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The Game of Life is an example of what is called a cellular automaton. These are mathematical experiments on the effects simple rules can have when applied at a large scale. They consist of a matrix of cells, each of which can have any one of a finite number of states, and whose state may change from one 'generation' to the next, depending on its state and that of the cells around it.

Cellular automata are interesting for several reasons. One is that they are a demonstration of chaos theory, which states that miniscule changes can produce profound and wide-ranging effects, and of emergent complexity, which states that very simple rules can lead to very complex and unpredictable situations.

Another is that they are in fact Turing machines – given an input, they will perform a specific operation, perhaps producing an output. Some cellular automata, including the Game of Life, can be shown to be universal Turing machines capable of emulating other universal Turing machines.

The Game of Life, as discussed here, was devised by John Horton Conway, a professor of mathematics at Cambridge University. He chose its rules such that it would not be too easy to predict how any pattern would evolve. Although the rules were specifically chosen for this effect, it is remarkable how unpredictable Life really is.

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