User:Tropylium/Generator

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A generator of a periodic pattern is a set of cells that is equal to the set of its parent cells one period ago.

Oscillators

Trivially, every stator cell (incl. every cell of a still life) is a generator of itself; and out of stator cells, only bushing cells can possibly be a part of the rotor's generator.

An oscillator that has no other generator cells may be called stator-generated. If the bare stator is a precedessor of the oscillator, it may be called naturally stator-generated. A special case of this are oscillators where the rotor comprises only off cells in one of the phases (e.g. on-offs).

Spaceships

The glider's generator is the alternating L/Z tetromino; the same generator reappears in many c/4 diagonal spaceships, such as Orion or Swan (both times in some phases as a part of a larger polyomino).

The generator of other standard spaceships is the alternating I trimino/T tetromino; this appears in most other c/2 spaceships as well.

A T-tetromino-based generator appears in many (most?) c/4 orthogonal spaceships.