A325953 - OEIS

%I #30 Jul 01 2019 16:38:29

%S 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 11,12,11,12,13,14,14,15,16,15,16,17,18,18,17,16,16,15,14,14,14,15,16,

%U 17,17,18,19,18,19,20,19,20,21,22,22,21,20,20

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

%C The ant starts on a completely white grid.

%C Order of operations: turn 90 degrees, change cell color, move forward one unit.

%C The rules governing the movement of the ant and the change of cell colors are shown in the following table:

%C     Cell color at    |  Direction of  | Color to which the

%C   start of iteration | 90-degree turn |  cell is changed

%C   -------------------+----------------+-------------------

%C         white        |     right      |       black

%C         black        |     left       |       blue

%C         blue         |     up         |       yellow

%C         yellow       |     down       |       white

%C The first differences of this sequence are ultimately periodic with period 28 beginning at generation 93475, see A308563. - _Charlie Neder_, Jun 10 2019

%H Felix Fröhlich, <a href="/A325953/a325953_1.pdf">Illustration of iterations 0-50 of the ant</a>

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

%H Charlie Neder, <a href="/A325953/a325953.py.txt">Python program for running this automaton</a>

%e See illustration in links.

%Y Cf. A255938, A325954, A325955.

%K nonn

%O 0,3

%A _Felix Fröhlich_, May 28 2019

%E a(51)-a(68) from _Charlie Neder_, Jun 06 2019