Oscillations spatio-temporelles engendrees par un automate cellulaire

Abstract We study a planar cellular automaton which is a simple model of a reaction-diffusion mechanism in excitable media; we are especially interested in the spatio-temporal organization which it generates. Under suitable assumptions, the sequence of the states of the plan is ultimately either stationary or periodic. In the latter case, we prove that there exists only one admissible period which is independent of the initial conditions and that a spatial organization of the plan appears, consisting of parallel equidistant target-wave-fronts growing with constant speed.