A309064 Langton's ant on a snub square tiling: number of black cells after n moves of the ant when starting on a square.

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

Offset

0,3

Comments

First differs from A276073 at n = 16.

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

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

Links

Lars Blomberg, Table of n, a(n) for n = 0..10000

Lars Blomberg, The state for n=104000, when 872 cells are set

Lars Blomberg, Animation illustrating n=1-3000

Lars Blomberg, Animation illustrating the transition from "chaos" to "avenue", n=96300-99608

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

Wikipedia, Langton's ant

Wikipedia, Snub square tiling

Formula

a(n+1025) = a(n) + 25 for n > 96420. Lars Blomberg, Aug 15 2019

Example

See illustrations in Fröhlich, 2019.

Crossrefs

Cf. A255938, A269757, A276073, A308590, A308937, A308973, A326167, A326352.

Sequence in context: A318126 A326167 A308590 * A325631 A276073 A341311

Adjacent sequences: A309061 A309062 A309063 * A309065 A309066 A309067

Keyword

nonn

Author

Felix Fröhlich, Jul 10 2019

Status

approved