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A308973 Langton's ant on a truncated square tiling: number of black cells after n moves of the ant when starting on an octagon and looking towards an edge where the tile meets another octagon.

%I A308973 #16 Jul 21 2019 08:21:57
%S A308973 0,1,2,3,4,5,6,5,6,7,8,9,8,7,8,9,10,11,10,11,10,9,10,11,12,13,14,15,
%T A308973 14,15,16,17,18,17,16,17,18,17,16,17,18,19,20,21,22,21,22,23,24,23,22,
%U A308973 23,24,25,26,27,28,27,28,29,30,29,28,29,30,31,32,33,34
%N A308973 Langton's ant on a truncated square tiling: number of black cells after n moves of the ant when starting on an octagon and looking towards an edge where the tile meets another octagon.
%C A308973 First differs from A269757 at n = 19.
%C A308973 On a white square, turn 90 degrees right, flip the color of the tile, then move forward one unit.
%C A308973 On a white octagon, turn 45 degrees right, flip the color of the tile, then move forward one unit.
%C A308973 On a black square, turn 90 degrees left, flip the color of the tile, then move forward one unit.
%C A308973 On a black octagon, turn 45 degrees left, flip the color of the tile, then move forward one unit.
%C A308973 As in the original variant, order emerges after a transition phase and the ant starts building a recurrent "highway" pattern of 12 steps that repeats indefinitely. - _Rémy Sigrist_, Jul 21 2019
%H A308973 Rémy Sigrist, <a href="/A308973/b308973.txt">Table of n, a(n) for n = 0..500</a>
%H A308973 Felix Fröhlich, <a href="/A308973/a308973.pdf">Illustration of iterations 0-50 of the ant</a>, 2019.
%H A308973 Rémy Sigrist, <a href="/A308973/a308973.png">Configuration after 100 steps</a>
%H A308973 Rémy Sigrist, <a href="/A308973/a308973.gp.txt">PARI program for A308973</a>
%H A308973 Wikipedia, <a href="https://en.wikipedia.org/wiki/Langton%27s_ant">Langton's ant</a>
%H A308973 Wikipedia, <a href="https://en.wikipedia.org/wiki/Truncated_square_tiling">Truncated square tiling</a>
%F A308973 a(n + 12) = a(n) + 6 for any n >= 34. - _Rémy Sigrist_, Jul 21 2019
%e A308973 See illustrations in Fröhlich, 2019.
%o A308973 (PARI) See Links section.
%Y A308973 Cf. A255938, A269757, A308590, A308937, A326167, A326352.
%K A308973 nonn
%O A308973 0,3
%A A308973 _Felix Fröhlich_, Jul 04 2019
%E A308973 More terms from _Rémy Sigrist_, Jul 21 2019