The chemical basis of morphogenesis
- The chemical basis of morphogenesis
The chemical basis of morphogenesis is an article written by Alan Turing in 1951 describing the way in which non-uniformity (stripes, spots, spirals, etc) may arise naturally out of a homogeneous, uniform state. The theory (which can be called a reaction–diffusion theory of morphogenesis), has served as a basic model in theoretical biology, [L.G. Harrison, Kinetic Theory of Living Pattern, Cambridge University Press (1993)] and is seen by some as the very beginning of chaos theory. [ Gribbon,John. Deep Simplicity. Random House 2004.]
Reaction–diffusion systems
Applications
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 processesconnected to animal coats and skin pigmentation. [H. Meinhardt, Models ofBiological Pattern Formation, Academic Press (1982)] [J. D. Murray,Mathematical Biology, Springer (1993)] Another reason for the interestin reaction-diffusion systems is thatalthough they represent nonlinear partial differential equation,there are often possibilities for an analytical treatment. [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 Problemsof Self-Organization and Turbulence, Kluwer Academic Publishers (1994)]
ource
* [http://www.dna.caltech.edu/courses/cs191/paperscs191/turing.pdf from caltech]
References
*Turing, Allen. The chemical basis of morphogenesis. University qf Manchester (Received 9 November 195 1-Revised 15 March 1952)
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