Unique father problem: Difference between revisions
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mention 278-cell unsynthesizable still life |
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:''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)? | ||
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 of [[block]]s and [[snake]]s 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. | 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 of [[block]]s and [[snake]]s 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. | ||
==Reduction== | |||
On September 4, {{year|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.<ref name="message1148473397018370048" /> | |||
{{gallery top}} | {{gallery top}} | ||
{{gallery item|{{EmbedViewer | {{gallery item|{{EmbedViewer | ||
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|position = center | |position = center | ||
|caption = {{times|34|28}} unconstructible still life with population 306 (minimum population) | |caption = {{times|34|28}} unconstructible still life with population 306 (minimum population) | ||
|style = width:300px; | |||
}}}} | |||
{{gallery item|{{EmbedViewer | |||
|pname = selfforcing21x6and23x20 | |||
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 16 WIDTH 600 HEIGHT 500 ]] | |||
|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 500 ]] | |||
|position = center | |||
|caption = {{times|31|28}} unconstructible still life, stabilizing the {{times|23|20}} self-forcing patch | |||
|style = width:300px; | |style = width:300px; | ||
}}}} | }}}} | ||
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|date = January 14, 2022 | |date = January 14, 2022 | ||
}}</ref> | }}</ref> | ||
<ref name="message1148473397018370048">{{CiteDiscord | |||
|author = mu.sicman | |||
|date = September 4, 2023 | |||
|channel = cgol | |||
|id = 1148473397018370048 | |||
}}</ref> | |||
https://discord.com/channels/357922255553953794/370571014654001154/ | |||
</references> | </references> | ||
Revision as of 18:43, 6 September 2023
| Unique father problem | |||||||
| 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.
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]
| 26 × 32 unconstructible still life with population 334 (minimum bounding box) (click above to open LifeViewer) RLE: here Plaintext: here |
| 34 × 28 unconstructible still life with population 306 (minimum population) (click above to open LifeViewer) RLE: here Plaintext: here |
| 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 |
| 31 × 28 unconstructible still life, stabilizing the 23 × 20 self-forcing patch (click above to open LifeViewer) RLE: here Plaintext: here |
See also
References
- ↑ Robert Wainwright (October 1972). Lifeline, vol 6, p. 1.
- ↑ Ilkka Törmä (January 13, 2022). Re: Unproven conjectures (discussion thread) at the ConwayLife.com forums
- ↑ dani (January 14, 2022). Re: Unproven conjectures (discussion thread) at the ConwayLife.com forums
- ↑ Oscar Cunningham (January 14, 2022). Re: Unproven conjectures (discussion thread) at the ConwayLife.com forums
- ↑ mu.sicman (September 4, 2023). Message in #cgol on the Conwaylife Lounge Discord server
External links
- 374-cell unconstructible still life at Adam P. Goucher's Catagolue (by Ilkka Törmä)
- 306-cell unconstructible still life at Adam P. Goucher's Catagolue (by Oscar Cunningham)
- Adam P. Goucher. 29-year-old Conway conjecture settled. January 14, 2022.