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A325953
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Langton's ant on a three-dimensional grid: number of black cells on the grid after n moves of the ant.
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9
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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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
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LINKS
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EXAMPLE
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See illustration in links.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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