Unique father problem: Difference between revisions

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Let's have an actual (if very short) article on this.
mention new record unconstructible still life
 
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__NOTOC__
{{Pattern
{{Pattern
|name        = Unique father problem
|name        = Unique father problem
|pname        = UnknownPattern
|pname        = uniquefatherproblemsolved
|type        = Problem
|type        = Problem
|nofile      = true
|c            = 258
|bx          = 28
|by          = 22
|symmetry    = C2_4
|synthesis    = 0
|discoverer  = Ilkka Törmä
|discoverer2  = Ville Salo
|discoveryear = 2022
|plaintext    = true
|rle          = true
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 16 WIDTH 600 HEIGHT 500 ]]
}}
}}
The '''unique father problem''' is the following question, posed by [[John Conway]] in 1972 in [[Lifeline Volume 6]],<ref name="lifelinevol6" /> along with the [[grandfather problem]]:
The '''unique father problem''' is the following question, posed by [[John Conway]] in 1972 in [[Lifeline Volume 6]] with an associated $50 cash prize,<ref name="lifelinevol6" /> 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)?  
:''Is there a stable configuration whose only father is itself (with some fading junk some distance away not being counted)?  


Although a 50$ cash prize was offered by Conway, the problem remains open as of August 2017.
The problem was answered positively by [[Ilkka Törmä]] and [[Ville Salo]] on January 13, {{year|2022}}, with a {{times|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 {{times|26|32}} [[still life]] consisting mostly of repeated [[four snakes around block]] units with population 374, which cannot be constructed from scratch by any means.<ref name="post140258" /> [[Dani]] reduced this still life by 40 cells within the same bounding box.<ref name="post140294" /> It was further reduced by [[Oscar Cunningham]] to its provably minimum population of 306 but with a larger bounding box.<ref name="post140295" /> In particular, there is no [[glider synthesis]] for any still life that contains this region.


==References==
{{gallery top}}
{{gallery item|{{EmbedViewer
|pname        = unconstructiblestilllife
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 16 WIDTH 600 HEIGHT 500 ]]
|position    = center
|caption      = {{times|26|32}} unconstructible still life with population 334 (minimum bounding box)
|style        = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|pname        = unconstructiblestilllife2
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 16 WIDTH 600 HEIGHT 500 ]]
|position    = center
|caption      = {{times|34|28}} unconstructible still life with population 306 (minimum population)
|style        = width:300px;
}}}}
{{gallery bottom}}
 
== Reductions ==
On September 4, {{year|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.<ref name="message1148473397018370048" />
 
{{gallery top}}
{{gallery item|{{EmbedViewer
|pname        = selfforcing21x6and23x20
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 16 WIDTH 600 HEIGHT 600 ]]
|position    = center
|caption      = {{times|21|6}} self-forcing agar found by 400spartans, and {{times|23|20}} self-forcing patch made from the agar
|style        = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|pname        = unconstructiblestilllifepop278
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 16 WIDTH 600 HEIGHT 600 ]]
|position    = center
|caption      = {{times|31|28}} unconstructible still life, stabilizing the {{times|23|20}} self-forcing patch
|style        = width:300px;
}}}}
{{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 have related infinite agars with this property.<ref name="p180133" />
 
On September 2, {{year|2024}}, 400spartans found a population-184 stabilization of a self-forcing patch with 283 specified cells.<ref name="p193366" /> The discovery process for the new unconstructible still life involved the use of 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. A self-forcing patch with as few as 271 specified cells exists for this still life.<ref name="p193510" />
 
In January 2025, 400spartans reduced the population record again to 162 live cells.<ref name="message1330285175996940398" /> On April 4, they reduced the population record to 154 cells by identifying small regions that don't appear in known self-forcing patches, searching for large irregular agars without these, finding each one's maximal self-forcing subset and checking whether random {{times|24|24}} subsections of this are self-forcing.<ref name="message1357522386236477543" /> The smallest known total required number of specified cells for the 154-live-cell patch is 272 -- i.e., 118 dead cells must also be specified.<ref name="post231519" />
 
In September 2026, 400spartans found another reduction, to 153 live cells with a 245-cell self-forcing patch.<ref name="post235953" />
 
{{gallery top}}
{{gallery item|{{EmbedViewer
|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
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!
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 16 WIDTH 600 HEIGHT 600 THEME LifeHistory ]]
|caption      = A population-236 unconstructible still life displayed in [[LifeHistory]]. A self-forcing patch is highlighted, with live cells being white and dead cells being red.
|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
$10.2A!
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 16 WIDTH 600 HEIGHT 600 THEME LifeHistory ]]
|caption      = A population-184 unconstructible still life, with a self-forcing patch containing 283 specified cells highlighted.
|style        = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|rle          = x = 22, y = 22, rule = LifeHistory
16.A$.2A12.A.A$.A2.2C.DCD2C2DCD.A$2.ADC2DCD2C2DCD2C.2A$3.C2D2C4D2C2DC
2.A$3.D2C2DCD2C2DC2DCD$3.2DC2D2CDC2D2CD2C$3.C2D2C4D2C2DC2DA$2.D2CDC2D
2CDC2DC2DC.A$.AC2DC2D2CDC2D2CD2CD.A$A.DC2D2C4D2C2DC2DC.A$A.D2CDC2D2CD
C2DC2DCDA$.AC2DC2D2CDC2D2CD2C$2.DC2D2C4D2C2DC2DC$2.D2CDC2D2CDC2DC2DCD
A$.AC2DC2D2CDC2D2CD2C2.A$A.DC2D2C4D2C2DC2D2A$.A.2CDC2D2CDC2DC2DC$2.A.
DC2D2CDC2.ACDAC$3.2A12.A$17.A.A$18.2A!
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 16 WIDTH 600 HEIGHT 600 THEME LifeHistory ]]
|caption      = A population-162 unconstructible still life, with a self-forcing patch of 272 specified cells.
|style        = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|rle          = x = 23, y = 22, rule = LifeHistory
6.2A$5.A2.A3.2A$4.DC2DCD2.A3.2A$3.ACD2CD2CDCD.C2.A$2.DC2DC2DC2D2C2DC2D
C$.AC2DC2DC2DC2D2CD2CDA$A.D2CD2CD2CDC2DC2DCDA$.A.C2DC2DC2D2C2DC2DC$2A
.2DC2DC2DC2D2CD2CD$.A.D2CD2CD2C2DC2DC2D.2A$.A.C2DC2DC2D2C2DC2DA2.A$2.
ADC2DC2DC2DCD2CDACDA$3.D2CD2CD2C2DC2DC2DC$3.A2DC2DC2D2C2DC2DCD$3.2A.2D
C2DC2D2CD2CD$7.2CD2C2DC2DC2D$6.A2DC2D2C2DC2DC$5.A.C2DC2DCD2C.2A$5.A.2C
D2C2DCD.A$6.A.DCD4.A.A$7.A.A6.A$8.A!
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 16 WIDTH 600 HEIGHT 600 THEME LifeHistory ]]
|caption      = A population-154 unconstructible still life, with a self-forcing patch of 252 specified cells.
|style        = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|rle          = x = 22, y = 23, rule = LifeHistory
13.2A$5.A6.A.A$4.A.A4.DCD5.2A$4.A2.C2DACDC2D2C2.A$2.2A.2CDC2DC2DC2DCD
A$2.A2.C2D2C2DCD2C2DC$3.DC2DC2D2CDC2D2CD$3.2CD2C2DC2DC2DC2D.2A$2.A2DC
2D2C2DCD2C2DA2.A$.A.C2DC2DCD2C2DCD2CDA$.A.ACD2C2DC2DC2DC2DC$2.A.DC2D2C
2DCD2C2DCD$3.DC2DC2D2CDC2D2CD$3.2CD2C2DC2DC2DC2D$2.A2DC2D2C2DCD2C2DC$
.A.C2DC2DCD2C2DC.2C$A.D2CD2C2DC2DC.A$A.C2DC2D2C2DC2.A$.ADC2DC2DCD2C.A
$3.ACD2C2DCD.A$2.A.DCD4.2A$3.A.A$4.A!
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 16 WIDTH 600 HEIGHT 600 THEME LifeHistory ]]
|caption      = A population-153 unconstructible still life, with a self-forcing patch of 245 specified cells.
|style        = width:300px;
}}}}
{{gallery bottom}}
== See also ==
* [[Grandfather problem]]
* [[Unsynthesizable oscillator 1]]
 
== References ==
<references>
<references>
<ref name="lifelinevol6">{{CiteLifeline
<ref name="lifelinevol6">{{CiteLifeline
|vol  = 6
|vol   = 6
|date  = October 1972
|pages  = p. 1
|pages = p. 1
}}</ref>
}}</Ref>
<ref name="post140258">{{LinkForumThread
|format = ref
|p      = 140258
|title  = Re: Unproven conjectures
|author = Ilkka Törmä
|date  = January 13, 2022
}}</ref>
<ref name="post140294">{{LinkForumThread
|format = ref
|p      = 140294
|title  = Re: Unproven conjectures
|author = dani
|date  = January 14, 2022
}}</ref>
<ref name="post140295">{{LinkForumThread
|format = ref
|p      = 140295
|title  = Re: Unproven conjectures
|author = Oscar Cunningham
|date  = January 14, 2022
}}</ref>
<ref name="message1148473397018370048">{{CiteDiscord
|author  = mu.sicman
|date    = September 4, 2023
|channel = cgol
|id      = 1148473397018370048
}}</ref>
https://discord.com/channels/357922255553953794/370571014654001154/
<ref name="p180119">{{LinkForumThread
|format = ref
|f      = 7
|t      = 3180
|p      = 180119
|title  = Re: Unproven conjectures
|author = 400spartans
|date   = March 12, 2024
}}</ref>
<ref name="p180133">{{LinkForumThread
|format = ref
|p      = 180133
|title  = Re: Unproven conjectures
|author = 400spartans
|date   = March 12, 2024
}}</ref>
<ref name="p193366">{{LinkForumThread
|format = ref
|p      = 193366
|title = Re: Unproven conjectures
|author = 400spartans
|date  = September 2, 2024
}}</ref>
<ref name="p193510">{{LinkForumThread
|format = ref
|p     = 193510
|title  = Re: Unproven conjectures
|author = Matthias Merzenich
|date  = September 4, 2024
}}</ref>
<ref name="message1330285175996940398">{{CiteDiscord
|author  = mu.sicman
|date    = January 18, 2025
|channel = cgol
|id      = 1330285175996940398
}}</ref>
<ref name="message1357522386236477543">{{CiteDiscord
|author  = mu.sicman
|date    = April 4, 2025
|channel = cgol
|id      = 1357522386236477543
}}</ref>
<ref name="post231519">{{LinkForumThread
|format = ref
|p      = 231519
|title  = Re: Stable patterns which are not glider-constructible
|author = Keith Amling
|date  = July 15, 2026
}}</ref>
<ref name="post235953">{{LinkForumThread
|format = ref
|p      = 235953
|title  = Re: Stable patterns which are not glider-constructible
|author = 400spartans
|date  = September 27, 2026
}}</ref>
</references>
</references>
== External links ==
* {{LinkCatagolue|xs374_ck3qp3ck3qp3ck3qp3ck3qp3ckzp96ki6p96ki6p96ki6p96ki6p9zijc95cijc95cijc95cijc95cijz56ojbo56ojbo56ojbo56ojbo56zbdg6mgbdg6mgbdg6mgbdg6mgbdzmq1dc1mq1dc1mq1dc1mq1dc1mqzw3213w3213w3213w3213|patternname=374-cell unconstructible still life}} (by Ilkka Törmä)
* {{LinkCatagolue|xs306_wgg0g84s0gg39s0gg08o0kczw1c59cjic59cjic59cjic59aczg08objo65objo65objo65objog4cz11ggm6gdbgm6gdbgm6gdbgm6g08oz3201cd1qm1cd1qm1cd1qm1cd11zw359q3kc3pq3kc3pq3kc3pajozy032011y039cx321|patternname=306-cell unconstructible still life}} (by Oscar Cunningham)
* [[Adam P. Goucher]]. [https://cp4space.hatsya.com/2022/01/14/conway-conjecture-settled/ 29-year-old Conway conjecture settled]. January 14, 2022.
[[Category:Synthesis]]

Latest revision as of 09:30, 27 September 2026

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 mostly of repeated four snakes around block units 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 2, 2024, 400spartans found a population-184 stabilization of a self-forcing patch with 283 specified cells.[8] The discovery process for the new unconstructible still life involved the use of 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. A self-forcing patch with as few as 271 specified cells exists for this still life.[9]

In January 2025, 400spartans reduced the population record again to 162 live cells.[10] On April 4, they reduced the population record to 154 cells by identifying small regions that don't appear in known self-forcing patches, searching for large irregular agars without these, finding each one's maximal self-forcing subset and checking whether random 24 × 24 subsections of this are self-forcing.[11] The smallest known total required number of specified cells for the 154-live-cell patch is 272 -- i.e., 118 dead cells must also be specified.[12]

In September 2026, 400spartans found another reduction, to 153 live cells with a 245-cell self-forcing patch.[13]


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. A 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 $10.2A! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 16 WIDTH 600 HEIGHT 600 THEME LifeHistory ]]
A population-184 unconstructible still life, with a self-forcing patch containing 283 specified cells highlighted.
(click above to open LifeViewer)
x = 22, y = 22, rule = LifeHistory 16.A$.2A12.A.A$.A2.2C.DCD2C2DCD.A$2.ADC2DCD2C2DCD2C.2A$3.C2D2C4D2C2DC 2.A$3.D2C2DCD2C2DC2DCD$3.2DC2D2CDC2D2CD2C$3.C2D2C4D2C2DC2DA$2.D2CDC2D 2CDC2DC2DC.A$.AC2DC2D2CDC2D2CD2CD.A$A.DC2D2C4D2C2DC2DC.A$A.D2CDC2D2CD C2DC2DCDA$.AC2DC2D2CDC2D2CD2C$2.DC2D2C4D2C2DC2DC$2.D2CDC2D2CDC2DC2DCD A$.AC2DC2D2CDC2D2CD2C2.A$A.DC2D2C4D2C2DC2D2A$.A.2CDC2D2CDC2DC2DC$2.A. DC2D2CDC2.ACDAC$3.2A12.A$17.A.A$18.2A! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 16 WIDTH 600 HEIGHT 600 THEME LifeHistory ]]
A population-162 unconstructible still life, with a self-forcing patch of 272 specified cells.
(click above to open LifeViewer)
x = 23, y = 22, rule = LifeHistory 6.2A$5.A2.A3.2A$4.DC2DCD2.A3.2A$3.ACD2CD2CDCD.C2.A$2.DC2DC2DC2D2C2DC2D C$.AC2DC2DC2DC2D2CD2CDA$A.D2CD2CD2CDC2DC2DCDA$.A.C2DC2DC2D2C2DC2DC$2A .2DC2DC2DC2D2CD2CD$.A.D2CD2CD2C2DC2DC2D.2A$.A.C2DC2DC2D2C2DC2DA2.A$2. ADC2DC2DC2DCD2CDACDA$3.D2CD2CD2C2DC2DC2DC$3.A2DC2DC2D2C2DC2DCD$3.2A.2D C2DC2D2CD2CD$7.2CD2C2DC2DC2D$6.A2DC2D2C2DC2DC$5.A.C2DC2DCD2C.2A$5.A.2C D2C2DCD.A$6.A.DCD4.A.A$7.A.A6.A$8.A! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 16 WIDTH 600 HEIGHT 600 THEME LifeHistory ]]
A population-154 unconstructible still life, with a self-forcing patch of 252 specified cells.
(click above to open LifeViewer)
x = 22, y = 23, rule = LifeHistory 13.2A$5.A6.A.A$4.A.A4.DCD5.2A$4.A2.C2DACDC2D2C2.A$2.2A.2CDC2DC2DC2DCD A$2.A2.C2D2C2DCD2C2DC$3.DC2DC2D2CDC2D2CD$3.2CD2C2DC2DC2DC2D.2A$2.A2DC 2D2C2DCD2C2DA2.A$.A.C2DC2DCD2C2DCD2CDA$.A.ACD2C2DC2DC2DC2DC$2.A.DC2D2C 2DCD2C2DCD$3.DC2DC2D2CDC2D2CD$3.2CD2C2DC2DC2DC2D$2.A2DC2D2C2DCD2C2DC$ .A.C2DC2DCD2C2DC.2C$A.D2CD2C2DC2DC.A$A.C2DC2D2C2DC2.A$.ADC2DC2DCD2C.A $3.ACD2C2DCD.A$2.A.DCD4.2A$3.A.A$4.A! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 16 WIDTH 600 HEIGHT 600 THEME LifeHistory ]]
A population-153 unconstructible still life, with a self-forcing patch of 245 specified cells.
(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 2, 2024). Re: Unproven conjectures (discussion thread) at the ConwayLife.com forums
  9. ↑ Matthias Merzenich (September 4, 2024). Re: Unproven conjectures (discussion thread) at the ConwayLife.com forums
  10. ↑ mu.sicman (January 18, 2025). Message in #cgol on the Conwaylife Lounge Discord server
  11. ↑ mu.sicman (April 4, 2025). Message in #cgol on the Conwaylife Lounge Discord server
  12. ↑ Keith Amling (July 15, 2026). Re: Stable patterns which are not glider-constructible (discussion thread) at the ConwayLife.com forums
  13. ↑ 400spartans (September 27, 2026). Re: Stable patterns which are not glider-constructible (discussion thread) at the ConwayLife.com forums
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