A Turing pattern forms when a spatially homogeneous steady state, which is stable to small spatially homogeneous perturbations, loses its stability to small spatially inhomogeneous perturbations. The mechanism responsible for such instabilities was first described by Turing (1952), in his paper The chemical basis of morphogenesis, as a model for pattern formation in biology. The appearance ofTuring patterns relies on the interplay between autocatalytic chemical kinetics and diffusion. The basic Turing mechanism can be described in terms of the kinetics of two chemical species termed the activator and the inhibitor. The activator tends to increase the production of chemical species while the inhibitor tends to inhibit such concentration growth. A Turing pattern can form if the diffusion coefficient of the inhibitor is much greater than that of the activator. While there is still controversy over the role of Turing patterns in morphogenesis, these patterns have been unambiguously identified in chemically reacting media.

The formation of a chemicalTuring pattern in a continuously fed unstirred reactor was reported by Castets et al. (1990). The chlorite–iodide–malonic acid system was studied in a thin gel reactor schematically depicted in Fig. 23.1. The top and bottom sides of the thin hydrogel in which the reaction takes place are in contact with reservoirs containing chemical reagents. The chemical species diffuse into the gel, and reaction takes place in a thin layer within the gel shown in the center panel of the figure. Within this reaction zone a stationary inhomogeneous periodic pattern of chemical concentrations develops, as seen in the right panel of the figure.