Turing pattern

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. The pattern arises due to Turing instability which in turn arises due to the interplay between differential diffusion (i.e., different values of diffusion coefficients) of chemical species and chemical reaction. The instability mechanism is unforeseen because purely diffusion process is anticipated to have a stabilizing influence on the system. In his paper, Turing examined the behaviour of a system in which two diffusible substances interact with each other, and found that such a system is able to generate a spatially periodic pattern even from a random or almost uniform initial condition. Prior to the discovery of this instability mechanism arising due to unequal diffusion coefficients of the two substances, diffusional effects were always presumed to have stabilizing influences on the system. Turing hypothesized that the resulting wavelike patterns are the chemical basis of morphogenesis. Turing patterning is often found in combination with other patterns: vertebrate limb development is one of the many phenotypes exhibiting Turing patterning overlapped with a complementary pattern (in this case a French flag model). Before Turing, Yakov Zeldovich in 1944 discovered this instability mechanism in connection with the cellular structures observed in lean hydrogen flames. Zeldovich explained the cellular structure as a consequence of hydrogen's diffusion coefficient being larger than the thermal diffusion coefficient. In combustion literature, Turing instability is referred to as diffusive–thermal instability. The original theory, a reaction–diffusion theory of morphogenesis, has served as an important model in theoretical biology. Reaction–diffusion systems have attracted much interest as a prototype model for pattern formation.