A308973 Langton's ant on a truncated square tiling: number of black cells after n moves of the ant when starting on an octagon and looking towards an edge where the tile meets another octagon.

0, 1, 2, 3, 4, 5, 6, 5, 6, 7, 8, 9, 8, 7, 8, 9, 10, 11, 10, 11, 10, 9, 10, 11, 12, 13, 14, 15, 14, 15, 16, 17, 18, 17, 16, 17, 18, 17, 16, 17, 18, 19, 20, 21, 22, 21, 22, 23, 24, 23, 22, 23, 24, 25, 26, 27, 28, 27, 28, 29, 30, 29, 28, 29, 30, 31, 32, 33, 34

Offset

0,3

Comments

First differs from A269757 at n = 19.

On a white square, turn 90 degrees right, flip the color of the tile, then move forward one unit.

On a white octagon, turn 45 degrees right, flip the color of the tile, then move forward one unit.

On a black square, turn 90 degrees left, flip the color of the tile, then move forward one unit.

On a black octagon, turn 45 degrees left, flip the color of the tile, then move forward one unit.

As in the original variant, order emerges after a transition phase and the ant starts building a recurrent "highway" pattern of 12 steps that repeats indefinitely. - Rémy Sigrist, Jul 21 2019

Links

Rémy Sigrist, Table of n, a(n) for n = 0..500

Felix Fröhlich, Illustration of iterations 0-50 of the ant, 2019.

Rémy Sigrist, Configuration after 100 steps

Rémy Sigrist, PARI program for A308973

Wikipedia, Langton's ant

Wikipedia, Truncated square tiling

Formula

a(n + 12) = a(n) + 6 for any n >= 34. - Rémy Sigrist, Jul 21 2019

Example

See illustrations in Fröhlich, 2019.

Prog

(PARI) See Links section.

Crossrefs

Cf. A255938, A269757, A308590, A308937, A326167, A326352.

Sequence in context: A102730 A165597 A269757 * A309279 A245352 A099033

Adjacent sequences: A308970 A308971 A308972 * A308974 A308975 A308976

Keyword

nonn

Author

Felix Fröhlich, Jul 04 2019

Extensions

More terms from Rémy Sigrist, Jul 21 2019

Status

approved