Universal self-replication using graph grammars

A graph grammar is described that can be used to replicate arbitrarily labeled strands of particles (modeled as linear graphs). The rules of the grammar dictate how pairs of particles should attach or disassociate upon random collisions, and thus describes a parallel and completely distributed algorithm for replication. The correctness of the algorithm is proved and the rate at which replication occurs is characterized. The algorithm may be applied to systems of programmable parts (stirred or agitated in a fluid) that can encode the (very simple) rules of the grammar and that can attach and dis-attach to create strands and other structures.