Unique father problem

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Unique father problem
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Pattern type Problem
Number of cells 258
Bounding box 28×22
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


  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

External links