Editing Pattern (section)

== Nature ==
{{main|Patterns in nature}}
Nature provides examples of many kinds of pattern, including [[symmetry|symmetries]], trees and other structures with a [[fractal]] dimension, [[spirals]], [[meander]]s, [[wave]]s, [[foam]]s, [[tessellation|tilings]], [[fracture|cracks]] and stripes.<ref>Stevens, Peter. ''Patterns in Nature'', 1974. Page 3.</ref>

=== Symmetry ===
[[File:First Snowfall (38115232341).jpg|thumb|upright|[[Snowflake]] [[dihedral symmetry|sixfold symmetry]]]]
Symmetry is widespread in living things. Animals that move usually have bilateral or [[Reflection symmetry|mirror symmetry]] as this favours movement.<ref name=":0" />{{Rp|pages=48–49}} Plants often have radial or [[rotational symmetry]], as do many flowers, as well as animals which are largely static as adults, such as [[sea anemone]]s. Fivefold symmetry is found in the [[echinoderms]], including [[starfish]], [[sea urchin]]s, and [[sea lilies]].<ref name=":0" />{{Rp|pages=64–65}}

Among non-living things, [[snowflake]]s have striking [[dihedral symmetry|sixfold symmetry]]: each flake is unique, its structure recording the varying conditions during its crystallisation similarly on each of its six arms.<ref name=":0" />{{Rp|page=52}} [[Crystal]]s have a highly specific set of possible [[crystal habit|crystal symmetries]]; they can be cubic or [[octahedral]], but cannot have fivefold symmetry (unlike [[quasicrystals]]).<ref name=":0" />{{Rp|pages=82–84}}

=== Spirals ===

[[File:Aloe polyphylla spiral.jpg|thumb|upright|''[[Aloe polyphylla]]'' [[phyllotaxis]]]]

Spiral patterns are found in the body plans of animals including [[molluscs]] such as the [[nautilus]], and in the [[phyllotaxis]] of many plants, both of leaves spiralling around stems, and in the multiple spirals found in flowerheads such as the [[sunflower]] and fruit structures like the [[pineapple]].<ref>{{cite journal | url=http://www.scipress.org/journals/forma/pdf/1904/19040335.pdf | title=Growth in Plants: A Study in Number | author=Kappraff, Jay | journal=Forma | year=2004 | volume=19 | pages=335–354 | access-date=2013-01-18 | archive-date=2016-03-04 | archive-url=https://web.archive.org/web/20160304001606/http://www.scipress.org/journals/forma/pdf/1904/19040335.pdf | url-status=dead }}</ref>
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=== Chaos, turbulence, meanders and complexity ===
[[File:Vortex-street-1.jpg|thumb|upright=0.6|[[Vortex street]] turbulence]]

[[Chaos theory]] predicts that while the laws of [[physics]] are [[deterministic]], there are events and patterns in nature that never exactly repeat because extremely small differences in starting conditions can lead to widely differing outcomes.<ref>{{cite journal | title=Chaos |author1=Crutchfield, James P |author2=Farmer, J Doyne |author3=Packard, Norman H |author4=Shaw, Robert S | journal=Scientific American |date=December 1986 | volume=254 | issue=12 | pages=46–57|doi=10.1038/scientificamerican1286-46 |bibcode=1986SciAm.255f..46C }}</ref> 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.<ref>{{cite journal |last1=Clerc |first1=Marcel G. |last2=González-Cortés |first2=Gregorio |last3=Odent |first3=Vincent |last4=Wilson |first4=Mario |title=Optical textures: characterizing spatiotemporal chaos |journal=Optics Express |date=29 June 2016 |volume=24 |issue=14 |pages=15478–85 |doi=10.1364/OE.24.015478|pmid=27410822 |arxiv=1601.00844 |bibcode=2016OExpr..2415478C |s2cid=34610459 }}</ref> Many natural patterns are shaped by this complexity, including [[vortex street]]s,<ref>von Kármán, Theodore. ''Aerodynamics''. McGraw-Hill (1963): {{ISBN|978-0070676022}}. Dover (1994): {{ISBN|978-0486434858}}.</ref> other effects of turbulent flow such as [[meander]]s in rivers.<ref>{{cite book | first=Jacques | last=Lewalle | title=Lecture Notes in Incompressible Fluid Dynamics: Phenomenology, Concepts and Analytical Tools | chapter=Flow Separation and Secondary Flow: Section 9.1 | chapter-url=http://www.ecs.syr.edu/faculty/lewalle/FluidDynamics/fluidsCh9.pdf | year=2006 | location=Syracuse, NY | publisher=Syracuse University | url-status=dead | archive-url=https://web.archive.org/web/20110929075022/http://www.ecs.syr.edu/faculty/lewalle/FluidDynamics/fluidsCh9.pdf | archive-date=2011-09-29 }}</ref> or nonlinear interaction of the system <ref>{{cite journal |last1=Scroggie |first1=A.J |last2=Firth |first2=W.J |last3=McDonald |first3=G.S |last4=Tlidi |first4=M |last5=Lefever |first5=R |last6=Lugiato |first6=L.A |title=Pattern formation in a passive Kerr cavity |journal=Chaos, Solitons & Fractals |date=August 1994 |volume=4 |issue=8–9 |pages=1323–1354 |doi=10.1016/0960-0779(94)90084-1|bibcode=1994CSF.....4.1323S |url=https://dipot.ulb.ac.be/dspace/bitstream/2013/127366/1/1994Chaos_Solitons_and_Fractals_4_1323-1354.pdf }}</ref>
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=== Waves, dunes ===
[[File:Sand dune ripples.jpg|thumb|upright|[[Dune]] [[Capillary wave|ripple]]]]
[[File:Mönster - Sand - Brädor - 2021.jpg|thumb|upright|Dune ripples and boards form a symmetrical pattern.]]
[[Wave]]s are disturbances that carry energy as they move. [[Mechanical wave]]s propagate through a medium – air or water, making it [[Oscillation|oscillate]] as they pass by.<ref>French, A.P. ''Vibrations and Waves''. Nelson Thornes, 1971.{{full citation needed|date=February 2024}}</ref> [[Wind wave]]s are [[surface wave]]s 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 [[dune]]s.<ref>{{cite conference | first=H.L. | last=Tolman | title=Practical wind wave modeling | book-title=CBMS Conference Proceedings on Water Waves: Theory and Experiment | year=2008 | conference=Howard University, USA, 13–18 May 2008 | publisher=World Scientific Publ. | url=http://polar.ncep.noaa.gov/mmab/papers/tn270/Howard_08.pdf | editor-first=M.F. | editor-last=Mahmood}}</ref>
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=== Bubbles, foam ===

[[File:Foam - big.jpg|thumb|upright|[[Foam]] of [[soap bubble]]s]]

[[Foam]]s obey [[Plateau's laws]], which require films to be smooth and continuous, and to have a constant [[mean curvature|average curvature]]. Foam and bubble patterns occur widely in nature, for example in [[radiolarian]]s, [[sponge]] [[spicule (sponge)|spicule]]s, and the skeletons of [[silicoflagellate]]s and [[sea urchin]]s.<ref>Ball, Philip. ''Shapes'', 2009. pp. 68, 96-101.{{full citation needed|date=February 2024}}</ref><ref>[[Frederick J. Almgren, Jr.]] and [[Jean E. Taylor]], ''The geometry of soap films and soap bubbles'', Scientific American, vol. 235, pp. 82–93, July 1976.</ref>
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=== Cracks ===
[[File:Cracked earth in the Rann of Kutch.jpg|thumb|upright|Shrinkage [[Fracture|Cracks]]]]

[[Fracture|Crack]]s 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 old paintings and ceramics.<ref>Stevens, Peter. 1974. Page 207.</ref>
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=== Spots, stripes===
{{multiple image |direction=horizontal |total_width=440
|image1=Giant Pufferfish skin pattern detail.jpg|caption1=[[Mbu pufferfish]] skin
|image2=Animal skin.jpg|caption2=Skins of a [[South African giraffe]] and [[Burchell's zebra]]
}}
{{main|Pattern formation}}

[[Alan Turing]],<ref name=Turing>{{Cite journal| last= Turing | first= A. M. | title = The Chemical Basis of Morphogenesis | journal=[[Philosophical Transactions of the Royal Society B]] | volume = 237 | pages = 37–72 | year = 1952 | doi=10.1098/rstb.1952.0012| issue= 641|bibcode = 1952RSPTB.237...37T | s2cid= 937133 | doi-access=  }}</ref> and later the mathematical biologist [[James D. Murray]]<ref name="Murray2013">{{cite book |last=Murray |first=James D. |title=Mathematical Biology|url=https://books.google.com/books?id=K3LmCAAAQBAJ&pg=PA436 |date=9 March 2013 |publisher=Springer Science & Business Media |isbn=978-3-662-08539-4 |pages=436–450}}</ref> 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 [[reaction–diffusion]] system involving two counter-acting chemical mechanisms, one that activates and one that inhibits a development, such as of dark pigment in the skin.<ref name=Ball159>Ball, Philip. ''Shapes'', 2009. pp. 159–167.{{full citation needed|date=February 2024}}</ref> These  [[spatiotemporal pattern]]s slowly drift, the animals' appearance changing imperceptibly as Turing predicted.