3D Newton fractals

[JosLeys]

If you read French, see this article 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..

[trafassel]

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

[ker2x]

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

[fractalrebel]

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.

[DarkBeam]

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?

[fractalrebel]

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

[trafassel]

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

[fractalrebel]

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.

[fractalrebel]

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

[DarkBeam]

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

Nobody tried?