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

Author

Felix Fröhlich, Jul 21 2019

Keywords

• nonn

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

Examples

			See illustrations in Fröhlich, 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

Crossrefs

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

Extensions

More terms from Lars Blomberg, Aug 01 2019