Lessons on pattern formation from planet WATOR

It is well known that if reacting species experience unequal diffusion rate s, then dynamics that lead to a constant steady state in a "well-mixed" env ironment can in a spatial setting lead to interesting patterns. In this pap er, we focus on complementary pattern formation mechanisms that operate eve n when the diffusion rates are equal. In particular, we can say that when t he mean-field ODE has an attracting periodic orbit then the stochastic spat ial model will have large-scale spatial structures in equilibrium. We explo re this mechanism in depth through the dynamics of the simulator WATOR. (C) 2000 Academic Press.