Re: Unproven conjectures
Posted: 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.
I think you're looking for the unsynthesizable oscillator.Haycat2009 wrote: ↑August 25th, 2023, 11:04 amAre there any higher-period oscillators/ spaceships / sparklers where each phrase has only one predecessor ( With sparks a distance away not being counted )
Aha, so are there any p3 or higher? What about a spaceship/sparkler?wirehead wrote: ↑August 27th, 2023, 11:07 amI think you're looking for the unsynthesizable oscillator.Haycat2009 wrote: ↑August 25th, 2023, 11:04 amAre there any higher-period oscillators/ spaceships / sparklers where each phrase has only one predecessor ( With sparks a distance away not being counted )
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.Haycat2009 wrote: ↑August 28th, 2023, 5:00 amAha, so are there any p3 or higher? What about a spaceship/sparkler?
A question along these lines was asked when the unsynthesizable p2 first came out.
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.
Super chaotic!
Well, a version of the read mechanism that doesn't shift the blinkers is definitely possibledvgrn wrote: ↑August 21st, 2023, 11:52 amYes, 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.
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 bound was *(provisionally) improved to 278 cells on Discord by "400spartans", using a different self-forcing patch:Macbi wrote: ↑January 14th, 2022, 11:44 amThe smallest you can get it is population 306. (Confirmed with LLS.)Code: Select all
x = 34, y = 28, rule = LifeHistory 12.2C4.2C$12.C5.C$7.2C5.C5.C7.2C$6.C.A4D2A4D2A4D2AD.C$2.2C.A2DAD2A2DA D2A2DAD2A2DADA$2.C.2ADA2D2ADA2D2ADA2D2ADA2D2A$3.4D2A4D2A4D2A4D2A3DC$ 3.2ADA2D2ADA2D2ADA2D2ADA2D2AD.C$3.AD2A2DAD2A2DAD2A2DAD2A2DAD2AC$3.4D 2A4D2A4D2A4D2A4D$3.D2A2DAD2A2DAD2A2DAD2A2DAD2AD$3.D2ADA2D2ADA2D2ADA2D 2ADA2D2AD$3.4D2A4D2A4D2A4D2A4D.2C$2.C2ADA2D2ADA2D2ADA2D2ADA2D2ADA2.C$ C2.AD2A2DAD2A2DAD2A2DAD2A2DAD2AC$2C.4D2A4D2A4D2A4D2A4D$3.D2A2DAD2A2DA D2A2DAD2A2DAD2AD$3.D2ADA2D2ADA2D2ADA2D2ADA2D2AD$3.4D2A4D2A4D2A4D2A4D$ 2.C2ADA2D2ADA2D2ADA2D2ADA2D2ADA$2.C.D2A2DAD2A2DAD2A2DAD2A2DAD2A$3.C3D 2A4D2A4D2A4D2A4D$4.2A2DAD2A2DAD2A2DAD2A2DAD2A.C$5.ADA2D2ADA2D2ADA2D2A DA2DA.2C$4.C.D2A4D2A4D2A4DA.C$4.2C7.C5.C5.2C$15.C5.C$14.2C4.2C!
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!
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.carsoncheng wrote: ↑September 5th, 2023, 4:55 amThe bound was *(provisionally) improved to 278 cells on Discord by "400spartans", using a different self-forcing patch:* the result has not been verified independently yet; can anyone verify this?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!
Obviously yes. There is no proof that knightships must be self-forcing.Entity Valkyrie 2 wrote: ↑September 15th, 2023, 7:12 amDoes there exist a synthesizable, elementary knightship?
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.Haycat2009 wrote: ↑September 19th, 2023, 6:14 amObviously yes. There is no proof that knightships must be self-forcing.Entity Valkyrie 2 wrote: ↑September 15th, 2023, 7:12 amDoes there exist a synthesizable, elementary knightship?
None of the following: yes, no, obviously yes, obviously no, obviously not no, obviously not yes.Haycat2009 wrote: ↑September 19th, 2023, 6:14 amsnipEntity Valkyrie 2 wrote: ↑September 15th, 2023, 7:12 amDoes there exist a synthesizable, elementary knightship?
Entity Valkyrie 2 wrote: ↑September 15th, 2023, 7:12 amDoes there exist a synthesizable, elementary knightship?
In reality, most likely nobody knows. (Unless someone just solved the problem and is about to post about it.)everyone else wrote:...
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).
Ah, my favorite proof technique:Haycat2009 wrote: ↑September 19th, 2023, 6:14 amObviously yes. There is no proof that knightships must be self-forcing.Entity Valkyrie 2 wrote: ↑September 15th, 2023, 7:12 amDoes there exist a synthesizable, elementary knightship?