A Simple Model of the Belousov-zhabotinsky Reaction from First Principles

The Belousov-Zhabotinsky (BZ) reaction is an example of a temporally oscillating chemical reaction. An unusual and interesting feature of the reaction is that as it progresses on a twodimensional plate, self-organized spirals are formed. Many computer models have been constructed of the BZ reaction to simulate the evolution of these spirals. The models typically use cellular automata to allow progression of a wavefront through a notional substrate. Usually a single substrate is used with somewhat arbitrary transference rules. Here it is shown that cellular automata models of BZ spirals can be created by using a very simple set of equations based on a three substrate model with close connection to reaction-diffusion models, more closely resembling the actual BZ reaction. Source code for the model is given in the Processing language.