Turing pattern

Mechanism

Consider two substances: an "activator", which promotes its own production, and an "inhibitor", which suppresses it. When certain conditions are met, such as a large difference in the two diffusion rates, the state that ought to mix toward uniformity becomes unstable, and a pattern in which regions of high and low concentration line up regularly appears on its own. Mathematically this is expressed by reaction-diffusion equations, a system of partial differential equations in two variables, and this phenomenon in which fluctuations of a particular wavelength are amplified is called "diffusion-driven instability" or "Turing instability".

Turing's paper

In 1952 Turing published the paper "The Chemical Basis of Morphogenesis" in Philosophical Transactions of the Royal Society of London B. It attempted to answer, through a combination of chemical reaction and diffusion, the question of how spatial structure arises from an initially uniform state in biological development.

Experimental confirmation

It long remained a theoretical construct, but in 1990 Castets and colleagues (Castets, Dulos, Boissonade, De Kepper) demonstrated a Turing-type pattern experimentally for the first time by running the chlorite-iodide-malonic acid reaction (CIMA reaction) in an unstirred gel.

In living things, in 1995 Shigeru Kondo and Rihito Asai showed that the way the stripes on the body of the emperor angelfish change as the fish grows matched simulations of reaction-diffusion equations, experimentally confirming that an animal's markings are a Turing pattern. The result was published in Nature.

Examples in nature

A variety of phenomena are explained within this framework, including the markings on fish, the coat patterns of mammals, the arrangement of feathers and hair (the placement of follicles), and fingerprints.