A life configuration which exhibits a pattern which repeats in n generations is called a pn oscillator. A still life is therefore a period 1 oscillator, and a flip-flop or on-off a period 2 oscillator. The term is usually restricted to unstable finite patterns. In general cellular automaton theory the term "oscillator" usually covers spaceships as well, but this usage is not normal in Life (Silver).

An oscillator is divided into a rotor and a stator. Any oscillator (or spaceship) that forms its mirror image at half its period is called a flipper. Koenig gives an extensive tabulation of oscillators grouped by number of bits and oscillation period.

At the time of writing, the only periods for which no oscillator is known are 19, 23, 27, 31, 37, 38, 41, 43, 49 and 53 (Silver). If we insist that the oscillator must contain a cell oscillating at the full period, then 33, 34, 39 and 51 must be added to this list.

The unique 3-cell oscillator is called the period 2 blinker.

There are no oscillators for 4- and 5- cell Life forms.

6-cell period 2 oscillators are the toad, beacon, and clock.

The only known 8-cell oscillator is the period 2 bipole (barberpole).

The only known 9-cell oscillator is the unnamed period 2 bipole-analog.

The only known 10-cell oscillator is the period 2 quapole bipole-analog.

The only known 11-cell oscillator is the unnamed period 2 bipole-analog.

There are a number of nontrivial 12-cell oscillators, including the period 2 phoenix (the middle 12-cell form in the list below).

The miscellaneous period 2 oscillators are the great on-off, light bulb, negentropy, phoenix, revolver, scrubber, skewed quad, snake pit, spark coil, and traffic light.

Hassler, Inductor, Omniperiodic, Rake, Rotor, Space Dust, Spark, Stator

References

Koenig, H. "Oscillating Objects." http://pentadecathlon.com/LifeInfo/Objects/Class2/Oscillators.html.

Silver, S. A. "Life Lexicon." Release 17, 2000 August 24. http://www.argentum.freeserve.co.uk/lex.htm.