The Chemical Basis of Morphogenesis

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"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. 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

  1. Turing, A. M. (1952). "The Chemical Basis of Morphogenesis" (PDF). Philosophical Transactions of the Royal Society of London. 237 (641): 37–72. doi:10.1098/rstb.1952.0012. JSTOR 92463.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
  2. L.G. Harrison, Kinetic Theory of Living Pattern, Cambridge University Press (1993)
  3. Gribbin, John. Deep Simplicity. Random House 2004.
  4. H. Meinhardt, Models of Biological Pattern Formation, Academic Press (1982)
  5. J. D. Murray, Mathematical Biology, Springer (1993)
  6. P. Grindrod, Patterns and Waves: The Theory and Applications of Reaction-Diffusion Equations, Clarendon Press (1991)
  7. J. Smoller, Shock Waves and Reaction Diffusion Equations, Springer (1994)
  8. B. S. Kerner and V. V. Osipov, Autosolitons. A New Approach to Problems of Self-Organization and Turbulence, Kluwer Academic Publishers. (1994)

External links