Three-dimensional Cellular Automata for Reaction-Diffusion Systems
Jörg R. Weimar · 2002
Cellular automata for reaction-diffusion systems are efficient enough to make the simulation of large three-dimensional systems feasible. The principal construction mechanisms used here are not much different from those for two-dimensional cellular automata. Diffusion is realized through a local averageing, and all the nonlinear reaction terms are collected in a table-lookup. The special issue in three dimensions is the need to increase time- and spacescales as much as possible to achieve sufficient system sizes. This can be done through the use of numerical integration schemes for constructing the lookup table, and through the use of special diffusion operators. We present examples of complex three-dimensional behaviours in an excitable reaction-diffusion system and in a model of a pattern-forming chemical reaction. 1 Introduction Nonlinear reaction-diffusion systems arise in many different contexts. Examples include the spreading of infectious diseases (e.g., rabies in foxes) or of ...