Evolving Reaction-Diffusion Systems on GPU

Reaction-diffusion systems contribute to various morphogenetic processes, and can also be used as computation models in real and artificial chemistries. Evolving reaction-diffusion solutions automatically is interesting because it is otherwise difficult to engineer them to achieve a target pattern or to perform a desired task. However most of the existing work focuses on the optimization of parameters of a fixed reaction network. In this paper we extend this state of the art by also exploring the space of alternative reaction networks, with the help of GPU hardware. We compare parameter optimization and reaction network optimization on the evolution of reaction-diffusion solutions leading to simple spot patterns. Our results indicate that these two optimization modes tend to exhibit qualitatively different evolutionary dynamics: in the former, the fitness tends to improve continuously in gentle slopes, while the latter tends to exhibit large periods of stagnation followed by sudden jumps, a sign of punctuated equilibria.