The dynamics of defect ensembles in one-dimensional cellular automata

We investigate the dynamics of ensembles of diffusive defects in one-dimensional deterministic cellular automata. The work builds on earlier results on individual random walks in cellular automata. Here we give a natural condition guaranteeing diffusive behavior also in the presence of other defects. Simple branching and birth mechanisms are introduced and prototype classes of cellular automata exhibiting weakly interacting walks capable of annihilation and coalescence are studied. Their equilibrium behavior is also characterized. The design principles of cellular automata with desired diffusive interaction properties become transparent from this analysis.