Self-organized pattern formation and noise-induced control based on particle computations
Thimo Rohlf, Stefan Bornholdt · Journal of Statistical Mechanics Theory and Experiment · 2005
We propose a new non-equilibrium model for spatial pattern formation based on local information transfer. Unlike most standard models of pattern formation it is not based on the Turing instability or initially laid down morphogen gradients. Information is transmitted through the system via particle-like excitations whose collective dynamics results in pattern formation and control. Here, a simple problem of domain formation is addressed by means of this model in an implementation as stochastic cellular automata, and then generalized to a system of coupled dynamical networks. One observes stable pattern formation, even in the presence of noise and cell flow. Noise contributes through the production of quasi-particles to de novo pattern formation as well as to robust control of the domain boundary position. Pattern proportions are scale independent as regards system size. The dynamics of pattern formation is stable over large parameter ranges, with a discontinuity at vanishing noise and a second-order phase transition at increased cell flow.