A308973 - OEIS

%I #16 Jul 21 2019 08:21:57

%S 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 14,15,16,17,18,17,16,17,18,17,16,17,18,19,20,21,22,21,22,23,24,23,22,

%U 23,24,25,26,27,28,27,28,29,30,29,28,29,30,31,32,33,34

%N 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 First differs from A269757 at n = 19.

%C On a white square, turn 90 degrees right, flip the color of the tile, then move forward one unit.

%C On a white octagon, turn 45 degrees right, flip the color of the tile, then move forward one unit.

%C On a black square, turn 90 degrees left, flip the color of the tile, then move forward one unit.

%C On a black octagon, turn 45 degrees left, flip the color of the tile, then move forward one unit.

%C 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 Rémy Sigrist, <a href="/A308973/b308973.txt">Table of n, a(n) for n = 0..500</a>

%H Felix Fröhlich, <a href="/A308973/a308973.pdf">Illustration of iterations 0-50 of the ant</a>, 2019.

%H Rémy Sigrist, <a href="/A308973/a308973.png">Configuration after 100 steps</a>

%H Rémy Sigrist, <a href="/A308973/a308973.gp.txt">PARI program for A308973</a>

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

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Truncated_square_tiling">Truncated square tiling</a>

%F a(n + 12) = a(n) + 6 for any n >= 34. - _Rémy Sigrist_, Jul 21 2019

%e See illustrations in Fröhlich, 2019.

%o (PARI) See Links section.

%Y Cf. A255938, A269757, A308590, A308937, A326167, A326352.

%K nonn

%O 0,3

%A _Felix Fröhlich_, Jul 04 2019

%E More terms from _Rémy Sigrist_, Jul 21 2019