Hi, I am a fractal programmer.
I have a question about Newton's complex boundaries:
The classic formula used to illustrate Newton's boundaries is
x^3-1=0
This produces an image with three basins of attractions,
each basin representing a root of the equation. Now, my question is:
What formula produces images with copies of the Mandelbrot set inside?
or maybe even Julia sets? I have looked through many books, but
they usually just skim the surface and dont go in too deep about newtons
complex boundaries. Any help would be highly appreciated.
Thank you.
-Ivan