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Large-scale Simulations on FPGAs: Finding the Asymptotic Critical Threshold of the Greenberg-Hastings Cellular Automata
Nikolaos Vlassopoulos, Nazim Fates, Hugues Berry and Bernard Girau

The stochastic Greenberg-Hastings cellular automaton is a model that mimics the propagation of reaction-diffusion waves in an active medium. Notably, this model undergoes a phase transition from an “alive” state to a “dead” state when the probability of excitation of a cell varies.We develop a specific Field Programmable Gate Array (FPGA) design to study the critical behaviour of this model. Using dedicated architectural optimisations, we obtain a significant speed-up with respect to software simulation for lattice sizes of 512 × 512. We exploit this speed-up to obtain improved estimations of the critical threshold. Our results indicate the existence of a non-trivial asymptotic value of this threshold when the number of cell states increases.

Keywords: Stochastic Greenberg-Hastings Cellular Automata, Field Programmable Gate Array Simulations, Reaction-Diffusion Media, Parallel Computing Device

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