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 × 32still 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.
34 × 28 unconstructible still life with population 306 (minimum population) (click above to open LifeViewer) RLE:herePlaintext: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]
21 × 6 self-forcing agar found by 400spartans, and 23 × 20 self-forcing patch made from the agar (click above to open LifeViewer) RLE:herePlaintext:here
31 × 28 unconstructible still life, stabilizing the 23 × 20 self-forcing patch (click above to open LifeViewer) RLE:herePlaintext: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]
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)
A population-184 unconstructible still life displayed in LifeHistory, with a self-forcing patch containing 283 specified cells highlighted. (click above to open LifeViewer)
