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A Conway 'Game of Life' Conjecture Settled After 29 years

Sunday January 23, 2022. 04:34 PM , from Slashdot
In 1992 John Conway raised a question about the patterns in his famous mathematical Game of Life: 'Is there a Godlike still-life, one that can only have existed for all time (apart from things that don't interfere with it)?'

Conway closed his note by adding 'Well, I'm going out to get a hot dog now...' And then, nearly 30 years later, a mathematical blog reports:

Ilkka Törmä and Ville Salo, a pair of researchers at the University of Turku in Finland, have found a finite configuration in Conway's Game of Life such that, if it occurs within a universe at time T, it must have existed in that same position at time T-1 (and therefore, by induction, at time 0)...

The configuration was discovered by experimenting with finite patches of repeating 'agar' and using a SAT solver to check whether any of them possess this property.

The blogger also shares some other Game of Life-related news:

David Raucci discovered the first oscillator of period 38. The remaining unsolved periods are 19, 34, and 41.Darren Li has connected Charity Engine to Catagolue, providing approximately 2000 CPU cores of continuous effort and searching slightly more than 10^12 random initial configurations per day.Nathaniel Johnston and Dave Greene have published a book on Conway's Game of Life, featuring both the theoretical aspects and engineering that's been accomplished in the half-century since its conception. Unfortunately it was released slightly too early to include the Törmä-Salo result or Raucci's period-38 oscillator.
Thanks to Slashdot reader joshuark for sharing the story.

Read more of this story at Slashdot.

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