Unique father problem: Difference between revisions
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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 which cannot be constructed from scratch by any means.<ref name="post140258" /> 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, population 374, which cannot be constructed from scratch by any means.<ref name="post140258" /> This still life was reduced by [[Oscar Cunningham]] to its provably minimum population of 306 but with a larger bounding box. In particular, there is no [[glider synthesis]] for any still life that contains this region. | ||
{{EmbedViewer | {|style="margin:auto;width:300px;" | ||
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|pname = unconstructiblestilllife | |pname = unconstructiblestilllife | ||
|position = center | |position = center | ||
|viewerconfig = #C [[ THUMBSIZE 3 ZOOM 12 WIDTH 500 HEIGHT 500 ]] | |viewerconfig = #C [[ THUMBSIZE 3 ZOOM 12 WIDTH 500 HEIGHT 500 ]] | ||
|caption = | |caption = {{Times|26|32}} unconstructible still life with population 374 (minimum bounding box) | ||
}} | }} | ||
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|pname = unconstructiblestilllife2 | |||
|position = center | |||
|viewerconfig = #C [[ THUMBSIZE 3 ZOOM 12 WIDTH 500 HEIGHT 500 ]] | |||
|caption = {{Times|34|28}} unconstructible still life with population 306 (minimum population) | |||
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==See also== | ==See also== | ||
Revision as of 01:27, 3 January 2023
| Unique father problem | |||||||
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| Pattern type | Problem | ||||||
|---|---|---|---|---|---|---|---|
| Number of cells | 258 | ||||||
| Bounding box | 28 × 22 | ||||||
| Static symmetry | Unspecified | ||||||
| Discovered by | Ilkka Törmä Ville Salo | ||||||
| Year of discovery | 2022 | ||||||
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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, population 374, which cannot be constructed from scratch by any means.[2] This still life was reduced by Oscar Cunningham to its provably minimum population of 306 but with a larger bounding box. In particular, there is no glider synthesis for any still life that contains this region.
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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
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.