
Newton & Halley
Molten Filigree XX Rosette
Newton Fractal
Newton's method applied to f(z) = z^20 - z = z(z^19 - 1), framed on the whole nineteenfold corona. The twenty roots are the origin and the nineteen 19th roots of unity, so the origin's basin throws nineteen arms out to infinity and the boundary between them beads into scrollwork. Colour runs on dwell = steps - ln(max|z|) / ln(20/19), the total step count minus the unavoidable far-field travel time.