In spatial computing, there is a fundamental tension between discrete and continuous models of computation: computational devices are generally discrete, yet it is often useful to program them in terms of the continuous environment through which they are embedded. Aggregate programming models for spatial computers have attempted to resolve this tension in a variety of different ways, generating a profusion of approaches that are difficult to compare or combine. Recently, however, two minimal models have been proposed: continuous space-time universality and a discrete field calculus. This paper unifies these two models by proving that field calculus is space-time universal, and thus provides the first formal connection between continuous and discrete approaches to spatial computing.