Dynamics of Defect Ensembles in One-Dimensional Cellular Automata

摘要

We investigate the dynamics of ensembles of defects in one-dimensionaldeterministic cellular automata. In individual confinement the motions from disordered initial state are perfect random walks as shown in a 1992 paper by the author. Here we give a natural condition guaranteeing this also in the presence of other defects. Simple branching and birth mechanisms are introduced, and prototype classes of 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 becomes transparent from this analysis.