Fractal of the Week for June 14, 1998
Spiny Newton
...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."
Below is a link to an 832 X 624 rendering of the image. For those who want to use this as a screen image and need 800 X 600, this image can be cropped to that size without any significant loss. JPEG rendering unfortunately introduces a small amount of Moire patterning in this one.
