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.