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Our member, Turtle, already has a thread on Fractals, and has linked to an excellent website that delves deeply into 3d fractals. I think you will enjoy it.

 

http://hypography.com/forums/physics-and-mathematics/5625-fractal-geometry-of-nature-9.html#post286915

 

I think you will find the "Mandelbulb" to be a better approximation of a 3d Mandelbrot function than just rotating along an axis. The linked site also has many other links to explore as well. Have fun :)

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