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Conway's Game of Life (GOL for short) is a game created by John Horton Conway in the late-middle 20th century[1][2] and is an example of a very complex system arising from a set of simple rules. The rules of GOL dictate how squares are turned "on" or "off" in an infinite arena of squares over time, where one set of changes is called a "generation".

Every square in this grid of squares is surrounded by eight squares. The number of switched on squares in this eight-square ring is called the "count". There are three rules that dictate the cells' status:[3]

1. Death: if the count is less than 2 or greater than 3, the current square is switched off.
2. Survival: if the count is exactly 2 or 3 and the current square is on, the current square is left unchanged.
3. Birth: if the current square is off and the count is exactly 3, the current square is switched on.

These simple rules allow a great variety of structures and behaviors to manifest in the Game of Life, which are being extensively researched.[4][5][6] These patterns include a prime-number calculator[7][8] as well as a simulation of GOL itself in GOL.[9][10] The Game of Life is also Turing-complete, which means that any function computable on a finite-state Turing machine can also be computed in GOL.[11][12]

In the Game of Life, there is a fastest speed activated squares may spread, referred to as the "speed of light"[13] and is used to describe the speed of periodic structures such as the glider[14] or spaceships in general.[15] For example, a glider move one cell diagonally every 4 generations, so its speed is denoted c/4.

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