Self-organized pattern formation and noise-induced control from particle computation

Abstract

We propose a new non-equilibrium model for spatial pattern formation on the basis of local information transfer. Unlike standard models of pattern formation it is not based on the Turing instability. Information is transmitted through the system via particle-like excitations whose collective dynamics result in pattern formation and control. Here, a simple problem of domain formation is addressed by this model in an implementation as stochastic cellular automata. One observes stable pattern formation, even in the presence of noise and cell flow. Noise stabilizes the system through the production of quasi-particles that control the position of the domain boundary. Self-organized boundaries become sharp for large system with fluctuations vanishing with a power of the system size. Pattern proportions are scale-independent with system size. Pattern formation is stable over large parameter ranges with two phase transitions occurring at vanishing noise and increased cell flow.