In 2004, Klavins et al. introduced the use of graph grammars to describe--and to program--systems of self-assembly. It turns out that these graph grammars can be embedded in a graph rewriting characterization of distributed systems that was proposed by Degano and Montanari over twenty years ago. By applying techniques obtained from this observation, we prove a generalized version of Soloveichik and Winfree's theorem on local determinism. We also obtain a canonical method to simulate asynchronous constant-size-message-passing models of distributed computing with systems of self-assembly.