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Welcome to Fractal Forums > Fractal Math, Chaos Theory & Research > Mandelbrot & Julia Set > The 3D Mandelbulb > Theory > Mandelbulb - non-divergent == point or periodic ?
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Author Topic: Mandelbulb - non-divergent == point or periodic ?  (Read 598 times)
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David Makin
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« on: August 01, 2012, 11:17:55 PM »
Has anyone attempted to determine (reasonably certainly) that all points of the Mandelbulb that do not diverge are either point or periodic attractors (excluding the infinite limit of course)...either analytically or quantitatively ?

Or are some strange attractors ? Or simply infinitely varied orbits ?

I confess I don't know if or how the above was or could be proved for the complex Mandy let alone the Mandelbulb wink
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hobold
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« Reply #1 on: August 02, 2012, 10:44:38 AM »
If I recall correctly, the respective proof for the classical Mandelbrot set had the scope of a PhD thesis ... this could be a bit of work. smiley

I am not sure if this existing work can be leveraged for the Mandelbulb. The triplex numbers lack some of the properties required for some existing mathematical tools to work. But I admit it would be interesting to try and see how far one can come. (But don't hold your breath; my mind is currently occupied with surfaces that are anything but fractal.)
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