Bravais mark BRAVAIS
← Fractals
Molten Filigree XX Column
Newton & Halley

Molten Filigree XX Column

Newton Fractal

Newton's method applied to f(z) = z^20 - z = z(z^19 - 1), cropped onto one arm axis, which is a mirror line of the field. 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.