Turing Structures in Anisotropic Media

Abstract

When a convection-free chemical system is kept far from equilibrium by a permanent supply of fresh reactants, stationary spatial concentration patterns may spontaneously form as a result of the coupling of the sole reaction and diffusion processes. In view of its possible implication in morphogenesis, this phenomenon, first predicted by Turing in 1952 [1], has instigated numerous theoretical studies. Various well documented reviews can be found, both from the nonlinear physics [2–4] and biological [5–8] standpoints. However, their experimental observation has long been delayed in regard of practical impediments. Recently, we have reported the first experimental evidence of a Turing-type pattern [9,10]. The key to the success was the use of open spatial reactors with nonhomogeneous distribution of the feeding species, which induces a basic anisotropy in the reactive medium. Thus, all properties of Turing patterns have to be revisited in consideration of this anisotropy. Here we report numerical simulations performed with a geometry and boundary conditions similar to those of the experiments. Our results are in excellent agreement with the observations. They also raise a new class of problems, namely the formation of pattern defects present both in the computations and in the real experiments.