Spiny Newton

June 14, 1998

…not to be confused with “Spiny Norman” of Monty Python fame. It isn’t hard to tell the difference. Spiny Newton is a fractal and Spiny Norman is a 50 foot high hedgehog.

This is another preview of the next version of Fractal Domains. I still haven’t implemented saving these fractals as a parameter file (soon, I promise!), but I think I can remember how to reproduce this one. This is the Julia set of Newton’s method applied to f(x) = x^3 – 1 with angular decomposition. Even and odd dwell regions are rendered with separate color maps. An unusual convergence criterion discovered by Clifford Pickover produces the “spines.”