A326166 Total number of ants after n iterations in male/female Langton's ant variation.

2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7

Offset

0,1

Comments

There are male (blue) and female (pink) ants.

The rules governing the behavior of the ants are as follows:

1. On a white square, turn 90 degrees right, flip the color of the square, then move forward one unit.

2. On a black square, turn 90 degrees left, flip the color of the square, then move forward one unit.

3. If a male ant and a female ant occupy the same square, they mate and leave behind an egg.

4. When two ants of the same sex meet on a square, nothing happens.

5. Any ant can only mate with exactly one ant of the other sex each iteration.

6. The egg hatches when the square where the egg is located is no longer occupied by another ant.

7. When there is more than one egg on a square, only one of them can hatch per iteration.

8. The gender of the new ant is male if the square it hatches on is white in that iteration, female otherwise.

9. The color referred to in the previous rule is the color the square has in the first iteration where the new ant is alive.

10. The new ant always looks in north direction (upwards) at birth.

Links

R. J. Mathar, Table of n, a(n) for n = 0..399

Felix Fröhlich, Illustration of iterations 0-100

R. J. Mathar, More illustrations

Example

See illustration in links.

Crossrefs

Cf. A326167, A326168, A326169.

Sequence in context: A360391 A165024 A300402 * A211020 A157639 A010096

Adjacent sequences: A326163 A326164 A326165 * A326167 A326168 A326169

Keyword

nonn

Author

Felix Fröhlich, Jun 09 2019

Status

approved