Sierpinski Gasket in a Reaction-Diffusion System

Abstract

We shall show by computer simulations that a Bonhoeffer van der Pol type reaction-diffusion system in one dimension reveals a curious spatiotemporal pattern in the motion of interacting pulses. For suitably chosen nonlinearity and parameters, the trajectory of pulses exhibits a self-similar regular pattern like a Sierpinski gasket in the space-time coordinate. This is caused by self-replication of a pulse and annihilation and/or preservation of propagating pulses upon collision. The formation of the Sierpinski gasket can be understood by mapping the time evolution of pulses to an equivalent cellular automaton.