Kazyan wrote:Omniperiodicity is the big one, in my opinion--the question of whether there exists a oscillator for every possible period. Herschel conduits prove the existence of p58 and above, and snark loops prove p43 and above. Almost every period between p1 and p42 also has an example, except for p19, p34 (only trivial examples), and p38.
A p19 oscillator is the past piece of the puzzle to show that Life is sort of omniperiodic; a trivial p38 could be constructed from the p19 and a blinker. To show true omniperiodicity, however, one would need to provide a p19, p34, and p38 that have a cell that cycles at the full period.
Tom Mazanec wrote:Are there any interesting unproven conjectures in the Game of Life?
Majestas32 wrote:You forgot p23 and p41.
Tom Mazanec wrote:dvgrn
I thought conjectures by definition were things unknown, if suspected, or I would have checked the Did you know[s]
Tom Mazanec wrote:How about things where we don't even have a conjecture as to the answer, much less a theorem?
simsim314 wrote:Tom Mazanec wrote:How about things where we don't even have a conjecture as to the answer, much less a theorem?
I've demonstrated the concept of constructible ship of any speed and direction - but the period of the constructed speed is extremely high. It's completely unknown and we don't have any clue whether there exists ships with relatively low period and very high speed...
Macbi wrote:I think the existence of a (2,1)c/6 knightship is also pretty difficult to guess. A least for omniperiodicity you can imagine finding a fast signal-turner and therefore being able to build oscillators of all periods. But I see no way at all to build a max-speed knightship with any kind of technology. You just have to hope one appears.
calcyman wrote:I counter-conjecture Dave's claim about the existence of a 16x16 Methuselah with a stabilisation time exceeding 10^9. I strongly believe such patterns do exist.
As evidence, there's a b38s23/C1 soup which takes 750 000 ticks to stabilise, and it's entirely conceivable that analogous patterns exist in b3s23. 2^256 is a very large number, after all.
The simplest version of that kaleidoscope-maker [~19.7M ticks to settle] takes a similar length of time to stabilize [~17.7M ticks]:Code: Select allx = 60, y = 60, rule = B3/S23
21bo16bo$20bobo14bobo2$20bo2bo12bo2bo$22b2o12b2o$23bo12bo15$bobo52bobo
$o58bo$bo2bo50bo2bo$3b3o48b3o13$3b3o48b3o$bo2bo50bo2bo$o58bo$bobo52bob
o15$23bo12bo$22b2o12b2o$20bo2bo12bo2bo2$20bobo14bobo$21bo16bo!
Now I'm thinking about the umpteen gazillion ways of scattering, say, no more than eighty cells' worth of still lifes symmetrically in the center of the above circle. I bet the time to stabilization follows some kind of interesting power-law distribution... so there should be an occasional arrangement that runs billions of ticks before stabilizing.
I was going to postulate a trillion-tick kaleidoscope, but it would take a Catagolue-sized effort to locate that, I suppose.
calcyman wrote:Also, there's a 'lucky 1-engine Cordership' where a c/12 universal constructor or swarm of diagonal Caterloopillars chases a block-laying switch engine and removes its debris. You'll need some very arbitrary definition to disallow that as a 'switch engine with complicated clean exhaust'.
dvgrn wrote:calcyman wrote:Also, there's a 'lucky 1-engine Cordership' where a c/12 universal constructor or swarm of diagonal Caterloopillars chases a block-laying switch engine and removes its debris. You'll need some very arbitrary definition to disallow that as a 'switch engine with complicated clean exhaust'.
Yes... but... 2^256 may be a very big number, but it's not nearly big enough to have any realistic chance of including any Caterloopillar or universal-constructor predecessors. I think you're meaning that we can't rule out the possibility that there's a lucky one-engine Cordership with a smallish exhaust eater that happens to have a 16x16 predecessor. That's certainly true. On the other hand, it's also equally (!?) possible that no such thing exists. In the absence of an example it's hard to assign probabilities either way.
dvgrn wrote:-- I did think for a good while about that 10^9 number. My original statement was just "no 16x16 methuselah takes more than a million ticks to stabilize" -- but I wasn't at all confident about that one.
After some discussion of methuselah power laws with Nathaniel way back in 2009, for 20x20 soups, the rough guess we came up with was that the most long-lived 20x20 "normal methuselah" (that just makes a large patch of random ash) would end up lasting something like 200,000 to 500,000 ticks. That's way too close to a million for comfort, though 20x20 is a lot bigger than 16x16.
Jumping up to a billion-tick limit makes it pretty sure that any super-long-lasting methuselah won't be a simple random-ash generator. Instead it will probably be something that produces occasional gliders aimed at some central junk, to keep chaos going as long as possible.
The likeliest arrangement might be a 16x16 predecessor of a pattern vaguely along the following lines. (This is from an offline discussion of "soup eye candy" with Bill Gosper in May 2015.)
calcyman wrote:dvgrn wrote:Yes... but... 2^256 may be a very big number, but it's not nearly big enough to have any realistic chance of including any Caterloopillar or universal-constructor predecessors. I think you're meaning that we can't rule out the possibility that there's a lucky one-engine Cordership with a smallish exhaust eater that happens to have a 16x16 predecessor... (?)
That statement (beyond the 'Also,') was in reference to your sixth question, which didn't impose any size restrictions whatsoever (other than there being <= 2 switch-engines in the construction).
calcyman wrote:With the possible exception of the small true-period p14 glider gun; I see no reason why it should exist.
calcyman wrote:if the frequency of a backward-glider-emitting puffer in b3s23/C1 is 2^-50 -- which I think is pessimistic -- then we can expect about 2^150 soups with two perpendicular backward-glider-emitting puffers. I'd be very surprised if none of these happen to last for over 10^9 ticks.
#C nikk-nikkm1r90-w4s164
x = 38, y = 198, rule = S23/B3
6bo$5bobo$$4bobbo$4boo$4bo25$34bobo$37bo$33bobbo$32b3o131$28bo3bo$29bo
bo$30bobbo$33bo$33bo24$o$bo$bbo$bo$o$bb3o!
muzik wrote:How about these?
dvgrn wrote:Conjecture: Reasonably small "elementary" oblique spaceships exist -- fitting in a 50x50 bounding box, let's say.
(No elementary knightships have been discovered as of 2016, but there has been at least one very close call.)
danny wrote:UPDATE: This one's been proven. Its bounding box is smaller in area than 50*50, and even just barely (31*79 = 2449 = 2500 - 51)
77topaz wrote:danny wrote:UPDATE: This one's been proven. Its bounding box is smaller in area than 50*50, and even just barely (31*79 = 2449 = 2500 - 51)
Technically, it doesn't actually fit in a 50*50 box, though.
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