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I believe amling was using an SAT solver to find the most recent update to the number -- in that case there already is an algorithm.
Welcome to the forums!!
Hi! I'm happy to be welcomed!
Here's a still life which gives a new bound of 236 cells: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: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!
* 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!
Code: Select all
x = 28, y = 26, rule = B3/S23
2bo8b2o$2b3o5bobo$5bo4bo2b2o2b2o$4bo2b2ob2obo2bo2bobo$4b2ob2o2bo2bob2o
b2obo$5bo4bo2b2o2bo4bo$2obo2bob2ob2o2bo2bob2ob2o$ob3ob2obo2bo2b2ob2obo
2bo$5bo4bo2b2o2bo4bo$4bo2b2ob2obo2bo2b2ob2o$4b2ob2o2bo2bob2ob2o2bo$5bo
4bo2b2o2bo4bo$2obo2bob2ob2o2bo2bob2ob3obo$ob3ob2obo2bo2b2ob2obo2bob2o$
5bo4bo2b2o2bo4bo$4bo2b2ob2obo2bo2b2ob2o$4b2ob2o2bo2bob2ob2o2bo$5bo4bo
2b2o2bo4bo$3bo2bob2ob2o2bo2bob2ob3obo$3b2ob2obo2bo2b2ob2obo2bob2o$5bo
4bo2b2o2bo4bo$5bob2ob2obo2bo2b2ob2o$6bobo2bo2bob2ob2o2bo$9b2o2b2o2bo4b
o$15bobo5b3o$15b2o8bo!
I checked this with JLS. The pattern below shows a highlighted self-forcing patch. I don't know if it's a minimal patch (Edit: it's not).400spartans wrote: ↑March 12th, 2024, 2:44 pmHere's a still life which gives a new bound of 236 cells:Code: Select all
x = 28, y = 26, rule = B3/S23 2bo8b2o$2b3o5bobo$5bo4bo2b2o2b2o$4bo2b2ob2obo2bo2bobo$4b2ob2o2bo2bob2o b2obo$5bo4bo2b2o2bo4bo$2obo2bob2ob2o2bo2bob2ob2o$ob3ob2obo2bo2b2ob2obo 2bo$5bo4bo2b2o2bo4bo$4bo2b2ob2obo2bo2b2ob2o$4b2ob2o2bo2bob2ob2o2bo$5bo 4bo2b2o2bo4bo$2obo2bob2ob2o2bo2bob2ob3obo$ob3ob2obo2bo2b2ob2obo2bob2o$ 5bo4bo2b2o2bo4bo$4bo2b2ob2obo2bo2b2ob2o$4b2ob2o2bo2bob2ob2o2bo$5bo4bo 2b2o2bo4bo$3bo2bob2ob2o2bo2bob2ob3obo$3b2ob2obo2bo2b2ob2obo2bob2o$5bo 4bo2b2o2bo4bo$5bob2ob2obo2bo2b2ob2o$6bobo2bo2bob2ob2o2bo$9b2o2b2o2bo4b o$15bobo5b3o$15b2o8bo!
Code: Select all
x = 28, y = 26, rule = LifeHistory
2.A8.2A$2.3A5.A.A$3.2DC4DC2DCA2.2A$3.DC2D2CD2CDC2DC2DC.A$3.D2CD2C2DC
2DCD2CD2CDA$3.2DC4DC2D2C2DC4DC2D$2A.C2DCD2CD2C2DC2DCD2CD2C$A.A2CD2CDC
2DC2D2CD2CDC2DC$3.2DC4DC2D2C2DC4DC2D$3.DC2D2CD2CDC2DC2D2CD2CD$3.D2CD
2C2DC2DCD2CD2C2DCD$3.2DC4DC2D2C2DC4DC2D$2A.C2DCD2CD2C2DC2DCD2CD2CA.A$
A.A2CD2CDC2DC2D2CD2CDC2DC.2A$3.2DC4DC2D2C2DC4DC2D$3.DC2D2CD2CDC2DC2D
2CD2CD$3.D2CD2C2DC2DCD2CD2C2DCD$3.2DC4DC2D2C2DC4DC2D$3.C2DCD2CD2C2DC
2DCD2CD2CA.A$3.2CD2CDC2DC2D2CD2CDC2DC.2A$3.2DC4DC2D2C2DC4DC2D$5.AD2CD
2CDC2DC2D2CD2CD$6.A.C2DC2DCD2CD2C2DCD$9.2A2.AC2DC4DC2D$15.A.A5.3A$15.
2A8.A!
Code: Select all
x = 28, y = 26, rule = LifeHistory
2.A8.2A$2.3A5.A.A$5.A4.A2.2A2.2A$4.C2D2CD2CDC2DCD.A.A$4.2CD2C2DC2DCD
2CD2C.A$4.DC4DC2D2C2DC3D.A$2A.C2DCD2CD2C2DC2DCD2CDCA$A.A2CD2CDC2DC2D
2CD2CDC2DA$3.2DC4DC2D2C2DC4DCD$3.DC2D2CD2CDC2DC2D2CD2C$3.D2CD2C2DC2DC
D2CD2C2DC$3.2DC4DC2D2C2DC4DCD$2A.C2DCD2CD2C2DC2DCD2CDC2A.A$A.2ACD2CDC
2DC2D2CD2CDC2DC.2A$4.DC4DC2D2C2DC4DC2D$4.C2D2CD2CDC2DC2D2CD2CD$4.2CD
2C2DC2DCD2CD2C2DCD$4.DC4DC2D2C2DC4DC2D$3.A2DCD2CD2C2DC2DCD2CD2CA.A$3.
ACD2CDC2DC2D2CD2CDC2DA.2A$5.A.3DC2D2C2DC4DCD$5.A.2CD2CDC2DC2D2CD2C$6.
A.A.DC2DCD2CD2C2DC$9.2A2.2A2.A4.A$15.A.A5.3A$15.2A8.A!
I'm just using Torma and Salo's program (https://github.com/ilkka-torma/gol-agars) with two minor tweaks to speed things up. First, I exclude patterns which are just a repetition of some smaller tiling. And second, this came up in a search which only looks at p1 agars in which every live cell is adjacent to 3 live cells and every dead cell is adjacent to 4 live cells. There are plenty of infinite self-forcing p1 agars which do not have this property, but the only known finite self-forcing p1 agar patterns all seem to have this property.
Code: Select all
x = 22, y = 48, rule = B3/S23
3o$obo$3o$3o$3o$3o$obo$3o4$o$b2o$2o27$19b3o$19bobo$19b3o$19b3o$19b3o$19b3o$
19bobo$19b3o!
I believe it. I think the lower bound will always be three more than whatever cell count for which we've fully enumerated all infinitely growth patterns. Right now this is 9+3 = 12. There is still technically the possibility of a 10-cell puffer/wickstretcher/gun that travels/fires towards a far off blinker which, upon reaching the blinker causes a burning reaction along the puffer trail/wick/glider stream until the pattern collapses back into the original 10-cell infinite growth + blinker.
This 8-by-8 patch should count as a counterexample. (Because the 36-bit 3-by-3 block array is glider-constructible.)Haycat2009 wrote: ↑March 12th, 2024, 11:39 pmHelp me prove: Every patch where the dead cells have 4 neighbours and the alive cells have 3 neighbours is self-forcing.
Code: Select all
x = 8, y = 8, rule = B3/S23
2ob2ob2o$2ob2ob2o2$2ob2ob2o$2ob2ob2o2$2ob2ob2o$2ob2ob2o!
No, it wasn't.Haycat2009 wrote: ↑March 13th, 2024, 12:53 amThe only condition in the search was what I listed above.
You wrote:400spartans wrote: ↑March 12th, 2024, 7:06 pmI'm just using Torma and Salo's program (https://github.com/ilkka-torma/gol-agars) with two minor tweaks to speed things up. First, I exclude patterns which are just a repetition of some smaller tiling. And second, this came up in a search which only looks at p1 agars in which every live cell is adjacent to 3 live cells and every dead cell is adjacent to 4 live cells. There are plenty of infinite self-forcing p1 agars which do not have this property, but the only known finite self-forcing p1 agar patterns all seem to have this property.
Let the property P be "every specified alive cell has =3 alive neighbours, and every specified dead cell has =4 alive neighbours".Haycat2009 wrote: ↑March 12th, 2024, 11:39 pmHelp me prove: Every patch where the dead cells have 4 neighbours and the alive cells have 3 neighbours is self-forcing.
Code: Select all
x = 19, y = 37, rule = B3/S23
13b3o$12b4o$11b2obobo$13bobo$15bo12$10b2o$bobo7bobo$o7b2o3b2o$o3bo2b3o
3bo$o6b4obo$o2bo7bo$3o12bobo$18bo$14bo3bo$14bo3bo$18bo$9bo5bo2bo$8b3o
5b3o2$10bo$2bobo4b2o$5bo2b3o$5bo2b3o$2bo2bo2b2obo$3b3o3b3o$10bo!
A proof would need to rely on some precise definition of elementary.
Code: Select all
x = 30, y = 25, rule = LifeHistory
3$26.A.A$26.2A$27.A$24.A$22.2A$23.2A2$19.A.A$19.2A$20.A$17.A$15.2A$
16.2A6$3.2A$3.A2.A$5.2A!