Editing Pattern (section)

=== 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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