Isotropic Cellular Automaton for Excitable Media with Random Neighbor Selection

Abstract

This paper proposes a new isotropic cellular automaton (CA) model for reproducing the Belousov–Zhabotinsky reaction observed in excitable media. Although several CA models have been proposed that exhibit isotropic patterns of the reaction, most of them need complicated rules, a large number of neighboring cells, and multiple thresholds to decide the excitation condition of cells. The proposed model uses only one threshold and simple time-evolution rules on the basis of states of selected neighboring cells; the selected cells are randomly chosen from eight neighboring cells. It is this randomness in selecting neighboring cells that causes the model to generate isotropic patterns. This study shows that patterns generated by the proposed model are highly isotropic. Furthermore, we use simulation results to elucidate how generated patterns are related to the initial states assigned to central cells.