A309241 Langton's ant on a rhombitrihexagonal tiling: number of black cells after n moves of the ant when starting on a hexagon.

0, 1, 2, 3, 4, 3, 4, 5, 6, 7, 8, 9, 8, 9, 10, 11, 12, 11, 12, 13, 14, 15, 16, 15, 14, 13, 12, 11, 10, 11, 10, 9, 8, 7, 8, 9, 10, 11, 12, 13, 12, 13, 14, 13, 12, 13, 14, 15, 16, 15, 14, 15, 14, 13, 14, 15, 14, 15, 16, 17, 18, 17, 18, 19, 20, 21, 22, 21, 20, 21

Offset: 0

Author

Felix Fröhlich, Jul 17 2019

Keywords

• nonn

Comments

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

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

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

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

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

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

Examples

			See illustrations in Fröhlich, 2019.
		

Links

• Lars Blomberg, Table of n, a(n) for n = 0..1000
• Lars Blomberg, The state for n=185, when 33 cells are set which is the maximum within the cycle
• Lars Blomberg, Animation illustrating n=1-1000
• Felix Fröhlich, Illustration of iterations 0-50, 2019.
• Wikipedia, Langton's ant
• Wikipedia, Rhombitrihexagonal tiling

Crossrefs

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

Formula

a(n+448) = a(n). - Lars Blomberg, Aug 16 2019

Extensions

More terms from Lars Blomberg, Aug 16 2019