New class of cellular automata for reaction-diffusion systems applied to the CIMA reaction
Joerg Weimar, Jean Pierre Boon · 1995
We present a class of cellular automata (CAs) for modelling reaction-diffusion systems. The construction of the CA is general enough to be applicable to a large class of reactiondiffusion equations. The automata are based on a running average procedure to implement diffusion, and on a probabilistic table-lookup to implement the reaction. As an example application we present the Brandeisator (Lengyl-Epstein model for the chlorite-iodide-malonic acid reaction CIMA), which exhibits a rich set of behaviors: oscillations, hexagonal structures, stripes, and spirals. We investigate cases showing mixed states, in which different structures coexist in space: isolated spots, isolated regions of hexagons in a surrounding homogeneous region, coexistence between stripes and oscillations, and hexagons and stripes. The cellular automaton approach has the following advantages: fast simulations of large systems, easy implementation of noise in the system, and connections to other, more phenomenological...