Zi Dawn Ladder

Newton's method applied to f(z) = z^i - 1 on the principal branch. Every root is simple, since |f'| = e^(-Arg z) / |z| never vanishes, and the map is exactly self-similar under z -> e^(2 pi) z, so the render is made in the log plane with ln|z| running up and Arg z across. The window holds three rungs of the root ladder and its edges are the branch cut. Newton drift carries orbits up the ladder, so the mean root index climbs from 0.5 to 3.5 bottom to top and drives the hue.