A308937 - OEIS

%I #32 Aug 06 2024 11:09:06

%S 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,

%T 10,11,12,13,12,13,14,15,14,15,14,15,16,17,16,15,14,15,14,15,16

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

%C The ant begins on the inner corner of a subtile.

%C 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.

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

%C 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.

%H Felix Fröhlich, <a href="/A308937/a308937.pdf">Illustration of iterations 0-50 of the ant</a>, 2019.

%H Felix Fröhlich, <a href="/A308937/a308937_1.pdf">Remarks specifying the tiling used for generating the sequence</a>, 2019.

%H Chaim Goodman-Strauss, <a href="https://citeseerx.ist.psu.edu/pdf/22d654a2db56e6f2d48a679a4ed9543f5ddbf703">Aperiodic Hierarchical Tilings</a>, in: J. F. Sadoc and N. Rivier, Foams and Emulsions, NATO Science Series, Series E, Vol. 354, Springer, pp 481-496, DOI:<a href="https://doi.org/10.1007/978-94-015-9157-7_28">10.1007/978-94-015-9157-7_28</a>.

%H Tilings Encyclopedia, <a href="https://tilings.math.uni-bielefeld.de/substitution/chair/">Chair</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Langton%27s_ant">Langton's ant</a>

%e See illustrations in Fröhlich, 2019.

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

%K nonn,more

%O 0,3

%A _Felix Fröhlich_, Jul 01 2019