A308937 Langton's ant on a chair tiling: number of black cells after n moves of the ant.

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

Offset

0,3

Comments

The ant begins on the inner corner of a subtile.

On a white tile, turn 90 degrees right, flip the color of the tile, then move forward until reaching a new tile, moving as far as possible within the tile.

On a black tile, turn 90 degrees left, then continue as above.

The chair tiling used for this automaton is, like all aperiodic hierarchical tilings, not unique (see for example Goodman-Strauss, p. 490). See "Remarks, 2019" in links for clarification which tiling the ant lives on.

Links

Table of n, a(n) for n=0..50.

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

Felix Fröhlich, Remarks specifying the tiling used for generating the sequence, 2019.

Chaim Goodman-Strauss, Aperiodic Hierarchical Tilings, in: J. F. Sadoc and N. Rivier, Foams and Emulsions, NATO Science Series, Series E, Vol. 354, Springer, pp 481-496, DOI:10.1007/978-94-015-9157-7_28.

Tilings Encyclopedia, Chair

Wikipedia, Langton's ant

Example

See illustrations in Fröhlich, 2019.

Crossrefs

Cf. A255938, A269757, A308590, A325953, A325954, A325955.

Sequence in context: A349946 A262519 A225320 * A123066 A330239 A235121

Adjacent sequences: A308934 A308935 A308936 * A308938 A308939 A308940

Keyword

nonn,more

Author

Felix Fröhlich, Jul 01 2019

Status

approved