The rules established by Conway seek to mimic the success or demise of life based on environment if the number of live cells in the Moore neighborhood is too high or too low the cell dies due to overcrowding or loneliness but flourishes if the surrounding liveness is optimum. The rules are applied simultaneously to each cell at each time step, called a generation Gardner ( 1970), so that the game is homogeneous in space and time. The game therefore transmits information one cell at a time and is deterministic, its evolution depends solely on the initial state. The system evolves in discrete time steps according to a set of simple rules Gardner ( 1970) which depend only on the number of live cells contained in its 8 surrounding cells, known as the Moore neighborhood Ceccherini-Silberstein and Coornaert ( 2013). Probably the most well-known game is Conway’s classic game of life Gardner ( 1970) (CGOL) based on a two-dimensional (2D) cellular automaton where each cell is either 0 (dead) or 1 (alive). John von Neumann and Oskar Morgenstern are credited with introducing game theory in 1944 Von Neumann ( 1928) Von Neumann and Morgenstern ( 1944) prompting applications in economics, business, and the sciences. Evolutionary outcomes scale in a fractal-like manner. Evolution to the quantum cloud occurs chaotically with floating-point errors providing the butterfly effect. A solitary qutub placed in an otherwise empty universe may act as a seed to reproduce child qutubs, one or more classical and/or semi-quantum lifeforms, oscillators, a quantum cloud or death depending on the initial state. Semi-quantum still-lifes are discovered including the qutub which contains 4 live cells and 4 semi-quantum cells. Transient lifeforms emerge from the cloud. Systems evolve to a “quantum cloud” with a liveness distribution of mean = 0.3480 ± 0.0001 and standard deviation σ = 0.0071 which is dependent solely on the evolutionary rules.
Computer simulation of the SQGOL reveals remarkable complexity and previously unseen game behaviors. The semi-quantum game of life (SQGOL) is an adaptation in which each cell is in a superposed state of both dead and alive and evolves according to modified rules. Conway’s classic game of life is a two-dimensional cellular automaton in which each cell, either alive or dead, evolves according to rules based on its local environment.
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