Emergence in the Game of Life

William Sulis
McMaster University

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Abstract
Emergence in the Game of Life
William Sulis
McMaster University, Ontario, Canada
sulisw@mcmaster.ca

Conway’s Game of Life provides a classic example of emergence in a formal model of a complex system. In this emergent situation certain configurations of Life patterns can be arranged so as to simulate the flow of bits through a configuration of logic gates. Archetypal dynamics, a formal framework for understanding emergence through a study of information flows in complex systems, is applied to this particular emergent situation. Archetypal dynamics describes a complex system as a tapestry ( “observations” ) evolving via a two player combinatorial game ( “dynamics”) whose players, Proposer and Disposer, extend the tapestry using constructor tapestries ( “actions” ) subject to constraints provided a by a formal tapestry ( “context/rule space/symmetries” ). Complete reality games are exhibited for the Game of Life and for systems of logic gates. These are shown to be mutually irreducible. Two complete tapestries are exhibited for the emergent situation and it is shown that these tapestries evolve in a manner consistent either with Life or the logic gate game. This emergent situation in Life arises through the presence of an ambiguous subsystem, one that admits two complete descriptions that evolve under mutually irreducible games.