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. A cellular automaton (plural: cellular automata) is a discrete model studied in computability theory and mathematics. ... In a cellular automaton, a finite pattern is called a spaceship if it reappears after a certain number of generations in the same orientation but different position. ...

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.