Simple individual—based models of population dynamics and spatial patterns are developed using cellular automata theory. These models assume that individuals within a population are distributed in space and that important interactions among individuals take place over some predefined local scale. Local density dependence in the model produces dynamics that depend on the scale of the dispersal distance. When dispersal occurs over long distances, the population enters a stable limit cycle. However, when colonization is limited to the same local neighborhood where competition is taking place, the spatial and temporal patterns become chaotic. Habitat size also affects the dynamics. Chaotic dynamics become cyclical as habitat size decreased. These results illustrate how a wide array of complex dynamics can arise with simple spatially distributed models and that the resulting dynamics can depend on the habitat size.