## Unproven conjectures

For general discussion about Conway's Game of Life.
TYCF
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### Re: Unproven conjectures

Could there be a one cell thick gun?

Code: Select all

``````x = 5, y = 3, rule = B3/S23
obobo\$2ob2o\$obobo!

``````

dvgrn
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### Re: Unproven conjectures

TYCF wrote:
August 21st, 2023, 11:39 am
Could there be a one cell thick gun?
Yes, I think so. Sort of. As long as it's allowed to fire in two 90-degree mirror image directions at once.

It's kind of a corollary of the one-cell-thick spaceship project: build a version of the spaceship with velocity zero, and then emit a glider every cycle. With non-zero velocity you'd end up with a rake instead of a gun.

As soon as the gun emits its first gliders, the pattern is permanently not one cell thick any more, but I guess that's probably okay. The same kind of thing is true for the bounding boxes of all of our optimized glider guns.

TYCF
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### Re: Unproven conjectures

dvgrn wrote:
August 21st, 2023, 11:52 am
Thank you!

Code: Select all

``````x = 5, y = 3, rule = B3/S23
obobo\$2ob2o\$obobo!

``````

Haycat2009
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### Re: Unproven conjectures

Are there any higher-period oscillators/ spaceships / sparklers where each phrase has only one predecessor ( With sparks a distance away not being counted )
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### Re: Unproven conjectures

Haycat2009 wrote:
August 25th, 2023, 11:04 am
Are there any higher-period oscillators/ spaceships / sparklers where each phrase has only one predecessor ( With sparks a distance away not being counted )
I think you're looking for the unsynthesizable oscillator.
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Haycat2009
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### Re: Unproven conjectures

August 27th, 2023, 11:07 am
Haycat2009 wrote:
August 25th, 2023, 11:04 am
Are there any higher-period oscillators/ spaceships / sparklers where each phrase has only one predecessor ( With sparks a distance away not being counted )
I think you're looking for the unsynthesizable oscillator.
Aha, so are there any p3 or higher? What about a spaceship/sparkler?
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### Re: Unproven conjectures

Haycat2009 wrote:
August 28th, 2023, 5:00 am
Aha, so are there any p3 or higher? What about a spaceship/sparkler?
I don't know of any p3+ oscillators that are proven unsynthesizable. That would probably be another question (and another research paper) for Ilkka Törmä and Ville Salo.

In terms of spaceships, (so far) Sir Robin is unsynthesizable.
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dvgrn
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### Re: Unproven conjectures

August 28th, 2023, 3:57 pm
I don't know of any p3+ oscillators that are proven unsynthesizable. That would probably be another question (and another research paper) for Ilkka Törmä and Ville Salo.
A question along these lines was asked when the unsynthesizable p2 first came out.

However, I would think that it wouldn't take a terribly long search to figure out a p4 oscillator that includes the unsynthesizable p2 patch as part of its rotor. This seems kind of like cheating, but then again it would be a real p4 (as long it's not just the same p2 oscillator with a separate p4 added nearby).

AlbertArmStain
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### Re: Unproven conjectures

How chaotic can infinite novelty be?

dvgrn
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### Re: Unproven conjectures

AlbertArmStain wrote:
August 28th, 2023, 8:59 pm
How chaotic can infinite novelty be?
Very very chaotic, I bet! We haven't built a quadratic-growth replicator yet that maximizes chaos, but I suspect we know how to do it by now.

For example, we could put together a replicator that replicates at fairly near the orthogonal speed limit, that self-destructs after replicating except that it leaves behind a spacefiller seed on a very long-delay timer.

We'd have no hope of actually running a pattern like that long enough to see what it does in the long-term -- chaotically collapsing spacefillers use an awful lot of memory. But for some replication offsets and some values of "long-delay", there might be a high probability that some replicators would continue to survive indefinitely.

unname4798
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### Re: Unproven conjectures

AlbertArmStain wrote:
August 28th, 2023, 8:59 pm
How chaotic can infinite novelty be?
Super chaotic!
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EvinZL
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### Re: Unproven conjectures

dvgrn wrote:
August 21st, 2023, 11:52 am
Yes, I think so. Sort of. As long as it's allowed to fire in two 90-degree mirror image directions at once.

It's kind of a corollary of the one-cell-thick spaceship project: build a version of the spaceship with velocity zero, and then emit a glider every cycle. With non-zero velocity you'd end up with a rake instead of a gun.

As soon as the gun emits its first gliders, the pattern is permanently not one cell thick any more, but I guess that's probably okay. The same kind of thing is true for the bounding boxes of all of our optimized glider guns.
Well, a version of the read mechanism that doesn't shift the blinkers is definitely possible

Also, the one-cell-thick ship can be contructed via symmetric p2-slow gliders starting from a blinker, so you can have the gun fire 1-cell thick spaceships (nothing said it has to fire gliders!). Or maybe mwss-on-mwss would be better. Well, you could probably implement a 1-cekk thick binary counter or whatever if you wanted.

dvgrn
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### Re: Unproven conjectures

EvinZL wrote:
August 29th, 2023, 8:57 am
dvgrn wrote:
August 21st, 2023, 11:52 am
As soon as the gun emits its first gliders, the pattern is permanently not one cell thick any more...
... you can have the gun fire 1-cell thick spaceships (nothing said it has to fire gliders!). Or maybe mwss-on-mwss would be better.
Oh, my -- I should have thought of that. The one-cell-thick one-cell-thick spaceship gun somehow seems much more awesome, because with the right timing the whole pattern can go back to being one cell thick every now and then, including the output -- an actual linear linear-growth pattern.

The construction problem is about twice as big as a "simple" spaceship or oscillator, and then I guess the gun will have to build an ILD unit (Incredibly Long Delay) on each cycle, so that the gun waits for each emitted spaceship to crawl safely out of the way before it starts trying to build the next one.

carsoncheng
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### Re: Unproven conjectures

Macbi wrote:
January 14th, 2022, 11:44 am
The smallest you can get it is population 306. (Confirmed with LLS.)

Code: Select all

``````x = 34, y = 28, rule = LifeHistory
DA2DA.2C\$4.C.D2A4D2A4D2A4DA.C\$4.2C7.C5.C5.2C\$15.C5.C\$14.2C4.2C!``````
The bound was *(provisionally) improved to 278 cells on Discord by "400spartans", using a different self-forcing patch:

Code: Select all

``````x = 31, y = 28, rule = B3/S23
16bo4b2o\$15bobo2bo2bo\$7b2o6bo2bo2bo2bo\$6bobo4b2ob2ob2ob2obo\$2b2obo2bob2o2bo2b
o2bo2bobo\$2bob2obo2b2obo2bo2bo2bo2b2o\$7b2o4b2ob2ob2ob2o3bo\$3b2obo2b2obo2bo2bo
2bo2b2o2bo\$3bob2o2bob2o2bo2bo2bo2bob3o\$7b2o4b2ob2ob2ob2o\$4b2o2bob2o2bo2bo2bo
2bob2o\$4b2obo2b2obo2bo2bo2bo2b2o\$7b2o4b2ob2ob2ob2o5b2o\$ob3obo2b2obo2bo2bo2bo
2b2obo2bo\$2obob2o2bob2o2bo2bo2bo2bob3o\$7b2o4b2ob2ob2ob2o\$4b2o2bob2o2bo2bo2bo
2bob2o\$4b2obo2b2obo2bo2bo2bo2b2o\$7b2o4b2ob2ob2ob2o\$2b3obo2b2obo2bo2bo2bo2b2ob
o\$2bo2b2o2bob2o2bo2bo2bo2bob2o\$3bo3b2o4b2ob2ob2ob2o\$4b2o2bob2o2bo2bo2bo2bob3o
\$5bobo2b2obo2bo2bo2bo2bo2bo\$4bo2b2o4b3o4b2o3bobo\$4b2o3b4o13bo\$9bo3bo\$12b2o!``````
* the result has not been verified independently yet; can anyone verify this?

AlbertArmStain
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### Re: Unproven conjectures

carsoncheng wrote:
September 5th, 2023, 4:55 am
The bound was *(provisionally) improved to 278 cells on Discord by "400spartans", using a different self-forcing patch:

Code: Select all

``````x = 31, y = 28, rule = B3/S23
16bo4b2o\$15bobo2bo2bo\$7b2o6bo2bo2bo2bo\$6bobo4b2ob2ob2ob2obo\$2b2obo2bob2o2bo2b
o2bo2bobo\$2bob2obo2b2obo2bo2bo2bo2b2o\$7b2o4b2ob2ob2ob2o3bo\$3b2obo2b2obo2bo2bo
2bo2b2o2bo\$3bob2o2bob2o2bo2bo2bo2bob3o\$7b2o4b2ob2ob2ob2o\$4b2o2bob2o2bo2bo2bo
2bob2o\$4b2obo2b2obo2bo2bo2bo2b2o\$7b2o4b2ob2ob2ob2o5b2o\$ob3obo2b2obo2bo2bo2bo
2b2obo2bo\$2obob2o2bob2o2bo2bo2bo2bob3o\$7b2o4b2ob2ob2ob2o\$4b2o2bob2o2bo2bo2bo
2bob2o\$4b2obo2b2obo2bo2bo2bo2b2o\$7b2o4b2ob2ob2ob2o\$2b3obo2b2obo2bo2bo2bo2b2ob
o\$2bo2b2o2bob2o2bo2bo2bo2bob2o\$3bo3b2o4b2ob2ob2ob2o\$4b2o2bob2o2bo2bo2bo2bob3o
\$5bobo2b2obo2bo2bo2bo2bo2bo\$4bo2b2o4b3o4b2o3bobo\$4b2o3b4o13bo\$9bo3bo\$12b2o!``````
* the result has not been verified independently yet; can anyone verify this?
It’s been verified on Discord by the same person, with the only result being the original patch. It looks like a hybrid between the original patch and a different patch.

HartmutHolzwart
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### Re: Unproven conjectures

I guess this is worth a mention in the life wiki news!

It’s the first reduction of the minimum non-constructible still life since the original post!

Entity Valkyrie 2
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### Re: Unproven conjectures

Does there exist a synthesizable, elementary knightship?
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Haycat2009
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### Re: Unproven conjectures

Entity Valkyrie 2 wrote:
September 15th, 2023, 7:12 am
Does there exist a synthesizable, elementary knightship?
Obviously yes. There is no proof that knightships must be self-forcing.
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dvgrn
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### Re: Unproven conjectures

Haycat2009 wrote:
September 19th, 2023, 6:14 am
Entity Valkyrie 2 wrote:
September 15th, 2023, 7:12 am
Does there exist a synthesizable, elementary knightship?
Obviously yes. There is no proof that knightships must be self-forcing.
That's actually an "Obviously not no", though, which is different from an "Obviously yes". It's probably only going to be "obviously yes" when somebody produces a synthesis.

IgnacyJ
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### Re: Unproven conjectures

You're both wrong, the answer is "Not obviously no", or dare I even say "Obviously not obviously no".
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unname4798
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### Re: Unproven conjectures

Haycat2009 wrote:
September 19th, 2023, 6:14 am
Entity Valkyrie 2 wrote:
September 15th, 2023, 7:12 am
Does there exist a synthesizable, elementary knightship?
snip
None of the following: yes, no, obviously yes, obviously no, obviously not no, obviously not yes.
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confocaloid
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### Re: Unproven conjectures

Entity Valkyrie 2 wrote:
September 15th, 2023, 7:12 am
Does there exist a synthesizable, elementary knightship?
everyone else wrote:...
In reality, most likely nobody knows. (Unless someone just solved the problem and is about to post about it.)
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Unlikely events happen.
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dvgrn
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### Re: Unproven conjectures

IgnacyJ wrote:
September 19th, 2023, 9:17 am
You're both wrong, the answer is "Not obviously no", or dare I even say "Obviously not obviously no".
Well, you know, it was obvious to me that the answer is not "no", precisely because there's no proof that knightships must be self-forcing (and indeed, Sir Robin and his clan are not self-forcing, so there's a proof that knightships don't have to be self-forcing).

So I guess I meant "(Obviously) (not no)", rather than "(Obviously not) (no)"... Apparently this discussion needs more parentheses!

Anyway, the original question was a fine thing to post on a thread called "Unproven conjectures", for sure.

olivia enessemir
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### Re: Unproven conjectures

Haycat2009 wrote:
September 19th, 2023, 6:14 am
Entity Valkyrie 2 wrote:
September 15th, 2023, 7:12 am
Does there exist a synthesizable, elementary knightship?
Obviously yes. There is no proof that knightships must be self-forcing.
Ah, my favorite proof technique:
Theorem. \$P\$

Proof.
Nobody has yet produced a proof of \$\neg P\$.
QED.
omelette

EvinZL
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### Re: Unproven conjectures

Of course, it might be possible for a spaceship to be unsynthesisable but not self-forcing. We have no hope of proving something like that though.