A cellular automaton is developed for simulating excitable media. First, general
"masks" as discrete approximations to the diffusion equation are examined, showing how
to calculate the diffusion coefficient from the elements of the mask. The mask is then combined
with a thresholding operation to simulate the propagation of waves (shock fronts)
in excitable media, showing that (for well-chosen masks) the waves obey a linear "speedcurvature"
relation with slope given by the predicted diffusion coefficient. The utility of different
masks in terms of computational efficiency and adherence to a linear speed-curvature
relation is assessed. Then, a cellular automaton model for wave propagation in reaction
diffusion systems is constructed based on these "masks" for the diffusion component and
on singular perturbation analysis for the reaction component. The cellular automaton is
used to model spiral waves in the Belousov-Zhabotinskii reaction. The behavior of the spiral
waves and the movement of the spiral tip are analyzed. By comparing these results to
solutions of the Oregonator PDE model, the automaton is shown to be a useful and efficient
replacement for the standard numerical solution of the PDE's.
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