A recurrent topic of interest in the theory of automata has been the possibility of self-reproducing automata, particularly those which could reproduce globally through an application of a algorithm. In such a device, the "growth" at any point would depend at any time only on the local environment, but overall effect would be the reproduction of complex structures. This paper gives an algorithm of this type (an extension of an algorithm brought to my attention by Professor Fredkin) and examines the conditions under which such replication will occur. The system on which it operates will be defined, and the main theorem on its operation will follow several lemmas.
