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 A294241 Longest non-repeating Game of Life on an n X n torus that ends with a fixed pattern. 0

%I #24 Jun 21 2024 03:54:35

%S 2,2,3,10,52,91,224

%N Longest non-repeating Game of Life on an n X n torus that ends with a fixed pattern.

%C We must have a(2n) >= a(n) because one can always place onto a 2n X 2n toroidal board four identical copies of a record-setting pattern for a(n), so that each copy of the pattern "thinks" that it is the sole occupant of an n X n toroidal board and thus acts accordingly. See also comments in A179412 for a related question about the longest repeating pattern on a toroidal board. - _Antti Karttunen_, Oct 30 2017

%H Code Golf Stack Exchange User "Per Alexandersson", <a href="https://codegolf.stackexchange.com/questions/9393/longest-non-repeating-game-of-life-sequence">Longest non-repeating Game-of-Life sequence</a>

%e For n = 3 the starting state is:

%e +---+---+---+

%e | * | * | * |

%e +---+---+---+

%e | | | |

%e +---+---+---+

%e | | | |

%e +---+---+---+

%e For n = 4 the starting state is:

%e +---+---+---+---+

%e | * | * | * | |

%e +---+---+---+---+

%e | | | * | |

%e +---+---+---+---+

%e | * | * | | |

%e +---+---+---+---+

%e | | | | |

%e +---+---+---+---+

%e For n = 5 the starting state is:

%e +---+---+---+---+---+

%e | * | * | | * | |

%e +---+---+---+---+---+

%e | * | | | | |

%e +---+---+---+---+---+

%e | * | * | | * | * |

%e +---+---+---+---+---+

%e | * | | * | | |

%e +---+---+---+---+---+

%e | | | | | |

%e +---+---+---+---+---+

%e From _Bert Dobbelaere_, Jun 20 2024: (Start)

%e For n = 6 the starting state is:

%e +---+---+---+---+---+---+

%e | | | * | | * | * |

%e +---+---+---+---+---+---+

%e | * | * | | | * | * |

%e +---+---+---+---+---+---+

%e | | | * | | * | |

%e +---+---+---+---+---+---+

%e | * | * | | | | * |

%e +---+---+---+---+---+---+

%e | | | | | | * |

%e +---+---+---+---+---+---+

%e | | | | * | | * |

%e +---+---+---+---+---+---+

%e For n = 7 the starting state is:

%e +---+---+---+---+---+---+---+

%e | * | | * | * | | | * |

%e +---+---+---+---+---+---+---+

%e | * | | | * | | * | |

%e +---+---+---+---+---+---+---+

%e | | * | | * | * | | |

%e +---+---+---+---+---+---+---+

%e | | * | * | | | | * |

%e +---+---+---+---+---+---+---+

%e | | * | * | | * | * | |

%e +---+---+---+---+---+---+---+

%e | | | | | * | | * |

%e +---+---+---+---+---+---+---+

%e | | | * | | * | * | |

%e +---+---+---+---+---+---+---+ (End)

%K nonn,more,hard

%O 1,1

%A _Peter Kagey_, Oct 25 2017

%E a(7) from _Bert Dobbelaere_, Jun 20 2024

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Last modified September 10 03:08 EDT 2024. Contains 375770 sequences. (Running on oeis4.)