DIFFUSION AND WAVE-PROPAGATION IN CELLULAR AUTOMATON MODELS OF EXCITABLE MEDIA

(1) We examine general "masks" as discrete approximations to the diffusion equation, showing how to calculate the diffusion coefficient from the elements of the mask. (2) We combine the mask with a thresholding operation to simulate the propagation of waves in excitable media, showing that (for well-chosen masks) the waves obey a linear "speed-curvature" relation with slope given by the predicted diffusion coefficient. (3) We assess the utility of different masks in terms of computational efficiency and adherence to a linear speed-curvature relation.