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If you read French, see this article http://images.math.cnrs.fr/La-methode-de-Newton-et-son,891.html (http://images.math.cnrs.fr/La-methode-de-Newton-et-son,891.html)

Google translate does not do a very good job if you want to try that..

Wow, there is a link between Mandelbrot Set and Newton fractals.

i was going to post the same link... too late ;)

The Newton-Mandlebrot connection has been known since at least 1999. Mark Townsend published Fractint formulas called Cayley-Mandel and Cayley-Julia about that time. I am rendering a 3D example in Ultrafractal using my Cubic Roots formula, which uses Newton's method. It should be available for posting in about an hour.

Well, Nova set is very old, and it is a clear example of connection between Newton set and Mandelbrot :) Never used a Nova set Trafassel? ;)

Here is the Newton-Mandelbrot connection I promised using my cubic roots formula.

There is so much, I didn't know. But I am here to learn.

Back at the very beginning of UltraFractal  a series of challenges were created by Janet Parke to help the new users learn about Ultrafractal. The image and the one in my next post were from some enties I made to the challenges. The date I have on the files is 1999. The image in this post was created with a Cayley Mandel formula, and is a Newton fractal.

Here is the next one - a Cayley Julia grey scale image.

I just ran into; http://www.fractalforums.com/new-theories-and-research/triplex-newton's-method/

Nobody tried? :sad1: