In Conway's Game of Life, there exist "periodic" patterns for all n>0 such that the n-th pattern has n distinct states which repeat in a loop.
A jargon-heavy history of the problem: https://conwaylife.com/wiki/Omniperiodic
A jargon-heavy history of the problem: https://conwaylife.com/wiki/Omniperiodic
Edit: ok so it seems they had solved for certain periods above some numbers but not for all periods - this month saw the last two being found.
The link has more https://conwaylife.com/wiki/Oscillator