The Chemical Basis of Morphogenesis
"The Chemical Basis of Morphogenesis" is an article written by the English mathematician Alan Turing in 1952 describing the way in which non-uniformity (natural patterns such as stripes, spots and spirals) may arise naturally out of a homogeneous, uniform state.[1] The theory (which can be called a reaction–diffusion theory of morphogenesis), has served as a basic model in theoretical biology,[2] and is seen by some as the very beginning of chaos theory.[3]
Reaction–diffusion systems
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Reaction–diffusion systems have attracted much interest as a prototype model for pattern formation. The above-mentioned patterns (fronts, spirals, targets, hexagons, stripes and dissipative solitons) can be found in various types of reaction-diffusion systems in spite of large discrepancies e.g. in the local reaction terms.
It has also been argued that reaction-diffusion processes are an essential basis for processes connected to animal coats and skin pigmentation.[4][5] Another reason for the interest in reaction-diffusion systems is that although they represent nonlinear partial differential equations, there are often possibilities for an analytical treatment.[6][7][8]
References
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- ↑ L.G. Harrison, Kinetic Theory of Living Pattern, Cambridge University Press (1993)
- ↑ Gribbin, John. Deep Simplicity. Random House 2004.
- ↑ H. Meinhardt, Models of Biological Pattern Formation, Academic Press (1982)
- ↑ J. D. Murray, Mathematical Biology, Springer (1993)
- ↑ P. Grindrod, Patterns and Waves: The Theory and Applications of Reaction-Diffusion Equations, Clarendon Press (1991)
- ↑ J. Smoller, Shock Waves and Reaction Diffusion Equations, Springer (1994)
- ↑ B. S. Kerner and V. V. Osipov, Autosolitons. A New Approach to Problems of Self-Organization and Turbulence, Kluwer Academic Publishers. (1994)
