  Understanding the pattern formation in communities has been at the center of
attention in various fields. Here we introduce a novel model, called an
"information-particle model," which is based on the reaction-diffusion model
and the distributed behavior model. The information particle drives competition
or coordination among species. Therefore, a traverse of information particles
in a social system makes it possible to express four different classes of
patterns (i.e. "stationary", "competitive-equilibrium", "chaotic", and
"periodic"). Remarkably, "competitive equilibrium" well expresses the complex
dynamics that is equilibrium macroscopically and non-equilibrium
microscopically. Although it is a fundamental phenomenon in pattern formation
in nature, it has not been obtained by conventional models. Furthermore, the
pattern transitions across the classes depending only on parameters of system,
namely, the number of species (vertices in network) and distance (edges)
between species. It means that one information-particle model successfully
develops the patterns with an in-situ computation under various environments.
