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. Conway’s 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.
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Asynchronous Continuous and MemoryEnriched Automata
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Adamatzky algorithm asynchronous automaton behaviour binary birth blinker block block cellular automaton block oscillator Bruijn diagram cells cellular automata computation constraint programming constructed Conway’s Game dead cells diagonal Diffusion Rule dynamics evolution evolves example Figure finite fleet g1 gliders gates glider guns global GoL rule gosper2 grid Griffeath half-diagonals infinite initial configuration interactions isomorphic kite and dart ladder lattice Life-like cellular automaton Life’s live cells live neighbors live sites logical gates LtL rules measure with density memory neighbourhood nodes links Orthogonal oscillator graph pair parameters patterns Penrose tiling phase transition Phys Physica produced product measure puffer trains quadratic growth quantum qubit random initial read/write head rectangle replicator rhomb shown in Fig shows simulation space spaceships standard collision sequence starting steps structures switch engines symbol symmetric synthesis tape Theorem Turing machine universal universal Turing machine updating vertex vertex configurations width Wolfram