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It sounds like you're holding back your erroneous method?
 :

I had a keyboard smashing time trying to learn UF version 5 HOW TO OPEN A CLASS
and now I've done it, I saw a blurry Newton set among few other alternatives. I realize this has artistic potential to the general extent of choosing light *beneath* the fractal.

Only now I realized my notebooks never had contents attached in any way... but, in file mt.ucl/Newton basin is the traditional outside coloring for Newton fractals.


color_newton.ucl

This ancient method depends from atan2 function to calculate the angular position of #z. The density is where fun is, because gradient contains colors of spectrum or anything else it can contain. Since colors go in circles, density is crude. It is used only to leave more room for all yellow colors for one root, all green colors for another... We can map the gradient discretely or continuously to one particular root. That function hold the beauty.
Normally, colors go in circles within gradient and there are too many fractal contours (if not even too many roots) so after a small number of contours AWAY from roots, colors start to spiral due to "delay" (shift) that occurred between roots (e.g. gradient/5 for 5 roots). If you count the contours away from root and remember the number of roots, you got some control over the design of DENSITY MAPPING (fun function).