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A308937 Langton's ant on a chair tiling: number of black cells after n moves of the ant. 9
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 (list; graph; refs; listen; history; text; internal format)
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: A125619 A262519 A225320 * A123066 A330239 A235121

Adjacent sequences:  A308934 A308935 A308936 * A308938 A308939 A308940

KEYWORD

nonn,more

AUTHOR

Felix Fröhlich, Jul 01 2019

STATUS

approved

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Last modified June 20 03:11 EDT 2021. Contains 345157 sequences. (Running on oeis4.)