Revisiting Turing's Chemical Basis of Morphogenesis

by John J. Tyson

Although Alan Turing’s 1952 paper on the chemical basis of morphogenesis is a classic of theoretical biology, it is notoriously difficult to read. His chemical examples are unusual, his linear stability analysis of the homogeneous steady state seems unnecessarily complex, and his numerical simulations are mysterious. To make Turing’s paper more accessible, I pose his reaction-diffusion equations in dimensionless form, place his linear stability analysis in the context of later approaches, revise his models in more chemically realistic terms, and provide help for computing Turing patterns in one- or two spatial dimensions. I also discuss how Turing’s stationary patterns relate to traveling waves in reaction-diffusion equations.