Many front propagation problems have been modeled using cellular automata. Some of the best-known examples of which are the "excitable media" which simulate the behavior of nerve cells, muscle cells, cardiac function and chemical

reaction. Here, the domain is broken into a finite number of cells each of which can have only a finite number of states (e.g, excited, refractory and resting). This crude discretization leads to several unwanted grid effects, including low order accuracy, unwanted anisotropy and incorrect front speeds. We discuss fast algorithms that give a much improved approximation of the front location and use a convolution step rather than discrete cell averages to avoid the grid effects prevalent in cellular automata methods. Preliminary studies indicate that the convolution-based approach accurately reproduces quantitative aspects of models (and hence has greater potential for quantitative comparisons to physical or biological data) whereas cellular automata are often only capable of reproducing certain qualitative properties.