This Demonstration shows a neural network evolving under rules similar to those for a four-neighbor outer totalistic cellular automaton. You can sample a variety of evolution rules exhibiting integrate-and-fire-like behavior. Red indicates cellular activity (a neuronal spike) while blue indicates inactivity. Color intensity encodes the value of a binary internal state variable. The weights between each cell and each of its neighbors have been adjusted to reflect Boltzmann-like transition probabilities appropriate for flow in a constant vector field on a torus (the angle of the field is an adjustable parameter in this Demonstration). Each network is initialized with a small region of activity, and neuronal activity patterns spread in ways that reflect the influence of the vector field.