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

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.[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

  1. ↑ 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.
  2. ↑ L.G. Harrison, Kinetic Theory of Living Pattern, Cambridge University Press (1993)
  3. ↑ Gribbin, John (2004). Deep Simplicity. Random House.
  4. ↑ Meinhardt, H. (1982). Models of Biological Pattern Formation. Academic Press.
  5. ↑ Murray, James D. (9 March 2013). Mathematical Biology. Springer Science & Business Media. pp. 436–450. ISBN 978-3-662-08539-4.
  6. ↑ Grindrod, P. Patterns and Waves: The Theory and Applications of Reaction-Diffusion Equations, Clarendon Press (1991)
  7. ↑ Smoller, J. Shock Waves and Reaction Diffusion Equations, Springer (1994)
  8. ↑ Kerner, B. S. and Osipov, V. V. Autosolitons. A New Approach to Problems of Self-Organization and Turbulence, Kluwer Academic Publishers. (1994)

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