Post
by hotdogPi » January 29th, 2022, 2:03 pm
Wyirm wrote: ↑January 29th, 2022, 1:56 pm
Ther Moore neighborhood contains 8 neighbors, each of which can be 0 or 1, with 51 possible combinations with permute symmetry, and 2^102 possible combinations for all isotropic non-totalistic cellular automaton. 5070602400912917605986812821504 possible combinations of rulesets, we don't care about the ones with b1c because periodicity cannot exist, so 2535301200456458802993406410752 rules we care about in total. Without permutations, there are 2^9 possible inputs, or 512. 512*2 = 1024, 2^1024 = 179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216
Soups are usually done with permutations and symmetries, but we don't have to think about permutations or symmetries if we are doing rules without them. so, with an 8x8 soup, we have 64 points, and 18446744073709551616 possible soups, with a ridiculous number of rules to search in, I think we can definitively say, we will never run out of soups to search, and there is an oscillator of every period, and a spaceship of every speed.
While that number is huge, it's still finite. That means we cannot find an oscillator of every period via 16×16 soup searching.
User:HotdogPi/My discoveries
Periods discovered: 5-16,⑱,⑳G,㉑G,㉒㉔㉕,㉗-㉛,㉜SG,㉞㉟㊱㊳㊵㊷㊹㊺㊽㊿,54G,55G,56,57G,60,62-66,68,70,73,74S,75,76S,80,84,88,90,96
100,02S,06,08,10,12,14G,16,17G,20,26G,28,38,44,47,48,54,56,72,74,80,92,96S
217,300,486,576
S: SKOP
G: gun
