Quasi-two-dimensional Turing patterns in an imposed gradient

Abstract

In experiments on quasi-two-dimensional Turing structures, patterns form perpendicular to a concentration gradient imposed by the boundary conditions. Using linear stability analysis, with the ${\mathrm{ClO}}_2$-${\mathrm{I}}_2$-MA (malonic acid) reaction as an example, we obtain conditions on the position along the gradient direction and possible three dimensionality of the structures. Experiments on the effects of MA and starch concentrations on the position of the structures support the theory. Simulations taking into account the starch indicator yield Turing patterns even with equal diffusion coefficients for the activator and inhibitor species.