A325955 Langton's ant on a three-dimensional grid: number of yellow cells on the grid after n moves of the ant.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 5

Offset: 0

Author

Felix Fröhlich, May 28 2019

Keywords

• nonn

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 the cell is

start of iteration | 90-degree turn | changed to

--------------------------------------------------------

white | right | black

black | left | blue

blue | up | yellow

yellow | down | white

Examples

			See illustration in links.
		

Links

• Jinyuan Wang, Table of n, a(n) for n = 0..10000
• Felix Fröhlich, Illustration of iterations 0-50 of the ant
• Wikipedia, Langton's ant

Crossrefs

Cf. A255938, A308563, A325953, A325954.

Formula

a(n) = a(n-28) + 4 for n >= 93504. - Jinyuan Wang, Jul 13 2025

Extensions

a(51)-a(81) from Charlie Neder, Jun 06 2019