In a cellular automaton, a gun is a pattern with a main part that repeats periodically, like an

oscillator Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum ...

, and that also periodically emits spaceships. There are then two periods that may be considered: the period of the spaceship output, and the period of the gun itself, which is necessarily a multiple of the spaceship output's period. A gun whose period is larger than the period of the output is a pseudoperiod gun. In the

Game of Life ''The Game of Life'', also known as ''Life'', is an 1860 board game by Milton Bradley. Game of Life also often refers to: *Conway's Game of Life, in mathematics, a cellular automaton Game of Life or The Game of Life may also refer to: Games * ' ...

, for every ''p'' greater than or equal to 14, it is possible to construct a

glider Glider may refer to: Aircraft and transport Aircraft * Glider (aircraft), heavier-than-air aircraft primarily intended for unpowered flight ** Glider (sailplane), a rigid-winged glider aircraft with an undercarriage, used in the sport of glidin ...

gun in which the gliders are emitted with period ''p''. Since guns continually emit spaceships, the existence of guns in Life means that initial patterns with finite numbers of cells can eventually lead to configurations with limitless numbers of cells, something that

John Conway John Horton Conway (26 December 1937 – 11 April 2020) was an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made contributions to many branches o ...

himself originally conjectured to be impossible. However, according to Conway's later testimony, this conjecture was explicitly intended to encourage someone to disprove it – i.e., Conway hoped that infinite-growth patterns did exist. Bill Gosper discovered the first glider gun in 1970, earning $50 from Conway. The discovery of the glider gun eventually led to the proof that Conway's Game of Life could function as a

Turing machine A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any computer algori ...

. For many years this glider gun was the smallest one known in Life, although other rules had smaller guns.

References

{{Conway's Game of Life Cellular automaton patterns