Cellular Automata for Spatiotemporal Pattern Formation from Reaction–Diffusion Partial Differential Equations
Shousuke Ohmori, Yoshihiro Yamazaki · Journal of the Physical Society of Japan · 2015
Ultradiscrete equations are derived from a set of reaction–diffusion partial differential equations, and cellular automaton rules are obtained on the basis of the ultradiscrete equations. Some rules reproduce the dynamical properties of the original reaction–diffusion equations, namely, bistability and pulse annihilation. Furthermore, other rules bring about soliton-like preservation and periodic pulse generation with a pacemaker, which are not obtained from the original reaction–diffusion equations.