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

Author

Felix Fröhlich, Jul 17 2019

Keywords

• nonn

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.

Examples

			See illustrations in Fröhlich, 2019.
		

Links

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

Crossrefs

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

Programs

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

Extensions

More terms from Jinyuan Wang, Jul 15 2025