Self-Referencing Cellular Automata: A Model of the Evolution of Information Control in Biological Systems

Abstract

Cellular automata have been useful artificial models for exploring how\nrelatively simple rules combined with spatial memory can give rise to complex\nemergent patterns. Moreover, studying the dynamics of how rules emerge under\nartificial selection for function has recently become a powerful tool for\nunderstanding how evolution can innovate within its genetic rule space.\nHowever, conventional cellular automata lack the kind of state feedback that is\nsurely present in natural evolving systems. Each new generation of a population\nleaves an indelible mark on its environment and thus affects the selective\npressures that shape future generations of that population. To model this\nphenomenon, we have augmented traditional cellular automata with\nstate-dependent feedback. Rather than generating automata executions from an\ninitial condition and a static rule, we introduce mappings which generate\niteration rules from the cellular automaton itself. We show that these new\nautomata contain disconnected regions which locally act like conventional\nautomata, thus encapsulating multiple functions into one structure.\nConsequently, we have provided a new model for processes like cell\ndifferentiation. Finally, by studying the size of these regions, we provide\nadditional evidence that the dynamics of self-reference may be critical to\nunderstanding the evolution of natural language. In particular, the rules of\nelementary cellular automata appear to be distributed in the same way as words\nin the corpus of a natural language.\n