Game of Life

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Conway's Game of Life (often simply Life) is a cellular automaton invented by John Horton Conway in 1970. It is notable for its complex and diverse emergent behaviour compared to other cellular automata, and the relative ease in which powerful artificial constructions (such as Turing machines) can be constructed within it.

It is universal (the cellular automaton analogue of Turing-completeness), and was proven to have a self-replicating pattern in 2010 with the discovery of the Gemini pattern. The fact that this pattern eluded construction for so long is surprising (although that one was incredibly likely to exist had been known for decades), as many other cellular automata of similar complexity have very trivial self-replicators; Gemini, on the other hand, is incredibly complex (with a bounding box of 4217807 by 4220191 cells).

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