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News from the world of maths: Pandora's 3D box
An amateur fractal programmer has discovered a new 3D version of the Mandelbrot set. Daniel White's new creation is based on similar mathematics as the original 2D Mandelbrot set, but its infinite intricacy extends into all three dimensions, revealing fractal worlds of amazing complexity and beauty at every level of magnification.
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posted by Plus @ 9:45 AM
6 Comments:
 At 12:56 PM, said...

I want this as screensaver,awesome
 At 2:27 PM, David Makin said...

Those interested in more about the Mandelbulb and the search for the "true 3D" Mandelbrot including an almost complete history of the last couple of years search may wish to look here http://www.fractalforums.com/
 At 10:30 AM, miner49er said...

What's the explanation for the fracvtal nature of the mandelbrot set? Is it an anomoly in the number system? Is it basically an error?
I have been fascinated by fractals for 20 years but never really thought about _why_ they (mandelbrot/escapetime) exist.
I wonder if discovering why they exist at all, may lead to a 'better' 3D analog?  At 7:06 AM, Djeimz said...

Interesting article. Interesting pictures.
However, I'm wondering if there isn't a typo in the formula given. If it is a direct generalization of complex multiplication using Euler angles, the zcomponent should be:
sin(n phi)
and not:
sin(n theta)
Am I wrong?
James  At 10:25 AM, said...

Thanks Djeimz, you're right and it's been corrected!
 At 12:12 AM, Paolo Bonzini said...

It is possible to describe this fractal also using quaternions. This is interesting in that it removes the need to define a special, nonstandard exponentiation function.
See http://github.com/bonzini/mbulb/raw/master/mbulb.pdf [PDF] (thanks to the people on reddit.com and fractalforums.com for proofreading!)