The stochastic Greenberg-Hastings cellular automaton is a model that mimics the propagation of reaction-diffusion waves in active media. Notably, this model undergoes a phase transition when the probability of excitation of a cell varies. We developed a specific FPGA design to study the critical behavior of this model. Using dedicated architectural optimizations, we obtain a significant speed-up with respect to software simulation for lattice sizes of 512×512. We exploited this speed-up to obtain improved estimations of the critical threshold.Our results indicate the existence of an asymptotic value of this threshold when the number of cell states increases.