Self Organization and Self Avoiding Limit Cycles

摘要

A simple periodically driven system displaying rich behavior is introducedand studied. The system self-organizes into a mosaic of static ordered regionswith three possible patterns, which are threaded by one-dimensional paths onwhich a small number of mobile particles travel. These trajectories areself-avoiding and non-intersecting, and their relationship to self-avoidingrandom walks is explored. Near $\rho=0.5$ the distribution of path lengthsbecomes power-law like up to some cutoff length, suggesting a possible criticalstate.