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add new smaller unconstructible still life
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{{gallery bottom}}
{{gallery bottom}}
On March 12, {{year|2024}}, 400spartans reduced this once more to a patch of 389 specified cells with a population-236 stabilisation.<ref name="p180119" /> The self-forcing region was found as a finite subset of a self-forcing [[agar]] with the constraint that all live cells in the agar have three living neighbours, and all dead cells have four. All known self-forcing still life patches are derived from agars with this property.<ref name="p180133" />
On March 12, {{year|2024}}, 400spartans reduced this once more to a patch of 389 specified cells with a population-236 stabilisation.<ref name="p180119" /> The self-forcing region was found as a finite subset of a self-forcing [[agar]] with the constraint that all live cells in the agar have three living neighbours, and all dead cells have four. All known self-forcing still life patches have related infinite agars with this property.<ref name="p180133" />
{{EmbedViewer
 
On September 1, {{year|2024}}, 400spartans found a population-184 stabilization of a self-forcing patch with 283 specified cells.<ref name="p193366" /> The new unconstructable still life used a hybrid tool incorporating ideas from Törmä and Salo's gol-agars program and [[mtve]]'s grandfatherless pattern algorithm, which builds up a pattern by adding overlapping 3x3 squares while keeping track of the number of predecessors within the same bounding box.
{{gallery top}}
{{gallery item|{{EmbedViewer
|rle          = x = 28, y = 26, rule = LifeHistory
|rle          = x = 28, y = 26, rule = LifeHistory
2.A8.2A$2.3A5.A.A$5.A4.A2.2A2.2A$4.C2D2CD2CDC2DCD.A.A$4.2CD2C2DC2DCD
2.A8.2A$2.3A5.A.A$5.A4.A2.2A2.2A$4.C2D2CD2CDC2DCD.A.A$4.2CD2C2DC2DCD
Line 70: Line 73:
A.A.DC2DCD2CD2C2DC$9.2A2.2A2.A4.A$15.A.A5.3A$15.2A8.A!
A.A.DC2DCD2CD2C2DC$9.2A2.2A2.A4.A$15.A.A5.3A$15.2A8.A!
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 16 WIDTH 600 HEIGHT 600 THEME LifeHistory ]]
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 16 WIDTH 600 HEIGHT 600 THEME LifeHistory ]]
|position    = center
|caption      = A population-236 unconstructible still life displayed in [[LifeHistory]]. The self-forcing patch is highlighted, with live cells being white and dead cells being red.
|caption      = A population-236 unconstructible still life displayed in [[LifeHistory]]. The self-forcing patch is highlighted, with live cells being white and dead cells being red.
|style        = width:300px;
|style        = width:300px;
}}
}}}}
 
{{gallery item|{{EmbedViewer
|rle          = x = 22, y = 25, rule = LifeHistory
10.2A$9.A2.A$7.A2.A.A$.2A3.D2CDC2D2A$.A2.2CDC2D2CDC2D2C$2.2ACDC2DC2DC
2D2CDA$4.3D2CDC2D2C3D.A$4.2CDC2D2CDC2D2C.A$2.2ACDC2DC2DC2D2CDA$.A2.3D
2CDC2D2C3D$2.A.2CDC2D2CDC2D2C$.ACD2C2DC2DC2DCD2C$2.5D2CDC2D2C3D$.A2CD
2C2DCD2C2DCDC2A$A2.2CDC2DC2DC2D2CDA.A$A2.4D2CDC2D2C3D3.A$.2ACD2C2DCD
2C2DCDC3A$3.2CDC2DC2DC2D2CDA$3.4D2CDC2D2C3D$2.AD2CDC2D2CDC2D2C$.A.2CD
C2DC2DC2D2CDA$.A3.2D2CDC2D2C3D.A$2.A.ACDC2D2CDC2DC2A$3.2A.A2.A2.A2.2A
$10.2A!
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 16 WIDTH 600 HEIGHT 600 THEME LifeHistory ]]
|caption      = A population-184 unconstructible still life displayed in [[LifeHistory]], with the self-forcing patch highlighted.
|style        = width:300px;
}}}}
{{gallery bottom}}
== See also ==
== See also ==
* [[Grandfather problem]]
* [[Grandfather problem]]
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|author = 400spartans
|author = 400spartans
|date  = March 12, 2024
|date  = March 12, 2024
}}</ref>
<ref name="p193366">{{LinkForumThread
|format = ref
|p      = 193366
|title  = Re: Unproven conjectures
|author = 400spartans
|date  = September 1, 2024
}}</ref>
}}</ref>
</references>
</references>

Revision as of 01:28, 3 September 2024

Unique father problem
x = 30, y = 24, rule = LifeHistory 5.22F$2.4FA4.2A4.2A4.2A.2F$.2FA2.A.2A2.A.2A2.A.2A2.A.A2F$2F2A.A2.2A.A 2.2A.A2.2A.A2.2AF$F4.2A4.2A4.2A4.2A3.F$F2A.A2.2A.A2.2A.A2.2A.A2.2A.2F $FA.2A2.A.2A2.A.2A2.A.2A2.A.2AF$F4.2A4.2A4.2A4.2A4.F$F.2A2.A.2A2.A.2A 2.A.2A2.A.2A.F$F.2A.A2.2A.A2.2A.A2.2A.A2.2A.F$F4.2A4.2A4.2A4.2A4.F$F 2A.A2.2A.A2.2A.A2.2A.A2.2A.AF$FA.2A2.A.2A2.A.2A2.A.2A2.A.2AF$F4.2A4. 2A4.2A4.2A4.F$F.2A2.A.2A2.A.2A2.A.2A2.A.2A.F$F.2A.A2.2A.A2.2A.A2.2A.A 2.2A.F$F4.2A4.2A4.2A4.2A4.F$F2A.A2.2A.A2.2A.A2.2A.A2.2A.AF$2F.2A2.A. 2A2.A.2A2.A.2A2.A.2AF$.F3.2A4.2A4.2A4.2A4.F$.F2A2.A.2A2.A.2A2.A.2A2.A .2A2F$.2FA.A2.2A.A2.2A.A2.2A.A2.A2F$2.2F.2A4.2A4.2A4.A4F$3.22F! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 16 WIDTH 600 HEIGHT 500 ]]
View static image
Pattern type Problem
Number of cells 258
Bounding box 28 × 22
Static symmetry C2_4
Discovered by Ilkka Törmä
Ville Salo
Year of discovery 2022

The unique father problem is the following question, posed by John Conway in 1972 in Lifeline Volume 6 with an associated $50 cash prize,[1] along with the grandfather problem:

Is there a stable configuration whose only father is itself (with some fading junk some distance away not being counted)?

The problem was answered positively by Ilkka Törmä and Ville Salo on January 13, 2022, with a 22 × 28 region that must appear in all of its predecessors. This is shown in the infobox to the right, with the gray cells indicating the boundary of this region. This can be stabilized to form a 26 × 32 still life consisting of blocks and snakes with population 374, which cannot be constructed from scratch by any means.[2] Dani reduced this still life by 40 cells within the same bounding box.[3] It was further reduced by Oscar Cunningham to its provably minimum population of 306 but with a larger bounding box.[4] In particular, there is no glider synthesis for any still life that contains this region.


x = 32, y = 26, rule = B3/S23 8b2obo2b2obo2b2obo$8bob2o2bob2o2bob2o3b2o$6b2o4b2o4b2o4b2o2bo$b2obo2b ob2o2bob2o2bob2o2bobo$bob2obo2b2obo2b2obo2b2obo2b2o$6b2o4b2o4b2o4b2o$ 2b2obo2b2obo2b2obo2b2obo2b2obo$2bob2o2bob2o2bob2o2bob2o2bob2o$2o4b2o4b 2o4b2o4b2o4b2o$bob2o2bob2o2bob2o2bob2o2bob2o2bo$o2b2obo2b2obo2b2obo2b 2obo2b2obo$2o4b2o4b2o4b2o4b2o4b2o$2b2obo2b2obo2b2obo2b2obo2b2obo$2bob 2o2bob2o2bob2o2bob2o2bob2o$2o4b2o4b2o4b2o4b2o4b2o$bob2o2bob2o2bob2o2b ob2o2bob2o2bo$o2b2obo2b2obo2b2obo2b2obo2b2obo$2o4b2o4b2o4b2o4b2o4b2o$ 2b2obo2b2obo2b2obo2b2obo2b2obo$2bob2o2bob2o2bob2o2bob2o2bob2o$6b2o4b2o 4b2o4b2o$3b2o2bob2o2bob2o2bob2o2bob2obo$4bobo2b2obo2b2obo2b2obo2bob2o $3bo2b2o4b2o4b2o4b2o$3b2o3b2obo2b2obo2b2obo$8bob2o2bob2o2bob2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 16 WIDTH 600 HEIGHT 500 ]]
26 × 32 unconstructible still life with population 334 (minimum bounding box)
(click above to open LifeViewer)
RLE: here Plaintext: here
x = 34, y = 28, rule = B3/S23 12b2o4b2o$12bo5bo$7b2o5bo5bo7b2o$6bobo4b2o4b2o4b2o2bo$2b2obo2bob2o2bob 2o2bob2o2bobo$2bob2obo2b2obo2b2obo2b2obo2b2o$7b2o4b2o4b2o4b2o3bo$3b2ob o2b2obo2b2obo2b2obo2b2o2bo$3bob2o2bob2o2bob2o2bob2o2bob3o$7b2o4b2o4b2o 4b2o$4b2o2bob2o2bob2o2bob2o2bob2o$4b2obo2b2obo2b2obo2b2obo2b2o$7b2o4b 2o4b2o4b2o5b2o$2b3obo2b2obo2b2obo2b2obo2b2obo2bo$o2bob2o2bob2o2bob2o2b ob2o2bob3o$2o5b2o4b2o4b2o4b2o$4b2o2bob2o2bob2o2bob2o2bob2o$4b2obo2b2ob o2b2obo2b2obo2b2o$7b2o4b2o4b2o4b2o$2b3obo2b2obo2b2obo2b2obo2b2obo$2bo 2b2o2bob2o2bob2o2bob2o2bob2o$3bo3b2o4b2o4b2o4b2o$4b2o2bob2o2bob2o2bob 2o2bob2obo$5bobo2b2obo2b2obo2b2obo2bob2o$4bo2b2o4b2o4b2o4bobo$4b2o7bo 5bo5b2o$15bo5bo$14b2o4b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 16 WIDTH 600 HEIGHT 500 ]]
34 × 28 unconstructible still life with population 306 (minimum population)
(click above to open LifeViewer)
RLE: here Plaintext: here


Reductions

On September 4, 2023, 400spartans used a modified version of Törmä and Salo's "gol-agars" search program to find several more self-forcing agar patches, including one that allowed for the creation of a 278-cell unsynthesizable still life.[5]


x = 23, y = 31, rule = B3/S23 bo2bob2o2bo2bo2bo2bobo$3b2o4b2ob2ob2ob2o$b2o2bob2o2bo2bo2bo2bo$2bo2b2o bo2bo2bo2bo2b2o$3b2o4b2ob2ob2ob2o$bobo2b2obo2bo2bo2bo2bo6$bobo2b2obo2b o2bo2bo2bo$2o2bob2o2bo2bo2bo2bob2o$3b2o4b2ob2ob2ob2o$b2o2bob2o2bo2bo2b o2bobo$obo2b2obo2bo2bo2bo2b2o$3b2o4b2ob2ob2ob2o$2obo2b2obo2bo2bo2bo2b 2o$2o2bob2o2bo2bo2bo2bob2o$3b2o4b2ob2ob2ob2o$b2o2bob2o2bo2bo2bo2bobo$o bo2b2obo2bo2bo2bo2b2o$3b2o4b2ob2ob2ob2o$2obo2b2obo2bo2bo2bo2b2o$2o2bob 2o2bo2bo2bo2bob2o$3b2o4b2ob2ob2ob2o$b2o2bob2o2bo2bo2bo2bobo$obo2b2obo 2bo2bo2bo2b2o$3b2o4b2ob2ob2ob2o$2obo2b2obo2bo2bo2bo2b2o$bo2bob2o2bo2bo 2bo2bobo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 16 WIDTH 600 HEIGHT 600 ]]
21 × 6 self-forcing agar found by 400spartans, and 23 × 20 self-forcing patch made from the agar
(click above to open LifeViewer)
RLE: here Plaintext: here
x = 31, y = 28, rule = B3/S23 12b2o$9bo3bo$4b2o3b4o13bo$4bo2b2o4b3o4b2o3bobo$5bobo2b2obo2bo2bo2bo2bo 2bo$4b2o2bob2o2bo2bo2bo2bob3o$3bo3b2o4b2ob2ob2ob2o$2bo2b2o2bob2o2bo2bo 2bo2bob2o$2b3obo2b2obo2bo2bo2bo2b2obo$7b2o4b2ob2ob2ob2o$4b2obo2b2obo2b o2bo2bo2b2o$4b2o2bob2o2bo2bo2bo2bob2o$7b2o4b2ob2ob2ob2o$2obob2o2bob2o 2bo2bo2bo2bob3o$ob3obo2b2obo2bo2bo2bo2b2obo2bo$7b2o4b2ob2ob2ob2o5b2o$ 4b2obo2b2obo2bo2bo2bo2b2o$4b2o2bob2o2bo2bo2bo2bob2o$7b2o4b2ob2ob2ob2o$ 3bob2o2bob2o2bo2bo2bo2bob3o$3b2obo2b2obo2bo2bo2bo2b2o2bo$7b2o4b2ob2ob 2ob2o3bo$2bob2obo2b2obo2bo2bo2bo2b2o$2b2obo2bob2o2bo2bo2bo2bobo$6bobo 4b2ob2ob2ob2obo$7b2o6bo2bo2bo2bo$15bobo2bo2bo$16bo4b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 16 WIDTH 600 HEIGHT 600 ]]
31 × 28 unconstructible still life, stabilizing the 23 × 20 self-forcing patch
(click above to open LifeViewer)
RLE: here Plaintext: here

On March 12, 2024, 400spartans reduced this once more to a patch of 389 specified cells with a population-236 stabilisation.[6] The self-forcing region was found as a finite subset of a self-forcing agar with the constraint that all live cells in the agar have three living neighbours, and all dead cells have four. All known self-forcing still life patches have related infinite agars with this property.[7]

On September 1, 2024, 400spartans found a population-184 stabilization of a self-forcing patch with 283 specified cells.[8] The new unconstructable still life used a hybrid tool incorporating ideas from Törmä and Salo's gol-agars program and mtve's grandfatherless pattern algorithm, which builds up a pattern by adding overlapping 3x3 squares while keeping track of the number of predecessors within the same bounding box.

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! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 16 WIDTH 600 HEIGHT 600 THEME LifeHistory ]]
A population-236 unconstructible still life displayed in LifeHistory. The self-forcing patch is highlighted, with live cells being white and dead cells being red.
(click above to open LifeViewer)
x = 22, y = 25, rule = LifeHistory 10.2A$9.A2.A$7.A2.A.A$.2A3.D2CDC2D2A$.A2.2CDC2D2CDC2D2C$2.2ACDC2DC2DC 2D2CDA$4.3D2CDC2D2C3D.A$4.2CDC2D2CDC2D2C.A$2.2ACDC2DC2DC2D2CDA$.A2.3D 2CDC2D2C3D$2.A.2CDC2D2CDC2D2C$.ACD2C2DC2DC2DCD2C$2.5D2CDC2D2C3D$.A2CD 2C2DCD2C2DCDC2A$A2.2CDC2DC2DC2D2CDA.A$A2.4D2CDC2D2C3D3.A$.2ACD2C2DCD 2C2DCDC3A$3.2CDC2DC2DC2D2CDA$3.4D2CDC2D2C3D$2.AD2CDC2D2CDC2D2C$.A.2CD C2DC2DC2D2CDA$.A3.2D2CDC2D2C3D.A$2.A.ACDC2D2CDC2DC2A$3.2A.A2.A2.A2.2A $10.2A! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 16 WIDTH 600 HEIGHT 600 THEME LifeHistory ]]
A population-184 unconstructible still life displayed in LifeHistory, with the self-forcing patch highlighted.
(click above to open LifeViewer)

See also

References

  1. ↑ Robert Wainwright (October 1972). Lifeline, vol 6, p. 1.
  2. ↑ Ilkka Törmä (January 13, 2022). Re: Unproven conjectures (discussion thread) at the ConwayLife.com forums
  3. ↑ dani (January 14, 2022). Re: Unproven conjectures (discussion thread) at the ConwayLife.com forums
  4. ↑ Oscar Cunningham (January 14, 2022). Re: Unproven conjectures (discussion thread) at the ConwayLife.com forums
  5. ↑ mu.sicman (September 4, 2023). Message in #cgol on the Conwaylife Lounge Discord server
  6. ↑ 400spartans (March 12, 2024). Re: Unproven conjectures (discussion thread) at the ConwayLife.com forums
  7. ↑ 400spartans (March 12, 2024). Re: Unproven conjectures (discussion thread) at the ConwayLife.com forums
  8. ↑ 400spartans (September 1, 2024). Re: Unproven conjectures (discussion thread) at the ConwayLife.com forums
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