  We derive both the finite and infinite population spatial replicator dynamics
as the fluid limit of a stochastic cellular automaton. The infinite population
spatial replicator is identical to the model used by Vickers and our derivation
justifies the addition of a diffusion to the replicator. The finite population
form generalizes the results by Durett and Levin on finite spatial replicator
games. We study the differences in the two equations as they pertain to a
one-dimensional rock-paper-scissors game.
