Oscillator (cellular automaton)

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. Depending on context, the term may also include spaceships as well.

An oscillator is considered non-trivial if it contains at least one cell that oscillates at the necessary period. This means, for example, the mere juxtaposition of a period-17 oscillator and a period-4 oscillator is not a period-68 oscillator.

This article by default considers non-trivial oscillators in Conway's Game of Life, though this concept generalizes to all cellular automata.

The smallest number of generations it takes before the pattern returns to its initial condition is called the period of the oscillator. An oscillator with a period of 1 is usually called a still life, as such a pattern never changes. Sometimes, still lifes are not taken to be oscillators. Another common stipulation is that an oscillator must be finite.