Simple Modeling of Branching Pattern Formation in a Reaction Diffusion System with Cellular Automaton
Ikuko N. Motoike · Journal of the Physical Society of Japan · 2007
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.