A309293 Langton's ant on a snub trihexagonal tiling: number of black cells after n moves of the ant when starting on a hexagon.

0, 1, 2, 3, 4, 5, 4, 5, 6, 7, 8, 9, 10, 11, 12, 11, 10, 11, 12, 13, 14, 15, 14, 15, 16, 17, 18, 19, 20, 21, 20, 19, 18, 17, 16, 15, 14, 13, 14, 13, 12, 11, 10, 9, 10, 11, 12, 13, 14, 15, 16, 17, 16, 15, 16, 17, 18, 17, 16, 17, 18, 19, 18, 17, 16, 15, 14, 15

Offset

0,3

Comments

On a white tile, turn 60 degrees right, flip the color of the tile, then move forward one unit.

On a black tile, turn 60 degrees left, flip the color of the tile, then move forward one unit.

The sequence has a cycle of length of 28292, that is, a(28292)=0 with the ant in the starting hexagon pointing in the start direction, so another cycle will follow. The maximum term in the cycle is a(8148)=174. - Lars Blomberg, Aug 01 2019

Links

Lars Blomberg, Table of n, a(n) for n = 0..28292

Lars Blomberg, The state for n=8148, when 174 cells are set

Lars Blomberg, Video illustrating a full cycle

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

Wikipedia, Langton's ant

Wikipedia, Snub trihexagonal tiling

Example

See illustrations in Fröhlich, 2019.

Crossrefs

Cf. A255938, A269757, A308590, A308937, A308973, A326167, A326352, A309064, A309166, A309241, A309279.

Sequence in context: A276073 A341311 A284000 * A244904 A338885 A238288

Adjacent sequences: A309290 A309291 A309292 * A309294 A309295 A309296

Keyword

nonn

Author

Felix Fröhlich, Jul 21 2019

Extensions

More terms from Lars Blomberg, Aug 01 2019

Status

approved