The spatial Lotka-Volterra (Rosenzweig-MacArthur) model on a 2D lattice: prey reproduce into empty cells; predators eat adjacent prey and reproduce; predators die randomly. Spatial structure produces spiral waves and irregular patches — patterns absent in the mean-field ODE. This is the May (1974) insight: spatial refugia stabilize the system. The phase portrait (right) traces local prey vs predator density, echoing the classical Lotka-Volterra cycle.