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

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

Links

Table of n, a(n) for n=0..68.

Felix Fröhlich, Illustration of iterations 0-50 of the ant

Wikipedia, Langton's ant

Charlie Neder, Python program for running this automaton

Example

See illustration in links.

Crossrefs

Cf. A255938, A325954, A325955.

Sequence in context: A270652 A326693 A280242 * A245343 A369858 A341019

Adjacent sequences: A325950 A325951 A325952 * A325954 A325955 A325956

Keyword

nonn

Author

Felix Fröhlich, May 28 2019

Extensions

a(51)-a(68) from Charlie Neder, Jun 06 2019

Status

approved