A CELLULAR AUTOMATON MODEL OF EXCITABLE MEDIA .2. CURVATURE, DISPERSION, ROTATING WAVES AND MEANDERING WAVES

A cellular automaton model of excitable media, recently introduced by the authors, is examined in more detail here. We show that (i) the model is consistent with a linear dependence of wave speed on wave-front curvature in two-dimensional space, (ii) the model exhibits a stepwise increasing relation between wave speed and temporal period (the "dispersion" relation), whose precise shape can be controlled by parameter settings, (iii) the model generates rigidly rotating spiral waves whose frequency, speed, and core size are consistent with theoretical expectations, and (iv) spiral wave solutions may also rotate non-rigidly, showing short-term "flowerlet" meandering which seems to arise by bifurcation from the rigidly rotating solution, and long-term irregular "wandering" over large distances. These observations are consistent with many known features of wave propagation in two-dimensional, continuous excitable media governed by reaction-diffusion equations, suggesting that our cellular automaton model is not only a fast but also a reliable method for investigating the behavior of excitable media.