Reaction-diffusion cellular automata model for the formation of Leisegang patterns

Cellular automata models for the formation of Liesegang structures are proposed. This novel approach, which takes into account the fluctuations for the first time, describes the problem at a microscopic scale, in terms of reaction, diffusion, nucleation, and aggregation processes. We present large scale numerical simulations which provide clear verifications of the time and spacing laws and predict a novel behavior for the widths of the patterns. We show that two different microscopic reaction schemes are possible for producing Liesegang structures and we propose a phase diagram showing the different types of possible patterns.