The dynamical behavior of species competing for a common resource is studie
d with a reaction-diffusion system based on cubic autocatalysis. Randomly s
eeded populations self-segregate to from a complex network of domains separ
ated by distinct interfaces. For chaotic populations in one-dimensional med
ia, the interfaces exhibit irregular motions on long time scales. In two-di
mensional media. the interface motions are governed by curvature-induced dr
ift.