# Oscillator

An **oscillator** is a pattern that is a predecessor of itself. That is, it is a pattern that repeats itself after a fixed number of generations (known as its period). The term is usually restricted to finite patterns that are not still lifes, though still lifes may be thought of as oscillators with period 1. An oscillator is divided into a rotor (the individual cells that actually oscillate) and a stator (the cells which remain alive throughout its whole period).

Cellular automaton theory recognizes shift periodicity, which refers to a configuration reappearing in shifted form after a lapse of one or more generations. Without the shift, it is an oscillator, but if it moves it would be called a spaceship.

## Important oscillators by period

A list of the first-discovered oscillator of each period,^{[1]} as well the current smallest-known oscillator of that period,^{[2]} is provided here. Note that only non-trivial oscillators are considered here, in the sense that there must be at least one cell that oscillates at the full period (i.e. the overall pattern must have a nonzero strict volatility). In some cases, it is not known for certain what the first-discovered oscillator of a given period is, and in such situations all possible candidates are listed.

For any period 61 or greater an oscillator can be constructed using the Herschel track method. In April, 2013 Mike Playle found a small 90-degree stable reflector known as the Snark that allows oscillators of all periods 43 or greater to be constructed.

The lowest population for which an infinite number of non-trivial oscillators are known to exist is 29, as two 12-cell pentadecathlons can reflect a 5-cell glider back and forth indefinitely in the correct position. The smallest example of this is the p60 glider shuttle, with period-180, 300, and all other periods of the form 120n+60 possible with no extra cells required.

## Flipper

A **flipper** is any oscillator that forms its mirror image halfway through its period. For example, see p60 toad flipper.

## Notes

- ↑
^{1.0}^{1.1}^{1.2}^{1.3}^{1.4}^{1.5}^{1.6}^{1.7}^{1.8}Non-trivial oscillators of this period could have been constructed from two oscillators of lower period (usually sparkers), both of which were known by an earlier date. However, no such LCM oscillators were attested prior to the discovery of this oscillator.

## References

- ↑ Dean Hickerson's oscillator stamp collection. Retrieved on April 11, 2009.
- ↑ Jeremy Tan (July 3, 2021). Re: Smallest Known Oscillators to p106 (and Beyond) (discussion thread) at the ConwayLife.com forums
- ↑ Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums

## See also

- List of common oscillators
- Flipping oscillators (category)
- Oscillators (category)
- Omniperiodic
- Table of oscillators by period
- Prime-period oscillators
- Oscillator periods status table
- Almost oscillator
- Oscillizer - analyze and get vital statistics for an oscillator

## External links

- Oscillator at Wikipedia

- Oscillator at the Life Lexicon

- Flipper at the Life Lexicon

### Forum threads

- Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums

- Smallest Known Oscillators to p106 (and Beyond) (discussion thread) at the ConwayLife.com forums

- First Known Oscillators for Each Period (discussion thread) at the ConwayLife.com forums