Chaos and diffusion in deterministic cellular automata

Abstract It is shown that some of the deterministic one-dimensional cellular automata studied recently by Wolfram exhibit a kind of spontaneous symmetry breaking. The associated kinks (Bloch walls) perform annihilating diffusive walks, for infinite lattices and large times. In addition, close analogies between these automata and strange attractors are exhibited, by mapping the automata onto dynamical systems defined by iterations of the unit square.