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Unproven conjectures

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Re: Unproven conjectures

Postby Gamedziner » March 7th, 2018, 5:43 pm

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. :P


Either way, the part in italics should now be updated IMO.
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Re: Unproven conjectures

Postby Scorbie » July 21st, 2018, 2:25 am

dvgrn wrote:Conjecture: No glider eater can be constructed with a recovery time of three ticks or less.
(All known glider eaters take at least four ticks to recover to their original state after eating a glider.)

I think this one is somewhat easier to tackle than others; Is it proved?

The definition of "recovery time" of a catalyst isn't very well-defined, I think...
1) Traditional catalyst searchers / gencols etc. define them as "having a common neighbor".
e.g. two blinkers in a row are "reacting" every 2 generations in this sense.
2) Personally I think it's appropriate to define as the following:
Pattern p, c; // Pattern and Catalyst
reaction_gen(p, c) = min{i | i∈ℕ, p[i] ∪ c[i] != (p∪c)[i]};
recovery_gen(p, c) = min{i | i∈ℕ, i >= first_reaction_gen(p, c), c[i] ⊆ (p∪c)[i]};
recovery_time(p, c) = recovery_gen(p, c) - reaction_gen(p, c);

That makes the eater1's recovery time 3 ticks, which smakes sense in a catalyst-program's perspective, but not so much in Real Life(TM), I guess.
Best wishes to you, Scorbie
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Re: Unproven conjectures

Postby Hdjensofjfnen » July 21st, 2018, 7:56 pm

Is the smallest possible Garden of Eden known?
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Re: Unproven conjectures

Postby dvgrn » July 22nd, 2018, 10:48 am

Hdjensofjfnen wrote:Is the smallest possible Garden of Eden known?

Probably not. There are no Gardens of Eden inside 6x6, as proved by exhaustive search. Extending that search to 6x7 or 7x7 will be quite a computational feat -- roughly 30 times or 8000 times as much work, respectively, as the 6x6 case.

My guess would be that all 7x7 patterns have at least one predecessor, and quite possibly all 8x8 patterns also. There might be a Garden of Eden hiding inside 9x9. Steven Eker has almost made it down to 9x10, but it appears to be very difficult to get rid of those last few cells sticking out into 9x11.
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Re: Unproven conjectures

Postby Hdjensofjfnen » August 3rd, 2018, 11:28 pm

What is the smallest pattern that has exactly one father?
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Re: Unproven conjectures

Postby Hunting » September 9th, 2018, 11:12 pm

dvgrn wrote:
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...

A huge number of existence questions are like this. The answer is "yes" or "no", but there isn't enough information to come up with even an educated guess.

Is there a true period-14 glider gun inside a 50x50 box?
Is there a glider collision that produces a 4x4 array of blocks?
Is there a 16x16 methuselah that takes more than a billion ticks to stabilize?
Is there a stable reflector smaller than a Snark?
Is there a 2c/3 signal elbow with a repeat time less than 20?
Is there a two-engine Cordership using a lucky clean c/12 debris-burning reaction?

... I'd guess yes, yes, no, yes, yes, no, but what do I know really? These aren't particularly long-standing or important questions, by the way -- there are hundreds more just like them.

I'd guess no, yes, no, no, yes, no.
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Re: Unproven conjectures

Postby calcyman » September 10th, 2018, 7:12 am

There is a known 2-engine Cordership.
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Re: Unproven conjectures

Postby Hunting » September 10th, 2018, 7:16 am

calcyman wrote:There is a known 2-engine Cordership.

Oh, I forget that.
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Re: Unproven conjectures

Postby KittyTac » September 20th, 2018, 6:25 am

A billion ticks is a lot.
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