A Fractal Approach to Pattern Formation in Biological Systems

The paper discusses the connection between pattern formation and nonlinear dynamics, focusing on the similarity between discrete patterns and fractal structures, and then describes different solutions to model reaction-diffusion systems as representative processes in morphogenesis. The option for a discrete model and the steps to design it as a fractal structure is argued. Construction of appropriate generic model is an important step towards understanding the bacteria. It is shown how a pattern with arbitrary complexity like a fractal pattern can be realized by a reaction-diffusion system. A specific example is the diffusion limited aggregation growth process, illustrated by the simulation of the evolution of a bacterial colony that shows the roles of instability and sensitivity in nonequilibrium pattern formation. Key-Words: morphogenesis, pattern formation, reaction-diffusion systems, fractal analysis, attractors, diffusion limited aggregation