It's not possible to have an oscillator in Conway's Game of Life that has just one cell that oscillates on and off, and the rest of it is a still life: "It is easy to see that any rotor cell must be adjacent to another rotor cell." (Life Lexicon)
(Maybe this is philosophically interesting.)
Therefore, the smallest oscillators have two oscillating cells: Beacon (diagonal pair), Test tube baby (domino rotor).
Is there a pattern in which two oscillating cells alternate back and forth which one is on?
What's a different rule that permits one-cell rotors?
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