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The mod of an oscillator or spaceship is the smallest number of generations that it takes for it to reappear in its original form, possibily subject to some rotation or reflection. The mod of a pattern may be equal to its period, but it may also be a quarter of the period (for oscillators that rotate 90 degrees every quarter period) or half the period (for other oscillators that rotate 180 degrees every half period, oscillators with 180 degree rotational symmetry that rotate 90 degrees every half period, and also for flippers).

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