A309236 Langton's ant on a circular grid with 4-fold rotational symmetry: number of black cells on the grid after n moves of the ant.

0, 1, 2, 3, 2, 3, 4, 5, 4, 3, 2, 3, 2, 3, 4, 3, 4, 5, 6, 5, 6, 7, 6, 7, 6, 5, 4, 5, 6, 7, 6, 7, 8, 9, 8, 7, 6, 7, 6, 5, 4, 3, 4, 5, 6, 5, 6, 5, 6, 7, 6, 7, 6, 7, 6, 5, 4, 5, 6, 7, 6, 7, 8, 9, 8, 7, 6, 7, 6, 7, 6, 7, 8, 7, 8, 7, 8, 9, 10, 9, 8, 7, 6, 7, 6, 5, 4

Offset

0,3

Comments

On a white circular segment, turn right to the next edge of the segment, flip the color of that segment, then move onto the segment adjacent to that edge.

On a black circular segment, turn left to the next edge of the segment, flip the color of that segment, then move onto the segment adjacent to that edge.

Links

Table of n, a(n) for n=0..86.

Felix Fröhlich, Illustration of iterations 0-50, 2019.

Example

See illustrations in Fröhlich, 2019.

Prog

(PARI) lista(nn) = my(c, d=1, x, y, u=1, v=List([])); print1(c); for(n=1, nn, if(x, if(x>#v, listput(v, [1, 1, 1, 1])); if(v[x][y]<0, d=d%4+1, d=(d+2)%4+1); c-=v[x][y]=-v[x][y]; if(d==3, x--; if(!x, d=(y+1)%4+1), x+=d%2; y=(y-d)%4+1), if(u<0, y=(d+2)%4+1, y=d%4+1); c-=u=-u; x=d=1); print1(", ", c)); \\ Jinyuan Wang, Jul 15 2025

Crossrefs

Cf. A255938, A269757, A308590, A308937, A308973, A309064, A326167, A326352.

Sequence in context: A213183 A386643 A125929 * A071933 A209802 A064672

Adjacent sequences: A309233 A309234 A309235 * A309237 A309238 A309239

Keyword

nonn

Author

Felix Fröhlich, Jul 17 2019

Extensions

More terms from Jinyuan Wang, Jul 15 2025

Status

approved