Turing pattern

Three examples of Turing patterns
Six stable states from Turing equations, the last one forms Turing patterns

The Turing pattern is a concept introduced by English mathematician Alan Turing in a 1952 paper titled "The Chemical Basis of Morphogenesis", which describes how patterns in nature, such as stripes and spots, can arise naturally and autonomously from a homogeneous, uniform state.[1][2] The pattern arises due to Turing instability, which in turn arises due to the interplay between differential diffusion of chemical species and chemical reaction. The instability mechanism is surprising because a pure diffusion, such as molecular diffusion, would be expected to have a stabilizing influence on the system (i.e., complete mixing).

  1. ^ Turing, Alan (1952). "The Chemical Basis of Morphogenesis" (PDF). Philosophical Transactions of the Royal Society of London B. 237 (641): 37–72. Bibcode:1952RSPTB.237...37T. doi:10.1098/rstb.1952.0012. JSTOR 92463. S2CID 120437796.
  2. ^ Stewart, Ian (1998). Life's Other Secret: The New Mathematics of the Living World. London: Allen Lane. pp. 138–140, 142–146, 148, 149, 151, 152. ISBN 0-713-99161-5. OCLC 43126766.

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