Crystallization and tile separation in the multi-agent systems

• We consider large populations of mobile agents coupled by binary interactions.
• We study the emergence of order by only changing the interaction rules.
• We show the formation 2D hexagonal or rectangular multi-agent crystals.
• We also show the complete separation of agents in regular hexagonal tiles.

This paper deals with the self-organization of simple mobile agents confined in a two-dimension rectangular area. Each agent interacts with its neighbors inside an interaction disk and moves following various types of force-driven couplings (e.g. repulsion or attraction). The agents do not know their absolute position, do not exchange messages, have no memory, and no learning capabilities. We first study the self-organization appearing in systems made-up with one sole type of agents, initially generated at random in the terrain. By changing the agent–agent repulsive interaction, we observe five different population reorganizations, namely, grouping, diffusion (that is classical), but especially interesting, crystallization (i.e., the agents group together on the vertices a regular hexagonal lattice), alignment along straight lines, and vortex dynamics. Then, we consider reorganization in systems made-up from two to five types of agents, where each pair of agent types has specific interaction parameters. The main result of this work is to show that, by only changing the agent–agent repulsion rules, one can generate hexagonal or rectangular multi-agent crystals or on the contrary, induce complete separation in regular hexagonal tiles.