Cellular Automata for Reaction Diffusion Systems

A class of cellular automata for reaction-diiusion systems is presented. It is based on a local average for the diiusive dynamics, and closely related to nite diierence schemes. The reactive dynamics is implemented as a lookup-table with probabilistic rules. The rules are derived directly and systematically from the given diierential equations, using probabilistic rounding to enforce the discretization of the concentration variables. For quantitatively correct modeling, such probabilistic rules are usually necessary, but in some cases a deterministic version proves suucient.