Almost oscillator

An almost-oscillator (or almost oscillator, or local oscillator) is a pattern such that every cell in the universe is periodic.

For patterns with finite population, this condition is equivalent to the condition that there exists a period p such that the pattern returns to its original state after p generations, i. e. that it is an oscillator in the usual sense. If patterns with infinite population are allowed, however, the first condition is strictly weaker; there are almost-oscillators that are not oscillators by the usual definition. A (necessarily infinitely-supported) almost-oscillator that never returns to its original state can be said to be a "period-infinity almost oscillator".

The disjoint union of oscillators of infinitely many different periods is a trivial example of an almost-oscillator that is not an oscillator. It is also possible to construct a period-infinity almost-oscillator which has finite population in each generation.