Turing Patterns and Excitable Media

Summary

In this chapter it has been shown by means of a Turing-type and an excitable interaction that CA are well suited to model and analyze pattern formation dynamics in reaction-diffusion systems. The presented CA models are basic modules that can be extended to include more particle types, further interactions, and other boundary conditions. Trying to understand the precise relations between particle-based models (e.g., LGCA) and continuous approaches (e.g., partial differential equations) leaves many challenging problems for the future.