What is the smallest group of cells in Conway's game of Life that dies completely in one generation, with...
competition/games/life.dying New
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Problem
What is the smallest group of cells in Conway's game of Life that dies completely in one generation, with no progeny, and includes at least one cell that dies by overcrowding?
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wft@math.canterbury.ac.nz (Bill Taylor) asked for the smallest dying group in Conway's Life, specifying > ... a group of stones that completely dies with no progeny, in one > generation. To exclude trivia it must include at least one stone that > dies by overcrowding. I also exclude non-minimal groups--groups that contain a nontrivial dying group as a proper subset. Bill gives the population-9 and -10 examples . . x . . . . . x . . . x . . x . x . . . . x x . . x x x x x . x x x . x x x x x x . . x . . . . x . x . . x x . . . . x . . . x . . . and asks for anything else of population 10 or less. A disappointingly large number of duplicate and incorrect examples were posted.... I wrote a program to search for minimal examples. There are no other groups of population 9, and only the three population-10 groups: . . . x . x . . . x . x . . . x . x . . x . . . x . x . . . x . x . . . x x x x x . . x x x x . . x x x x . . . x . . . . . x . . . . . x . . . . . x . . . . . x . . . . x . . . . You may consider these to be inessential modifications of the first two above, but that's all there are. Similar inessential modifications yield the three minimal population-11 groups: . . . . x . x . . . x . x . . x x . x . . . x . . . . . x . . . x x x x x . . x x x x x . x x x x x . . . x x . . . . . x . . . . . x . . . . . . . . x x . x . . . . . . . x . x It is not until population 12 that we see the significantly new form (in three variants) . . . x . . . . . x . . . . . x . . . . . x . . . . . x . . . . . x . . . . x x x x x . x x x x x . x x x . x x x x . . . x x x . . . x x x . x . . x . . . . . x . . . . . x . . . . . x . . . . . x . . . . . x . . . in addition to four more modifications of the population-9 and -10 examples. -- Dan Hoey <Hoey@AIC.NRL.Navy.Mil>