Despite the prevalence of deep neural networks, their single most cited drawback is that, even when successful, their operations are inscrutable. For many applications, the desired outputs are the composition of externally-defined bases. For such decomposable domains, we present a two-stage learning procedure producing combinations of the external bases which are trivially extractable from the network. In the first stage, the set of external bases that will form the solution are modeled as differentiable generator modules, controlled by the same parameters as the external bases. In the second stage, a controller network is created that selects parameters for those generators, either successively or in parallel, to compose the final solution. Through three tasks, we concretely demonstrate how our system yields readily understandable commands. In one, we introduce a new form of artistic style transfer, learning to draw and color with crayons, in which the transformation of a photograph or painting occurs not as a single monolithic computation, but by the composition of thousands of individual, visualizable strokes. The other two tasks, single-pass function approximation with arbitrary bases and shape-based synthesis, show how our approach produces understandable and extractable actions in two disparate domains.