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are found in various types of reaction-diffusion systems in spite of large discrepancies e.g. in the local reaction terms. Such patterns have been dubbed "
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of animal coats and skin pigmentation. Another reason for the interest in reaction-diffusion systems is that although they represent
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45:, such as stripes and spirals, can arise naturally from a homogeneous, uniform state. The theory, which can be called a
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Grindrod, P. Patterns and Waves: The Theory and
Applications of Reaction-Diffusion Equations, Clarendon Press (1991)
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Kerner, B. S. and Osipov, V. V. Autosolitons. A New
Approach to Problems of Self-Organization and Turbulence,
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Turing's paper explained how natural patterns, such as stripes, spots, and spirals, like those of the
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Smoller, J. Shock Waves and
Reaction Diffusion Equations, Springer (1994)
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Reaction–diffusion processes form one class of explanation for the
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116:, there are often possibilities for an analytical treatment.
362:. Springer Science & Business Media. pp. 436–450.
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235:"Can VEGFC form turing patterns in the Zebrafish embryo?"
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1952 article written by
English mathematician Alan Turing
61:. For example, it has been postulated that the protein
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have attracted much interest as a prototype model for
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57:. Such patterns have come to be known as
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339:Models of Biological Pattern Formation
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160:"The Chemical Basis of Morphogenesis"
524:Computing Machinery and Intelligence
531:The Chemical Basis of Morphogenesis
65:can form Turing patterns to govern
35:The Chemical Basis of Morphogenesis
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510:Systems of Logic Based on Ordinals
126:Evolutionary developmental biology
67:the formation of lymphatic vessels
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356:Murray, James D. (9 March 2013).
291:Turing's theory of morphogenesis
239:Bulletin of Mathematical Biology
217:Kinetic Theory of Living Pattern
41:wrote in 1952. It describes how
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402:Kluwer Academic Publishers
251:10.1007/s11538-018-00560-2
233:Wertheim, Kenneth (2019).
221:Cambridge University Press
88:Reaction–diffusion systems
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77:Reaction–diffusion systems
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83:Reaction–diffusion system
306:; Sprevak, Mark (2017).
606:Works by English people
314:Oxford University Press
215:Harrison, L.G. (1993).
337:Meinhardt, H. (1982).
187:10.1098/rstb.1952.0012
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586:Mathematical modeling
548:Legacy of Alan Turing
517:Intelligent Machinery
503:On Computable Numbers
107:embryonic development
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596:Biological processes
359:Mathematical Biology
96:dissipative solitons
456:Turing completeness
179:1952RSPTB.237...37T
55:theoretical biology
616:Mathematics papers
300:Bowen, Jonathan P.
47:reaction–diffusion
43:patterns in nature
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136:Symmetry breaking
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486:Turing test
445:Alan Turing
39:Alan Turing
570:Categories
142:References
49:theory of
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203:120437796
111:nonlinear
71:zebrafish
533:" (1952)
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519:" (1948)
512:" (1939)
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269:30607882
158:(1952).
120:See also
73:embryo.
541:Related
404:(1994).
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175:Bibcode
69:in the
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293:. In
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191:JSTOR
163:(PDF)
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364:ISBN
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