Emergence and Collapse of Order in Mutually Imitating Agents

A cellular automata (CA)-like model of mutually imitating agents, called imitating cellular automata (ICA), is presented. An agent of the model either imitates a behavior of neighboring agents or takes a random action to compute the next state of its own, based on elementary cellular automata (ECA) rules. When combined with another dynamic that determines an interaction distance to the neighborhood agents, ICA show complex spatiotemporal patterns and travel around between ordered and chaotic phases without being trapped in a fixed state. The patterns were robustly observed across a wide range of parameter values and also found to follow a power-law relationship.