Entropically driven agents

Populations of agents often exhibit surprising collective behavior emerging from simple local interactions. The common belief is that the agents must possess a certain level of cognitive abilities for such an emerging collective behavior to occur. However, contrary to this assumption, it is also well known that even noncognitive agents are capable of displaying nontrivial behavior. Here we consider an intermediate case, where the agents borrow a little bit from both extremes. We assume a population of agents performing random-walk in a bounded environment, on a square lattice. The agents can sense their immediate neighborhood, and they will attempt to move into a randomly selected empty site, by avoiding collisions. Also, the agents will temporary stop moving when they are in contact with at least two other agents. We show that surprisingly, such a rudimentary population of agents undergoes a percolation phase transition and self-organizes in a large polymer like structure, as a consequence of an attractive entropic force emerging from their restricted-valence and local spatial arrangement.