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 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).

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. Patterns such as fronts, hexagons, spirals, stripes and dissipative solitons are found as solutions of Turing-like reaction–diffusion equations.

Turing proposed a model wherein two homogeneously distributed substances (P and S) interact to produce stable patterns during morphogenesis. These patterns represent regional differences in the concentrations of the two substances. Their interactions would produce an ordered structure out of random chaos.

In Turing's model, substance P promotes the production of more substance P as well as substance S. However, substance S inhibits the production of substance P; if S diffuses more readily than P, sharp waves of concentration differences will be generated for substance P. An important feature of Turing's model is that particular wavelengths in the substances' distribution will be amplified while other wavelengths will be suppressed.

The parameters depend on the physical system under consideration. In the context of fish skin pigmentation, the associated equation is a three field reaction–diffusion one in which the linear parameters are associated with pigmentation cell concentration and the diffusion parameters are not the same for all fields. In dye-doped liquid crystals, a photoisomerization process in the liquid crystal matrix is described as a reaction–diffusion equation of two fields (liquid crystal order parameter and concentration of cis-isomer of the azo-dye). The systems have very different physical mechanisms on the chemical reactions and diffusive process, but on a phenomenological level, both have the same ingredients.