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

Author

Felix Fröhlich, Jul 04 2019

Keywords

• nonn

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

Examples

			See illustrations in Fröhlich, 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

Crossrefs

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

Programs

PARI

See Links section.

Formula

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

Extensions

More terms from Rémy Sigrist, Jul 21 2019