Simple modeling of branching pattern formation in a reaction diffusion system with cellular automaton

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.