Emergent phenomena in large sparse random arrays of Conway's 'Game of Life'

Abstract

This paper describes some well-defined types of emergence that occur in a class of large, initially random arrays of a well-known binary cellular automaton, Conway's 'Game of Life'. Results concerning the existence or non-existence of finite patterns with particular properties are used to advance the global analysis. It is shown that in infinite (and very large finite) arrays of the Game of Life with initially sparse and randomly distributed non-uniformities, self-organized construction processes will lead to the emergence of coherent structures which have crucial effects on the medium-term dynamics of the array. Directions for future research are suggested.