Transition from a uniform state to hexagonal and striped Turing patterns

Abstract

CHEMICAL travelling waves have been studied experimentally for more than two decades1–5, but the stationary patterns predicted by Turing6 in 1952 were observed only recently7–9, as patterns localized along a band in a gel reactor containing a concentration gradient in reagents. The observations are consistent with a mathematical model for their geometry of reactor10 (see also ref. 11). Here we report the observation of extended (quasi-two-dimensional) Turing patterns and of a Turing bifurcation—a transition, as a control parameter is varied, from a spatially uniform state to a patterned state. These patterns form spontaneously in a thin disc-shaped gel in contact with a reservoir of reagents of the chlorite–iodide–malonic acid reaction12. Figure 1 shows examples of the hexagonal, striped and mixed patterns that can occur. Turing patterns have similarities to hydrodynamic patterns (see, for example, ref. 13), but are of particular interest because they possess an intrinsic wavelength and have a possible relationship to biological patterns14–17.