A model for realizing ant-inspired algorithms that coordinate robots within a fixed, geographically constrained environment is proposed and illustrated. The model, dubbed Cellular ANTomata, inverts the relationship between ant-robots and the environment that they navigate: intelligence now resides in the environment rather than in the ants. The Cellular ANTomaton model is illustrated via three proof-of-concept problems: having ants `park` in the nearest corner; having ants seek `food items` (both with and without impenetrable obstacles); having a single ant thread a maze. In all cases, `unintelligent` Cellular-ANTomata-based ant-robots accomplish goals provably more efficiently than traditional `intelligent` ant-robots can; indeed, `intelligent` ant-robots cannot park at all! All of the presented algorithms are scalable and distributed: they provably work within any finite-size environment, and they require no central clock (so they are buildable).