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. 1 Overview and History 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 [1]. 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, continuous 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. Subsequently, we demonstrate both analytical and computational analysis of self-replicability factors for three distinct systems involving both discrete and continuous behaviors. Two prominent issues arise in examining how self-replication has been handled when trying to extend the concept universally: how to deal with non-ideal systems and how to address so-called ‘trivial’ cases [2,3]. Moore [4] requires that in order for a configuration to be considered self-reproducing it must be capable of causing arbitrarily many offspring; this requirement extends poorly to finite environments. Lohn and Reggia [5] put forward several cellular-automata (CA) -specific definitions, and result in a binary criterion. A second issue that arose in the consideration of selfreplicating automata was that some cases seemed too trivial for consideration, such as an ‘all-on’ CA, resulting in a requirement for Turing-universality [6]. The definition for self-replicability we propose here is motivated in part by (a) A desire to do more than look at self-replication as a binary property applicable only to certain automata, and, (b) The goal of encapsulating a general concept in a means not reliant upon (but compatible with) ideal conditions. We wish to do this by putting self-replication on a scale that is algorithmically calculable, quantifiable, and continuous. Such a scale would allow for comparisons, both between the same system in different environments, determining ideal environments for a system’s replication, as well as between different systems in the same environment, if optimizing replicability in a given environment is desired. Rather than viewing self-replicability as a property purely of the system in question, we view it as a property of the interaction between a system and its environment. Self-Replication, as we present it, is a property embedded and based upon information, rather than a specific material framework. We construct replicability as a property relative to two different environments, which indicates the degree to which one environment yields a higher presence of the system over time. Self-replicability, then, is a comparison between an environment lacking the system and an environment in which the system is present. We will first introduce a number of definitions, and then give examples of replicability of three types of systems.