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.

翻译：理解社群中的模式形成一直是各领域关注的焦点。本文提出了一种新颖的模型，称为“信息粒子模型”，该模型基于反应-扩散模型和分布式行为模型。信息粒子驱动物种间的竞争或协调。因此，信息粒子在社交系统中的遍历使得四种不同类别的模式得以表达（即“静态”、“竞争均衡”、“混沌”和“周期”）。值得注意的是，“竞争均衡”很好地表达了宏观均衡、微观非均衡的复杂动力学。尽管这是自然界模式形成中的基本现象，但传统模型尚未能实现。此外，模式的跨类别转变仅取决于系统参数，即物种数量（网络中的顶点）和物种间的距离（边）。这意味着一个信息粒子模型便能在各种环境下通过原位计算成功演化出这些模式。