Game of Life Cellular Automata In the late 1960s British mathematician John Conway invented a virtual mathematical machine that operates on a two dimensional array of square cell. Each cell takes two states live and dead. The cells states are updated simultaneously and in discrete time. A dead cell comes to life if it has exactly three live neighbours. A live cell remains alive if two or three of its neighbours are alive otherwise the cell dies. Conways Game of Life became the most programmed solitary game and the most known cellular automaton. The book brings together results of forty years of study into computational mathematical physical and engineering aspects of The Game of Life cellular automata. Selected topics include phenomenology and statistical behaviour space time dynamics on Penrose tilling and hyperbolic spaces generation of music algebraic properties modelling of financial markets semi quantum extensions predicting emergence dual graph based analysis fuzzy limit behaviour and threshold scaling evolving cell state transition rules localization dynamics in quasi chemical analogues of GoL self organisation towards criticality asynochrous implementations. The volume is unique because it gives a comprehensive presentation of the theoretical and experimental foundations cutting edge computation techniques and mathematical analysis of the fabulously complex self organized and emergent phenomena defined by incredibly simple rules.