Asymptotic Behavior of Excitable Cellular Automata

This research was partially supported by research grants to each of the authors from the National Science Foundation We study two families of excitable cellular automata known as the Greenberg–Hastings model and the cyclic cellular automaton. Each family consists of local deterministic oscillating lattice dynamics, with parallel discrete-time updating, parametrized by the range of interaction, l shape of its neighbor set, threshold for contact updating, and number of possible states per site. These models are mathematically tractable prototypes for the spatially distributed periodic wave activity of so-called excitable media observed in diverse disciplines of experimental science.