login
A325953
Langton's ant on a three-dimensional grid: number of black cells on the grid after n moves of the ant.
9
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, 11, 12, 11, 12, 13, 14, 14, 15, 16, 15, 16, 17, 18, 18, 17, 16, 16, 15, 14, 14, 14, 15, 16, 17, 17, 18, 19, 18, 19, 20, 19, 20, 21, 22, 22, 21, 20, 20
OFFSET
0,3
COMMENTS
The ant starts on a completely white grid.
Order of operations: turn 90 degrees, change cell color, move forward one unit.
The rules governing the movement of the ant and the change of cell colors are shown in the following table:
Cell color at | Direction of | Color to which the
start of iteration | 90-degree turn | cell is changed
-------------------+----------------+-------------------
white | right | black
black | left | blue
blue | up | yellow
yellow | down | white
The first differences of this sequence are ultimately periodic with period 28 beginning at generation 93475, see A308563. - Charlie Neder, Jun 10 2019
EXAMPLE
See illustration in links.
CROSSREFS
KEYWORD
nonn
AUTHOR
Felix Fröhlich, May 28 2019
EXTENSIONS
a(51)-a(68) from Charlie Neder, Jun 06 2019
STATUS
approved