vlissides, J.
1901:Pattern Theory: From Representation to Inference
1789:"MATH 012 Patterns in Mathematics - spring 2012"
167:, rarely exactly repeating, and often involve
27:Regularity in sensory qualia or abstract ideas
2186:
8:
1917:. Harvard Graduate School of Education. 2008
1283:"Pattern formation in a passive Kerr cavity"
345:, but cannot have fivefold symmetry (unlike
1379:The geometry of soap films and soap bubbles
2193:
2179:
2171:
1512:GrĂŒnbaum, Branko; Shephard, G. C. (1987).
426:, other effects of turbulent flow such as
396:Chaos, turbulence, meanders and complexity
1972:
1954:
1698:
1584:
1175:
2165:Pattern Recognition and Machine Learning
1899:Grenander, Ulf; Miller, Michael (2007).
1623:American Journal of Occupational Therapy
996:
614:, and later the mathematical biologist
337:have a highly specific set of possible
1852:Dennett, D. C. (1991). Real Patterns.
1741:. Indiana University Press. p. 2.
829:function to describe the most general
3236:Concepts in the philosophy of science
3025:Prolegomena to Any Future Metaphysics
1089:"Growth in Plants: A Study in Number"
1045:. London: Weidenfeld & Nicolson.
796:Fractal model of a fern illustrating
7:
3125:Interpretations of quantum mechanics
3045:The World as Will and Representation
2142:Mathematics as a Science of Patterns
1034:
1032:
1030:
1028:
1026:
306:. Fivefold symmetry is found in the
245:, trees and other structures with a
3231:Concepts in the philosophy of mind
1487:"Art, Design, and Visual Thinking"
25:
1445:Murray, James D. (9 March 2013).
1149:10.1038/scientificamerican1286-46
3188:
3178:
3177:
2072:. 1942 2nd ed. (1st ed., 1917).
1737:Jackson, William Joseph (2004).
584:
569:
414:predicts that while the laws of
219:, from ceramics and textiles to
101:
90:
81:
70:
61:
50:
41:
2975:Meditations on First Philosophy
1390:Stevens, Peter. 1974. Page 207.
129:is a kind of pattern formed of
1875:The fractal geometry of nature
1616:Chung, S.K. (September 2022).
1338:"Practical wind wave modeling"
1290:Chaos, Solitons & Fractals
1004:Garai, Achraf (3 March 2022).
770:-like way at different sizes.
388:and fruit structures like the
207:. Patterns have an underlying
136:and typically repeated like a
1:
3160:Philosophy of space and time
2121:V&A Pattern: The Fifties
2107:The Patterns of Architecture
1915:"Causal Patterns in Science"
1832:10.1126/science.240.4852.611
1485:Jirousek, Charlotte (1995).
1310:10.1016/0960-0779(94)90084-1
745:Mathematics and architecture
640:Mathematics and architecture
557:old paintings and ceramics.
111:Various examples of patterns
3035:The Phenomenology of Spirit
2123:. V&A Publishing, 2009.
1520:. New York: W. H. Freeman.
1006:"What are design patterns?"
653:Elaborate ceramic tiles at
171:. Natural patterns include
3257:
2128:In science and mathematics
1903:. Oxford University Press.
1726:. McGraw Hill. p. 99.
1683:10.1007/s12144-023-04536-x
1586:10.1016/j.puhe.2021.05.033
1343:. In Mahmood, M.F. (ed.).
1042:What shape is a snowflake?
780:
738:
659:
633:
604:
234:
29:
3173:
2059:Weidenfeld & Nicolson
1956:10.3389/fpsyg.2021.699962
1854:The Journal of Philosophy
1816:"The Science of Patterns"
1814:Steen, Lynn (June 1988).
1787:Bayne, Richard E (2012).
1371:Frederick J. Almgren, Jr.
1252:Lewalle, Jacques (2006).
1102:: 335â354. Archived from
825:whose application within
325:Among non-living things,
3221:Concepts in epistemology
3150:Philosophy of psychology
3085:Simulacra and Simulation
1724:A History of Western Art
1636:10.5014/ajot.2022.049113
32:Pattern (disambiguation)
3226:Metaphysical properties
3015:Critique of Pure Reason
2160:. Addison-Wesley, 1994.
2116:. Conran Octopus, 2010.
2084:In art and architecture
1943:Frontiers in Psychology
1565:Hsu, M.F. (July 2021).
1361:, 2009. pp. 68, 96-101.
1326:. Nelson Thornes, 1971.
985:Template method pattern
980:Software design pattern
788:Science and mathematics
624:spatiotemporal patterns
526:, and the skeletons of
341:; they can be cubic or
195:, and those created by
2606:Typeâtoken distinction
2434:Hypostatic abstraction
2216:Abstract object theory
1722:Adams, Laurie (2001).
1424:10.1098/rstb.1952.0012
1226:. McGraw-Hill (1963):
1222:von KĂĄrmĂĄn, Theodore.
1087:Kappraff, Jay (2004).
823:differential equations
800:
778:
741:Pattern (architecture)
736:
657:
550:
501:
456:
448:
408:
369:
291:
3195:Philosophy portal
3075:Being and Nothingness
2491:Mental representation
2023:Patterns of the Earth
1870:Mandelbrot, Benoit B.
1336:Tolman, H.L. (2008).
1039:Stewart, Ian (2001).
795:
776:
730:
660:Further information:
652:
634:Further information:
593:South African giraffe
545:
493:
454:
441:
403:
360:
284:
215:In many areas of the
3120:Feminist metaphysics
1516:Tilings and Patterns
1493:. Cornell University
1475:, 2009. pp. 159â167.
1448:Mathematical Biology
1324:Vibrations and Waves
1194:10.1364/OE.24.015478
975:Pedagogical patterns
882:can be simple (e.g.
630:Art and architecture
30:For other uses, see
2965:Daneshnameh-ye Alai
2476:Linguistic modality
2065:Thompson, D'Arcy W.
2037:Art Forms of Nature
1416:1952RSPTB.237...37T
1302:1994CSF.....4.1323S
1186:2016OExpr..2415478C
1141:1986SciAm.255f..46C
1129:Scientific American
965:Pattern recognition
929:Die (manufacturing)
884:Lindenmayer systems
636:Mathematics and art
300:rotational symmetry
3155:Philosophy of self
3145:Philosophy of mind
2409:Embodied cognition
2321:Scientific realism
2137:. Princeton, 2006.
2069:On Growth and Form
2045:Patterns in Nature
2043:Stevens, Peter S.
2007:. Princeton, 2006.
1795:on 7 February 2013
1671:Current Psychology
1296:(8â9): 1323â1354.
1075:Patterns in Nature
970:Patterns in nature
867:patterns in nature
801:
779:
737:
658:
620:reactionâdiffusion
551:
502:
457:
449:
409:
370:
339:crystal symmetries
292:
237:Patterns in nature
161:patterns in nature
3203:
3202:
2382:Category of being
2351:Truthmaker theory
2167:. Springer, 2007.
2020:Edmaier, Bernhard
1885:978-0-7167-1186-5
1826:(4852): 611â616.
1458:978-3-662-08539-4
945:Pattern (casting)
924:Cellular automata
854:centre of gravity
749:In architecture,
607:Pattern formation
528:silicoflagellates
513:average curvature
470:as they pass by.
127:geometric pattern
16:(Redirected from
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2586:Substantial form
2398:Cogito, ergo sum
2341:Substance theory
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2047:. Penguin, 1974.
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1258:
1249:
1243:
1234:. Dover (1994):
1220:
1214:
1213:
1179:
1170:(14): 15478â85.
1159:
1153:
1152:
1124:
1118:
1117:
1115:
1114:
1108:
1093:
1084:
1078:
1073:Stevens, Peter.
1071:
1065:
1064:
1036:
1021:
1020:
1018:
1016:
1001:
960:Pattern (sewing)
955:Pattern matching
833:patterns of the
597:Burchell's zebra
588:
573:
464:Mechanical waves
331:sixfold symmetry
289:sixfold symmetry
105:
94:
85:
74:
65:
54:
45:
21:
3256:
3255:
3251:
3250:
3249:
3247:
3246:
3245:
3206:
3205:
3204:
3199:
3189:
3187:
3169:
3093:
3088:
3078:
3068:
3058:
3048:
3038:
3028:
3018:
3008:
2998:
2988:
2978:
2968:
2958:
2948:
2938:
2935:De rerum natura
2928:
2918:
2908:
2892:
2632:
2536:Physical object
2372:Abstract object
2360:
2346:Theory of forms
2281:Meaning of life
2204:
2199:
2157:Design Patterns
2151:
2144:. Oxford, 1999.
2130:
2095:. Oxford, 1977.
2086:
2016:. Oxford, 2001.
2000:
1995:
1990:
1935:
1934:
1930:
1920:
1918:
1913:
1912:
1908:
1898:
1897:
1893:
1886:
1868:
1867:
1863:
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1847:
1836:
1834:
1813:
1812:
1808:
1798:
1796:
1786:
1785:
1781:
1766:10.2307/2214851
1751:
1750:
1746:
1736:
1735:
1731:
1721:
1720:
1716:
1664:
1663:
1659:
1615:
1614:
1610:
1564:
1563:
1559:
1550:
1548:
1540:
1539:
1535:
1528:
1511:
1510:
1506:
1496:
1494:
1484:
1483:
1479:
1470:
1466:
1459:
1444:
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1399:
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1389:
1385:
1369:
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1356:
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1334:
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1321:
1317:
1285:
1280:
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1267:
1256:
1251:
1250:
1246:
1221:
1217:
1161:
1160:
1156:
1126:
1125:
1121:
1112:
1110:
1106:
1091:
1086:
1085:
1081:
1077:, 1974. Page 3.
1072:
1068:
1053:
1038:
1037:
1024:
1014:
1012:
1010:achrafgarai.com
1003:
1002:
998:
994:
989:
914:
875:Self-similarity
863:
843:
798:self-similarity
790:
785:
747:
739:Main articles:
725:
723:In architecture
701:
668:
647:
642:
632:
616:James D. Murray
609:
603:
602:
601:
600:
599:
589:
581:
580:
574:
563:
540:
488:
436:
398:
363:Aloe polyphylla
355:
296:mirror symmetry
279:
239:
233:
217:decorative arts
115:
114:
113:
112:
108:
107:
106:
97:
96:
95:
87:
86:
77:
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75:
67:
66:
57:
56:
55:
47:
46:
35:
28:
23:
22:
15:
12:
11:
5:
3254:
3252:
3244:
3243:
3238:
3233:
3228:
3223:
3218:
3208:
3207:
3201:
3200:
3198:
3197:
3185:
3174:
3171:
3170:
3168:
3167:
3162:
3157:
3152:
3147:
3142:
3137:
3132:
3127:
3122:
3117:
3112:
3107:
3101:
3099:
3098:Related topics
3095:
3094:
3092:
3091:
3081:
3071:
3065:Being and Time
3061:
3051:
3041:
3031:
3021:
3011:
3001:
2991:
2981:
2971:
2961:
2951:
2941:
2931:
2921:
2911:
2900:
2898:
2894:
2893:
2891:
2890:
2883:
2878:
2873:
2868:
2863:
2858:
2853:
2848:
2843:
2838:
2833:
2828:
2823:
2818:
2813:
2808:
2803:
2798:
2793:
2788:
2783:
2778:
2773:
2768:
2763:
2758:
2753:
2748:
2743:
2738:
2733:
2728:
2723:
2718:
2713:
2708:
2703:
2698:
2693:
2688:
2683:
2678:
2673:
2668:
2663:
2658:
2653:
2648:
2642:
2640:
2638:Metaphysicians
2634:
2633:
2631:
2630:
2623:
2618:
2613:
2608:
2603:
2598:
2593:
2588:
2583:
2578:
2573:
2568:
2563:
2558:
2553:
2548:
2543:
2538:
2533:
2528:
2523:
2518:
2513:
2508:
2503:
2498:
2493:
2488:
2483:
2478:
2473:
2468:
2463:
2458:
2457:
2456:
2446:
2441:
2436:
2431:
2426:
2421:
2416:
2411:
2406:
2401:
2394:
2392:Causal closure
2389:
2384:
2379:
2374:
2368:
2366:
2362:
2361:
2359:
2358:
2353:
2348:
2343:
2338:
2333:
2328:
2323:
2318:
2313:
2308:
2303:
2298:
2293:
2288:
2283:
2278:
2273:
2268:
2266:Libertarianism
2263:
2258:
2253:
2251:Existentialism
2248:
2243:
2238:
2233:
2228:
2223:
2218:
2212:
2210:
2206:
2205:
2200:
2198:
2197:
2190:
2183:
2175:
2169:
2168:
2163:Bishop, C. M.
2161:
2150:
2147:
2146:
2145:
2140:Resnik, M. D.
2138:
2129:
2126:
2125:
2124:
2119:Pritchard, S.
2117:
2110:
2109:. Wiley, 2009.
2103:
2102:. Booqs, 2009.
2096:
2085:
2082:
2081:
2080:
2062:
2048:
2041:
2040:. Dover, 1974.
2033:Haeckel, Ernst
2030:
2017:
2008:
2003:Adam, John A.
1999:
1996:
1994:
1991:
1989:
1988:
1928:
1906:
1891:
1884:
1861:
1845:
1806:
1779:
1760:(4): 529â550.
1744:
1729:
1714:
1657:
1608:
1557:
1533:
1526:
1504:
1477:
1471:Ball, Philip.
1464:
1457:
1437:
1410:(641): 37â72.
1392:
1383:
1375:Jean E. Taylor
1363:
1357:Ball, Philip.
1350:
1328:
1315:
1273:
1270:on 2011-09-29.
1244:
1240:978-0486434858
1232:978-0070676022
1215:
1164:Optics Express
1154:
1119:
1079:
1066:
1051:
1022:
995:
993:
990:
988:
987:
982:
977:
972:
967:
962:
957:
952:
947:
942:
937:
932:
926:
921:
915:
913:
910:
895:pattern theory
862:
859:
846:Daniel Dennett
842:
839:
789:
786:
724:
721:
709:cross hatching
700:
697:
655:Topkapi Palace
646:
643:
631:
628:
605:Main article:
590:
583:
582:
577:Mbu pufferfish
575:
568:
567:
566:
565:
564:
562:
561:Spots, stripes
559:
539:
536:
509:Plateau's laws
487:
484:
435:
432:
424:vortex streets
397:
394:
354:
351:
329:have striking
278:
275:
235:Main article:
232:
229:
110:
109:
100:
99:
98:
89:
88:
80:
79:
78:
69:
68:
60:
59:
58:
49:
48:
40:
39:
38:
37:
36:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3253:
3242:
3239:
3237:
3234:
3232:
3229:
3227:
3224:
3222:
3219:
3217:
3214:
3213:
3211:
3196:
3186:
3184:
3176:
3175:
3172:
3166:
3163:
3161:
3158:
3156:
3153:
3151:
3148:
3146:
3143:
3141:
3140:Phenomenology
3138:
3136:
3133:
3131:
3128:
3126:
3123:
3121:
3118:
3116:
3113:
3111:
3108:
3106:
3103:
3102:
3100:
3096:
3087:
3086:
3082:
3077:
3076:
3072:
3067:
3066:
3062:
3057:
3056:
3052:
3047:
3046:
3042:
3037:
3036:
3032:
3027:
3026:
3022:
3017:
3016:
3012:
3007:
3006:
3002:
2997:
2996:
2992:
2987:
2986:
2982:
2977:
2976:
2972:
2967:
2966:
2962:
2957:
2956:
2952:
2947:
2946:
2942:
2937:
2936:
2932:
2927:
2926:
2922:
2917:
2916:
2912:
2907:
2906:
2902:
2901:
2899:
2897:Notable works
2895:
2889:
2888:
2884:
2882:
2879:
2877:
2874:
2872:
2869:
2867:
2864:
2862:
2859:
2857:
2854:
2852:
2849:
2847:
2844:
2842:
2839:
2837:
2834:
2832:
2829:
2827:
2824:
2822:
2819:
2817:
2814:
2812:
2809:
2807:
2804:
2802:
2799:
2797:
2794:
2792:
2789:
2787:
2784:
2782:
2779:
2777:
2774:
2772:
2769:
2767:
2764:
2762:
2759:
2757:
2754:
2752:
2749:
2747:
2744:
2742:
2739:
2737:
2734:
2732:
2729:
2727:
2724:
2722:
2719:
2717:
2714:
2712:
2709:
2707:
2704:
2702:
2699:
2697:
2694:
2692:
2689:
2687:
2684:
2682:
2679:
2677:
2674:
2672:
2669:
2667:
2664:
2662:
2659:
2657:
2654:
2652:
2649:
2647:
2644:
2643:
2641:
2639:
2635:
2629:
2628:
2624:
2622:
2619:
2617:
2614:
2612:
2609:
2607:
2604:
2602:
2599:
2597:
2594:
2592:
2589:
2587:
2584:
2582:
2579:
2577:
2574:
2572:
2569:
2567:
2564:
2562:
2559:
2557:
2554:
2552:
2549:
2547:
2544:
2542:
2539:
2537:
2534:
2532:
2529:
2527:
2524:
2522:
2519:
2517:
2514:
2512:
2509:
2507:
2504:
2502:
2499:
2497:
2494:
2492:
2489:
2487:
2484:
2482:
2479:
2477:
2474:
2472:
2469:
2467:
2464:
2462:
2459:
2455:
2452:
2451:
2450:
2447:
2445:
2442:
2440:
2437:
2435:
2432:
2430:
2427:
2425:
2422:
2420:
2417:
2415:
2412:
2410:
2407:
2405:
2402:
2400:
2399:
2395:
2393:
2390:
2388:
2385:
2383:
2380:
2378:
2375:
2373:
2370:
2369:
2367:
2363:
2357:
2354:
2352:
2349:
2347:
2344:
2342:
2339:
2337:
2334:
2332:
2329:
2327:
2324:
2322:
2319:
2317:
2314:
2312:
2309:
2307:
2304:
2302:
2301:Phenomenalism
2299:
2297:
2294:
2292:
2289:
2287:
2284:
2282:
2279:
2277:
2274:
2272:
2269:
2267:
2264:
2262:
2259:
2257:
2254:
2252:
2249:
2247:
2244:
2242:
2239:
2237:
2234:
2232:
2229:
2227:
2224:
2222:
2221:Action theory
2219:
2217:
2214:
2213:
2211:
2207:
2203:
2196:
2191:
2189:
2184:
2182:
2177:
2176:
2173:
2166:
2162:
2159:
2158:
2153:
2152:
2148:
2143:
2139:
2136:
2132:
2131:
2127:
2122:
2118:
2115:
2111:
2108:
2104:
2101:
2098:de Baeck, P.
2097:
2094:
2091:
2090:Alexander, C.
2088:
2087:
2083:
2079:
2078:0-486-67135-6
2075:
2071:
2070:
2066:
2063:
2060:
2056:
2052:
2049:
2046:
2042:
2039:
2038:
2034:
2031:
2028:
2027:Phaidon Press
2024:
2021:
2018:
2015:
2012:
2009:
2006:
2002:
2001:
1997:
1992:
1984:
1980:
1975:
1970:
1966:
1962:
1957:
1952:
1948:
1944:
1940:
1932:
1929:
1916:
1910:
1907:
1902:
1895:
1892:
1887:
1881:
1878:. Macmillan.
1877:
1876:
1871:
1865:
1862:
1858:
1855:
1849:
1846:
1833:
1829:
1825:
1821:
1817:
1810:
1807:
1794:
1790:
1783:
1780:
1775:
1771:
1767:
1763:
1759:
1755:
1748:
1745:
1740:
1733:
1730:
1725:
1718:
1715:
1710:
1706:
1701:
1696:
1692:
1688:
1684:
1680:
1676:
1672:
1668:
1661:
1658:
1653:
1649:
1645:
1641:
1637:
1633:
1629:
1625:
1624:
1619:
1612:
1609:
1604:
1600:
1596:
1592:
1587:
1582:
1578:
1574:
1573:
1572:Public Health
1568:
1561:
1558:
1547:
1543:
1537:
1534:
1529:
1527:9780716711933
1523:
1518:
1517:
1508:
1505:
1492:
1488:
1481:
1478:
1474:
1468:
1465:
1460:
1454:
1450:
1449:
1441:
1438:
1433:
1429:
1425:
1421:
1417:
1413:
1409:
1405:
1404:
1396:
1393:
1387:
1384:
1380:
1376:
1372:
1367:
1364:
1360:
1354:
1351:
1346:
1339:
1332:
1329:
1325:
1322:French, A.P.
1319:
1316:
1311:
1307:
1303:
1299:
1295:
1291:
1284:
1277:
1274:
1266:
1262:
1255:
1248:
1245:
1241:
1237:
1233:
1229:
1225:
1219:
1216:
1211:
1207:
1203:
1199:
1195:
1191:
1187:
1183:
1178:
1173:
1169:
1165:
1158:
1155:
1150:
1146:
1142:
1138:
1135:(12): 46â57.
1134:
1130:
1123:
1120:
1109:on 2016-03-04
1105:
1101:
1097:
1090:
1083:
1080:
1076:
1070:
1067:
1062:
1058:
1054:
1052:0-297-60723-5
1048:
1044:
1043:
1035:
1033:
1031:
1029:
1027:
1023:
1011:
1007:
1000:
997:
991:
986:
983:
981:
978:
976:
973:
971:
968:
966:
963:
961:
958:
956:
953:
951:
948:
946:
943:
941:
938:
936:
935:Form constant
933:
930:
927:
925:
922:
920:
917:
916:
911:
909:
905:
902:
900:
899:Ulf Grenander
897:, devised by
896:
891:
889:
885:
881:
876:
872:
868:
860:
858:
855:
851:
850:real patterns
848:'s notion of
847:
841:Real patterns
840:
838:
836:
832:
828:
824:
820:
815:
811:
809:
805:
799:
794:
787:
784:
775:
771:
769:
765:
761:
757:
752:
746:
742:
734:
729:
722:
720:
718:
714:
710:
706:
698:
696:
694:
690:
686:
682:
678:
674:
667:
663:
656:
651:
644:
641:
637:
629:
627:
625:
621:
617:
613:
608:
598:
594:
587:
578:
572:
560:
558:
555:
549:
544:
537:
535:
533:
529:
525:
522:
518:
514:
510:
506:
500:
496:
492:
486:Bubbles, foam
485:
483:
481:
477:
476:surface waves
473:
469:
465:
461:
453:
447:
444:
440:
433:
431:
429:
425:
421:
420:deterministic
417:
413:
406:
405:Vortex street
402:
395:
393:
391:
387:
383:
380:, and in the
379:
375:
368:
365:
364:
359:
352:
350:
348:
347:quasicrystals
344:
340:
336:
332:
328:
323:
321:
317:
313:
309:
305:
301:
297:
290:
287:
283:
276:
274:
273:and stripes.
272:
268:
264:
260:
256:
252:
248:
244:
238:
230:
228:
226:
225:visual motifs
222:
218:
213:
210:
206:
202:
198:
194:
190:
186:
182:
178:
174:
170:
166:
162:
158:
154:
150:
146:
141:
139:
135:
132:
128:
124:
120:
104:
93:
84:
73:
64:
53:
44:
33:
19:
3115:Epistemology
3083:
3073:
3063:
3053:
3043:
3033:
3023:
3013:
3003:
2993:
2983:
2973:
2963:
2953:
2943:
2933:
2925:NyÄya SĆ«tras
2923:
2913:
2903:
2885:
2801:Wittgenstein
2746:Schopenhauer
2625:
2616:Unobservable
2525:
2466:Intelligence
2396:
2336:Subjectivism
2331:Spiritualism
2246:Essentialism
2226:Anti-realism
2164:
2155:
2149:In computing
2141:
2134:
2133:Adam, J. A.
2120:
2113:
2106:
2099:
2092:
2067:
2054:
2051:Stewart, Ian
2044:
2035:
2022:
2013:
2011:Ball, Philip
2004:
1993:Bibliography
1946:
1942:
1931:
1919:. Retrieved
1909:
1900:
1894:
1874:
1864:
1856:
1853:
1848:
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1823:
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1793:the original
1782:
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1260:
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1224:Aerodynamics
1223:
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1128:
1122:
1111:. Retrieved
1104:the original
1099:
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1013:. Retrieved
1009:
999:
950:Pattern coin
906:
903:
892:
864:
849:
844:
812:
802:
783:pattern book
748:
702:
693:tessellation
669:
662:Tessellation
610:
552:
517:radiolarians
503:
499:soap bubbles
458:
434:Waves, dunes
412:Chaos theory
410:
376:such as the
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361:
324:
310:, including
304:sea anemones
293:
240:
214:
209:mathematical
142:
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116:
2945:Metaphysics
2929:(c. 200 BC)
2919:(c. 350 BC)
2909:(c. 350 BC)
2796:Collingwood
2701:Malebranche
2449:Information
2377:Anima mundi
2356:Type theory
2311:Physicalism
2276:Materialism
2231:Determinism
2202:Metaphysics
2105:Garcia, M.
1859:(1), 27â51.
1579:: 217â222.
1542:"Zentangle"
1497:12 December
886:describing
804:Mathematics
612:Alan Turing
591:Skins of a
532:sea urchins
382:phyllotaxis
367:phyllotaxis
316:sea urchins
308:echinoderms
249:dimension,
153:mathematics
143:Any of the
3210:Categories
3005:Monadology
2939:(c. 80 BC)
2646:Parmenides
2531:Perception
2429:Experience
2316:Relativism
2291:Naturalism
2241:Enactivism
2112:Kiely, O.
1921:16 January
1837:2024-08-11
1799:16 January
1551:2023-02-03
1177:1601.00844
1113:2013-01-18
992:References
931:(template)
781:See also:
683:, ceramic
546:Shrinkage
472:Wind waves
407:turbulence
343:octahedral
327:snowflakes
320:sea lilies
243:symmetries
205:reflection
197:symmetries
163:are often
3165:Teleology
3130:Mereology
3110:Cosmology
2969:(c. 1000)
2866:Plantinga
2856:Armstrong
2806:Heidegger
2781:Whitehead
2766:Nietzsche
2686:Descartes
2656:Aristotle
2611:Universal
2541:Principle
2511:Necessity
2471:Intention
2424:Existence
2387:Causality
2326:Solipsism
2256:Free will
1998:In nature
1965:1664-1078
1843:deserve."
1691:1936-4733
1652:251444115
1603:236092775
1546:Zentangle
1015:1 January
919:Archetype
890:shapes).
880:formation
831:empirical
760:pediments
699:Zentangle
468:oscillate
390:pineapple
386:sunflower
286:Snowflake
221:wallpaper
138:wallpaper
131:geometric
3216:Patterns
3183:Category
3105:Axiology
2959:(c.â270)
2887:more ...
2841:Anscombe
2836:Strawson
2831:Davidson
2726:Berkeley
2666:Plotinus
2627:more ...
2566:Relation
2546:Property
2521:Ontology
2444:Identity
2365:Concepts
2296:Nihilism
2261:Idealism
2209:Theories
2100:Patterns
1983:34484047
1872:(1983).
1709:37359601
1700:10161183
1644:35943847
1595:34274696
1210:34610459
1202:27410822
1061:50272461
912:See also
871:Fractals
861:Fractals
835:universe
808:sequence
681:tapestry
673:painting
524:spicules
428:meanders
378:nautilus
374:molluscs
335:Crystals
312:starfish
277:Symmetry
255:meanders
201:rotation
177:meanders
169:fractals
157:language
140:design.
123:abstract
18:Patterns
2955:Enneads
2949:(c. 50)
2915:Timaeus
2905:Sophist
2851:Dummett
2846:Deleuze
2786:Russell
2776:Bergson
2771:Meinong
2751:Bolzano
2711:Leibniz
2691:Spinoza
2676:Aquinas
2661:Proclus
2591:Thought
2581:Subject
2561:Reality
2556:Quality
2526:Pattern
2486:Meaning
2461:Insight
2419:Essence
2404:Concept
2306:Realism
2271:Liberty
2236:Dualism
2114:Pattern
2061:, 2001.
2029:, 2007.
1974:8416160
1820:Science
1774:2214851
1491:Pattern
1412:Bibcode
1298:Bibcode
1182:Bibcode
1137:Bibcode
940:Fractal
827:physics
814:Gravity
768:fractal
764:lintels
756:columns
733:fractal
677:drawing
645:Tilings
416:physics
353:Spirals
267:tilings
251:spirals
247:fractal
189:tilings
173:spirals
165:chaotic
149:science
119:pattern
3241:Design
3089:(1981)
3079:(1943)
3069:(1927)
3059:(1846)
3049:(1818)
3039:(1807)
3029:(1783)
3019:(1781)
3009:(1714)
2999:(1710)
2989:(1677)
2985:Ethics
2979:(1641)
2881:Parfit
2871:Kripke
2861:Putnam
2821:Sartre
2811:Carnap
2761:Peirce
2706:Newton
2681:SuĂĄrez
2671:Scotus
2551:Qualia
2516:Object
2506:Nature
2501:Motion
2481:Matter
2414:Entity
2286:Monism
2076:
1981:
1971:
1963:
1882:
1772:
1707:
1697:
1689:
1650:
1642:
1630:(76).
1601:
1593:
1524:
1473:Shapes
1455:
1432:937133
1430:
1359:Shapes
1238:
1230:
1208:
1200:
1059:
1049:
819:moon's
762:, and
751:motifs
717:doodle
713:mosaic
689:carpet
685:tiling
554:Cracks
548:Cracks
538:Cracks
521:sponge
446:ripple
318:, and
271:cracks
231:Nature
193:cracks
145:senses
134:shapes
3135:Meta-
2876:Lewis
2826:Quine
2791:Moore
2756:Lotze
2741:Hegel
2716:Wolff
2696:Locke
2651:Plato
2621:Value
2601:Truth
1770:JSTOR
1648:S2CID
1599:S2CID
1428:S2CID
1341:(PDF)
1286:(PDF)
1268:(PDF)
1257:(PDF)
1206:S2CID
1172:arXiv
1107:(PDF)
1096:Forma
1092:(PDF)
507:obey
505:Foams
480:dunes
460:Waves
263:foams
259:waves
185:foams
181:waves
155:, or
2816:Ryle
2736:Kant
2731:Hume
2721:Reid
2596:Time
2576:Soul
2571:Self
2496:Mind
2454:Data
2439:Idea
2074:ISBN
1979:PMID
1961:ISSN
1923:2013
1880:ISBN
1801:2013
1754:Noûs
1705:PMID
1687:ISSN
1640:PMID
1591:PMID
1522:ISBN
1499:2012
1453:ISBN
1373:and
1236:ISBN
1228:ISBN
1198:PMID
1057:OCLC
1047:ISBN
1017:2023
888:tree
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664:and
638:and
595:and
579:skin
530:and
495:Foam
474:are
443:Dune
418:are
203:and
1969:PMC
1951:doi
1828:doi
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1679:doi
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