We introduce a new theoretical model of ad hoc mobile computing in which agents have severely restricted memory, highly unpredictable movement and no initial knowledge of the system. Each agent’s memory can store O(1) bits, plus a unique identifier, and O(1) other agents’ identifiers. Inputs are distributed across n agents, and all agents must converge to the correct output value. We give a universal construction that proves the model is surprisingly strong: It can solve any decision problem in NSPACE(n log n). Moreover, the construction is robust with respect to Byzantine failures of a constant number of agents.