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 . Depending on context , the term may also include spaceships as well . 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 . In Conway 's Game of Life , finite oscillators are known to exist for almost any period . The exceptions are 19 , 23 , 31 , 37 , 38 , 41 , 43 , and 53 . It is not known whether oscillators of those periods exist , but it is strongly believed that they do . Additionally , while oscillators exist for periods 34 and 51 , the only known examples are considered trivial because they consist of essentially separate components that oscillate at smaller periods . For instance , one can create a period 34 oscillator by placing period 2 and period 17 oscillators so that they do not interact . An oscillator is considered non-trivial if it contains at least one cell that oscillates at the necessary period . Examples the smallest one period 3 period 3 period 3 period 4 period 4 octagon , period 5 period 5 period 5 period 15 External links A collection of oscillators in the Game of Life ( zip file ) Categories : Cellular automata In other languages : Français 