![]() Sorry – A non-(glider-)constructible configuration might be something Teaches us perhaps that there is no orphan, that almost all configurationsĭie down pretty soon – whereas almost all configurations ARE orphans, ofĬourse, and PROBABLY almost all configurations grow infinitely, as youĪsserted in your note, but I’m sure not meaning that it was provably true. Experience is a bad guide to large configurations – it This brings me to an interesting point – the false lessons experience Though obviously that sense must allow for fading configurations outside Of such delicacy that in some essential sense it is its only ancestor – Should NOT believe, however, that everything of infinite age is soīuildable (even if most of us do). Infinite “age” (at least if you define them correctly). ![]() The things buildable by gliders (an idea I think first popularizedīy Buckingham) are a nice class, mainly because they are provably of More importantly, the Törmä-Salo result positively answers a question first posed by John Conway himself on 24th August 1992: There exists a strict still-life with 306 cells that cannot be synthesised.Every strict still-life with ≤ 20 cells can be synthesised by gliders.Oscar moreover proved, again using SAT solvers, that this is the minimum-population stabilisation of the Törmä-Salo configuration.Ĭonsequently, we have the following pair of bounds: The first finite stabilisation was 374 cells, but this was promptly reduced to 334 cells by Danielle Conway and then to the 306-cell configuration above by Oscar Cunningham. Since this configuration can be stabilised (by the addition of further live cells, shown in yellow) into a finite still-life, this demonstrates that not every still-life can be constructed by colliding gliders. Similarly, one can use a SAT solver to verify that Törmä and Salo’s result is correct. 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. Here is the configuration of live and dead cells, surrounded by an infinite background of grey “don’t care” cells: 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).
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