Large-scale Simulations on FPGAs: Finding the Asymptotic Critical Threshold of the Greenberg-Hastings Cellular Automata

Nikolaos Vlassopoulos (1) , Nazim Fatès (1) , Hugues Berry (2, 3) , Bernard Girau (4)

1 MAIA - Autonomous intelligent machine
2 Inria Grenoble - Rhône-Alpes
3 COMBINING - COMputational BIology and data miNING
4 CORTEX - Neuromimetic intelligence

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 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.

Domaines: Automates cellulaires et gaz sur réseau [nlin.CG]

Nikolaos Vlassopoulos, Nazim Fatès, Hugues Berry, Bernard Girau. Large-scale Simulations on FPGAs: Finding the Asymptotic Critical Threshold of the Greenberg-Hastings Cellular Automata. Journal of Cellular Automata, 2012, 7 (1), pp.5-29. ⟨hal-00644660⟩