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

2, 2, 3, 10, 52, 91, 224

Offset: 1

Author

Peter Kagey, Oct 25 2017

Keywords

• nonn
• more
• hard

Comments

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

Examples

			For n = 3 the starting state is:
  +---+---+---+
  | * | * | * |
  +---+---+---+
  |   |   |   |
  +---+---+---+
  |   |   |   |
  +---+---+---+
For n = 4 the starting state is:
  +---+---+---+---+
  | * | * | * |   |
  +---+---+---+---+
  |   |   | * |   |
  +---+---+---+---+
  | * | * |   |   |
  +---+---+---+---+
  |   |   |   |   |
  +---+---+---+---+
For n = 5 the starting state is:
  +---+---+---+---+---+
  | * | * |   | * |   |
  +---+---+---+---+---+
  | * |   |   |   |   |
  +---+---+---+---+---+
  | * | * |   | * | * |
  +---+---+---+---+---+
  | * |   | * |   |   |
  +---+---+---+---+---+
  |   |   |   |   |   |
  +---+---+---+---+---+
From _Bert Dobbelaere_, Jun 20 2024: (Start)
For n = 6 the starting state is:
  +---+---+---+---+---+---+
  |   |   | * |   | * | * |
  +---+---+---+---+---+---+
  | * | * |   |   | * | * |
  +---+---+---+---+---+---+
  |   |   | * |   | * |   |
  +---+---+---+---+---+---+
  | * | * |   |   |   | * |
  +---+---+---+---+---+---+
  |   |   |   |   |   | * |
  +---+---+---+---+---+---+
  |   |   |   | * |   | * |
  +---+---+---+---+---+---+
For n = 7 the starting state is:
  +---+---+---+---+---+---+---+
  | * |   | * | * |   |   | * |
  +---+---+---+---+---+---+---+
  | * |   |   | * |   | * |   |
  +---+---+---+---+---+---+---+
  |   | * |   | * | * |   |   |
  +---+---+---+---+---+---+---+
  |   | * | * |   |   |   | * |
  +---+---+---+---+---+---+---+
  |   | * | * |   | * | * |   |
  +---+---+---+---+---+---+---+
  |   |   |   |   | * |   | * |
  +---+---+---+---+---+---+---+
  |   |   | * |   | * | * |   |
  +---+---+---+---+---+---+---+   (End)
		

Links

• Code Golf Stack Exchange User "Per Alexandersson", Longest non-repeating Game-of-Life sequence

Extensions

a(7) from Bert Dobbelaere, Jun 20 2024