In a cellular automaton

Cellular automaton

A cellular automaton is a discrete model studied in computability theory, mathematics, physics, complexity science, theoretical biology and microstructure modeling. It consists of a regular grid of cells, each in one of a finite number of states, such as "On" and "Off"...

, a gun is a pattern with a main part that repeats periodically, like an oscillator

Oscillator (CA)

In a cellular automaton, an oscillator is a pattern that returns to its original state, in the same orientation and position, after a finite number of generations. Thus the evolution of such a pattern repeats itself indefinitely...

, 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

Conway's Game of Life

The Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970....

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

Glider (Conway's Life)

The glider is a pattern that travels across the board in Conway's Game of Life. It was first discovered by Richard K. Guy in 1970, while John Conway's group was attempting to track the evolution of the R-pentomino. Gliders are the smallest spaceships, and they travel diagonally at a speed of c/4...

 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

John Horton Conway is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory...

 himself originally did not believe was possible. Bill Gosper

Bill Gosper

Ralph William Gosper, Jr. , known as Bill Gosper, is an American mathematician and programmer from Pennsauken Township, New Jersey...

 discovered the first glider gun (and, so far, the smallest one found) 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

Turing machine

A Turing machine is a theoretical device that manipulates symbols on a strip of tape according to a table of rules. Despite its simplicity, a Turing machine can be adapted to simulate the logic of any computer algorithm, and is particularly useful in explaining the functions of a CPU inside a...

.