Diffusion and Wave Propagation in Cellular Automaton Models of Excitable Media
Weimar, Joerg Richard
Tyson, John J.
Watson, Layne T.
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In this paper, the authors (1) examine general "masks" as discrete approximations to the diffusion equation, showing how to calculate the diffusion coefficient from the elements of the mask; (2) 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; and (3) assess the utility of different masks in terms of computational efficiency and adherence to a linear speed-curvature relation.