Unique father problem: Difference between revisions
Jump to navigation
Jump to search
infobox now shows which cells are actually part of the "orphaned" region |
added that there is no glider synthesis for still lifes containing this region |
||
| Line 18: | Line 18: | ||
:''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 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 [[block]]s and [[snake]]s which cannot be constructed from scratch by any means.<ref name="post140258" /> | The problem was answered positively by [[Ilkka Törmä]] and [[Ville Salo]] on January 13, {{year|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 [[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. | ||
==Also see== | ==Also see== | ||
Revision as of 09:41, 15 January 2022
| 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 which cannot be constructed from scratch by any means.[2] In particular, there is no glider synthesis for any still life that contains this region.
Also see
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