Conway's Game of Life finally proven to be omniperiodic after 54 years

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28 pointsAlanZucconi6 comments

I could not find any definition for “omniperiodic”.

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

How are these new periodic functions p19 and p41 different from those that came before. It seems like there many other previous cases of Omniperiodicity.

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

So how exactly does finding a 41p state prove omniperiodicity?

It was already known that periods of all other lengths were possible. 41 was the last remaining length that wasn't known to be possible.

Sad he did not live to see it due to Covid.

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