Moosey wrote:toroidalet wrote:Actually, the lifespan of bounded patterns is the busy beaver function of one of its sides (provided both sides are long enough; the other side can be constant), since there are finite Turing machines.

What would the answer be if Turing machines are not allowed? Just, hypothetically

Well, I just ran some crackpot numbers based on the current 16x16 methuselah results from Catagolue. If each 1K bin on average contains 5/9ths of the number of methuselahs in the previous bin, then if we ran all 2^256 possible 16x16 patterns and distributed them among 1K bins, the last bin that would be likely to have a methuselah in it would be the 329K bin.

Up to now we've found methuselahs that last as long as 47,575 ticks, but according to my very inaccurate math there should be one that lasts almost 330,000 ticks.

Slight changes in assumptions will make huge differences in the estimate of longest-lived 16x16, but it does seem pretty likely that the longest lifespan will be six digits long -- unless some lucky weird mechanism shows up that isn't like the random ash we've seen so far. Maybe there's something based on interacting natural glider guns, for example.