Simple Modeling of Branching Pattern Formation in a Reaction Diffusion System with Cellular Automaton(General)

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In the present paper, I propose a simple generic discretized model for the formation of various patterns based on a reaction-diffusion model of the growth patterns of bacterial colonies. Bacterial colonies show several patterns, with a characteristic pattern being a branching dendritic one with various branch densities. In addition to living systems, these branching patterns can also be observed in physical and chemical systems. Several reaction-diffusion models have been proposed to describe their formation. The model proposed here is a simplified discretized one based on previous models and involves three variables; namely, activators, inactivators, and the substrate. By changing only the mobility of the activators and the initial substrate, the proposed model can reproduce different patterns that are based on the branching patterns. I also investigate the characteristics of the shape and growth rate of the pattern formation.
社団法人日本物理学会の論文
2007-03-15