

A308590


Langton's ant on a Penrose rhomb tiling: number of black cells after n moves of the ant.


11



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

0,3


COMMENTS

The ant lives on a centrally symmetric Penrose rhomb tiling with a "Sun" patch (S configuration, cf. A242935) at the center and starts on one of the thick rhombs of that patch, looking towards one of the outward edges of that tile. On a white rhomb, turn to the next edge of that cell in clockwise direction, flip the color of the rhomb, then move forward one unit. On a black rhomb, turn to the next edge of that cell in counterclockwise direction, flip the color of the rhomb, then move forward one unit.
In contrast to the corresponding sequences for Langton's ant on periodic tilings, like the square tiling (A255938) or a hexagonal tiling (A269757), this sequence is most likely not unique. A Penrose tiling lacks translational symmetry, meaning any two finite regions in the tiling that are identical are surrounded by different patches of tiles when examining a large enough region of the surrounding tiles. Therefore I suspect that, unless the trajectory of the ant is bounded to stay inside a finite region of the tiling, the trajectories of any two ants placed at different starting points on the tiling will diverge at some point.


LINKS

Table of n, a(n) for n=0..72.
Felix Fröhlich, Illustration of iterations 072 of the ant
Wikipedia, Langton's ant
Wikipedia, Penrose tiling


EXAMPLE

See illustration in links.


CROSSREFS

Cf. A255938, A269757, A325953, A325954, A325955.
Sequence in context: A282062 A318126 A326167 * A309064 A325631 A276073
Adjacent sequences: A308587 A308588 A308589 * A308591 A308592 A308593


KEYWORD

nonn


AUTHOR

Felix Fröhlich, Jun 09 2019


STATUS

approved



