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A325953 Langton's ant on a three-dimensional grid: number of black cells on the grid after n moves of the ant.

%I A325953 #37 Jul 16 2025 17:55:05
%S A325953 0,1,2,3,4,3,4,5,6,6,7,8,7,8,9,10,10,9,8,8,7,6,6,6,7,8,9,9,10,11,10,
%T A325953 11,12,11,12,13,14,14,15,16,15,16,17,18,18,17,16,16,15,14,14,14,15,16,
%U A325953 17,17,18,19,18,19,20,19,20,21,22,22,21,20,20,21,20,21
%N A325953 Langton's ant on a three-dimensional grid: number of black cells on the grid after n moves of the ant.
%C A325953 The ant starts on a completely white grid.
%C A325953 Order of operations: turn 90 degrees, change cell color, move forward one unit.
%C A325953 The rules governing the movement of the ant and the change of cell colors are shown in the following table:
%C A325953     Cell color at    |  Direction of  | Color to which the
%C A325953   start of iteration | 90-degree turn |  cell is changed
%C A325953   -------------------+----------------+-------------------
%C A325953         white        |     right      |       black
%C A325953         black        |     left       |       blue
%C A325953         blue         |     up         |       yellow
%C A325953         yellow       |     down       |       white
%C A325953 The first differences of this sequence are ultimately periodic with period 28 beginning at generation 93475, see A308563. - _Charlie Neder_, Jun 10 2019
%H A325953 Jinyuan Wang, <a href="/A325953/b325953.txt">Table of n, a(n) for n = 0..10000</a>
%H A325953 Felix Fröhlich, <a href="/A325953/a325953_2.pdf">Illustration of iterations 0-50 of the ant</a>
%H A325953 Charlie Neder, <a href="/A325953/a325953.py.txt">Python program for running this automaton</a>
%H A325953 Wikipedia, <a href="https://en.wikipedia.org/wiki/Langton%27s_ant">Langton's ant</a>
%F A325953 a(n) = a(n-28) + 4 for n >= 93504. - _Jinyuan Wang_, Jul 13 2025
%e A325953 See illustration in links.
%Y A325953 Cf. A255938, A308563, A325954, A325955.
%K A325953 nonn
%O A325953 0,3
%A A325953 _Felix Fröhlich_, May 28 2019
%E A325953 a(51)-a(68) from _Charlie Neder_, Jun 06 2019