
Newton & Halley
Nova Tan Nebula
Halley-Newton Fractal
The map z -> z - tan(z) + c with c = 0.4 + 0.15i, which is Newton's method on sin z with a constant offset added each step. The map is exactly pi-periodic, so it is iterated on the cylinder with Re z wrapped into [-pi/2, pi/2) and a winding number accumulated. That winding number is the basin label and it sets the hue. Brightness follows the settle count over the band 13.2 to 27, and the white points are fast preimages of the fixed points.