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<references>
<references>
<ref name="lifelinevol6">{{CiteLifeline
<ref name="lifelinevol6">{{CiteLifeline
|vol   = 6
|vol   = 6
|pages = p. 1
|pages = p. 1
}}</ref>
}}</ref>
<ref name="post140258">{{LinkForumThread  
<ref name="post140258">{{LinkForumThread  
|format = ref  
|format = ref
|title = Re: Unproven conjectures
|p      = 140258
|p = 140258
|title = Re: Unproven conjectures
|author = Ilkka Törmä
|author = Ilkka Törmä
|date = January 13, 2022}}</ref>
|date   = January 13, 2022
}}</ref>
<ref name="post140295">{{LinkForumThread  
<ref name="post140295">{{LinkForumThread  
|format = ref  
|format = ref
|title = Re: Unproven conjectures
|p      = 140295
|p = 140295
|title = Re: Unproven conjectures
|author = Oscar Cunningham
|author = Oscar Cunningham
|date = January 14, 2022}}</ref>
|date   = January 14, 2022
}}</ref>
<ref name="post140294">{{LinkForumThread  
<ref name="post140294">{{LinkForumThread  
|format = ref  
|format = ref
|title = Re: Unproven conjectures
|p      = 140294
|p = 140294
|title = Re: Unproven conjectures
|author = Dani
|author = dani
|date = January 14, 2022}}</ref>
|date   = January 14, 2022
}}</ref>
</references>
</references>


Revision as of 18:58, 3 January 2023

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 [[ ZOOM 16 WIDTH 500 HEIGHT 400 ]]
View static image
Pattern type Problem
Number of cells 258
Bounding box 28 × 22
Static symmetry Unspecified
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 3 ZOOM 12 WIDTH 500 HEIGHT 500 ]]
26 × 32 unconstructible still life with population 374 (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 3 ZOOM 12 WIDTH 500 HEIGHT 500 ]]
34 × 28 unconstructible still life with population 306 (minimum population)
(click above to open LifeViewer)
RLE: here Plaintext: here

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
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