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. The theory (which can be called a reaction–diffusion theory of morphogenesis) has served as a basic model in theoretical biology, and is seen by some as the very beginning of chaos theory.
Reaction–diffusion systems have attracted much interest as a prototype model for pattern formation. Patterns such as fronts, spirals, targets, hexagons, stripes and dissipative solitons are found in various types of reaction-diffusion systems in spite of large discrepancies e.g. in the local reaction terms.
Reaction-diffusion processes form one class of explanation for the embryonic development of animal coats and skin pigmentation. 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.
- Turing, A. M. (1952). "The Chemical Basis of Morphogenesis" (PDF). Philosophical Transactions of the Royal Society of London B. 237 (641): 37–72. doi:10.1098/rstb.1952.0012. JSTOR 92463.
- L.G. Harrison, Kinetic Theory of Living Pattern, Cambridge University Press (1993)
- Gribbin, John (2004). Deep Simplicity. Random House.
- Meinhardt, H. (1982). Models of Biological Pattern Formation. Academic Press.
- Murray, James D. (9 March 2013). Mathematical Biology. Springer Science & Business Media. pp. 436–450. ISBN 978-3-662-08539-4.
- Grindrod, P. Patterns and Waves: The Theory and Applications of Reaction-Diffusion Equations, Clarendon Press (1991)
- Smoller, J. Shock Waves and Reaction Diffusion Equations, Springer (1994)
- Kerner, B. S. and Osipov, V. V. Autosolitons. A New Approach to Problems of Self-Organization and Turbulence, Kluwer Academic Publishers. (1994)
- Turing, Alan M. (14 August 1952). "The Chemical Basis of Morphogenesis". Philosophical Transactions of the Royal Society of London B. 237 (641). pp. 37–72. doi:10.1098/rstb.1952.0012.