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

Offset

1,1

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

Links

Table of n, a(n) for n=1..6.

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

Example

For n = 3 the starting state is:
  +---+---+---+
  | * | * | * |
  +---+---+---+
  |   |   |   |
  +---+---+---+
  |   |   |   |
  +---+---+---+
For n = 4 the starting state is:
  +---+---+---+---+
  | * | * | * |   |
  +---+---+---+---+
  |   |   | * |   |
  +---+---+---+---+
  | * | * |   |   |
  +---+---+---+---+
  |   |   |   |   |
  +---+---+---+---+
For n = 5 the starting state is:
  +---+---+---+---+---+
  | * | * |   | * |   |
  +---+---+---+---+---+
  | * |   |   |   |   |
  +---+---+---+---+---+
  | * | * |   | * | * |
  +---+---+---+---+---+
  | * |   | * |   |   |
  +---+---+---+---+---+
  |   |   |   |   |   |
  +---+---+---+---+---+

Crossrefs

Sequence in context: A338372 A153920 A300483 * A067579 A019143 A084650

Adjacent sequences: A294238 A294239 A294240 * A294242 A294243 A294244

Keyword

nonn,more,hard

Author

Peter Kagey, Oct 25 2017

Status

approved