Ian Stewart
(University of Warwick Mathematics Institute)
Turing Patterns and Animal Markings

In the early 1950s, Alan Turing showed his colleagues a drawing with irregular black-and-white patches, asking them whether they agreed that it looked like a cow. In 1952 he published 'the chemical basis of morphogenesis', in which he proposed a mechanism for the creation of animal markings. A chemical called a morphogen was produced by local reactions and diffused across the embryo, laying down a pre-pattern. At a late stage of development, this formed the basis of a pattern of pigments. Although these reaction-diffusion equations do not correspond in detail to many features of the biology, the patterns that they naturally form are remarkably similar to those found on many animals, including irregular and convoluted stripes on fish and some intricate patterns on seashells. The talk will be an informal illustrated discussion of these Turing patterns, from the point of view of modern theories of pattern formation.