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!
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Pattern type
Problem
Number of cells
258
Bounding box
28 × 22
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!
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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!
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34 × 28 unconstructible still life with population 306 (minimum population)(click above to open LifeViewer ) RLE : here Plaintext : here
Reduction
On September 4, 2023 , 400spartans used 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!
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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!
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31 × 28 unconstructible still life, stabilizing the 23 × 20 self-forcing patch(click above to open LifeViewer ) RLE : here Plaintext : here
See also
References
External links