Simulating Spatial Dynamics by Probabilistic Cellular Automata

Abstract

A method is proposed, which is intended for constructing a probabilistic cellular automaton (CA), whose evolution simulates a spatially distributed process, given by a PDE. The heart of the method is the transformation of a real spatial function into a Boolean array whose averaged form approximates the given function. Two parts of a given PDE (a differential operator and a function) are approximated by a combination of their Boolean counterparts. The resulting CA transition function has a basic (standard) part, modeling the differential operator and the updating part modifying it according to the function value. Special attention is paid to the reaction-diffusion type of PDE. Some experimental results of simple processes simulation are given and perspectives of the proposed method application are discussed.