

A325953


Langton's ant on a threedimensional 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
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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  90degree 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 050 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 A255938 A081748
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



