Newton fractal

Newton’s method hunts for a root of zⁿ − 1 from a starting guess. Shade each start by the root it reaches, a different tone of ink for each. Near the borders the basins interleave without end: every boundary point touches all of them at once.

zₖ₊₁ = zₖ − a (zₖⁿ − 1) / (n zₖⁿ⁻¹)

On mathcurve.com as Fractale de Newton