A Universal Framework for Self-Replication

Self-replication is a fundamental property of many interesting physical, formal and biological systems, such as crystals, waves, automata, and especially forms of natural and artificial life. Despite its importance to many phenomena, self-replication has not been consistently defined or quantified in a rigorous, universal way. In this paper we propose a universal, continuously valued property of the interaction between a system and its environment. This property represents the effect of the presence of such a system upon the future presence of similar systems. We demonstrate both analytical and computational analysis of self-replicability factors for three distinct systems involving both discrete and continuous behaviors.