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Welcome to Fractal Forums > Fractal Math, Chaos Theory & Research > Mandelbrot & Julia Set > The 3D Mandelbulb > Theory > Periodic orbits of mandelbulb and mandelbox
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Author Topic: Periodic orbits of mandelbulb and mandelbox  (Read 1701 times)
Description: chaotic dynamics on the mandel* sets
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Tater
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Posts: 71
« on: December 11, 2010, 05:55:18 PM »
Hi everyone. I just joined a few days ago after being turned on to the wonders of the bulbs and boxes.

I am interested in looking at these objects dynamically and determining the periodic orbit sets. I'll use the mandelbulb as an example because its formula is the simplest.

The bulb is the invariant set of the transformation v_n = r < \cos\, \theta\, \cos\, \phi,\, \sin \theta\, \cos \phi, \,- \sin \phi > \rightarrow v_{n+1} = r^n < \cos\, n\, \theta\, \cos\, n\, \phi,\, \sin\, n\, \theta\, \cos\, n\, \phi ,\, - \sin\, n\, \phi > + <c_1,\, c_2,\, c_3> so a period one orbit would be a fixed point v_{n+1} = v_n, a period two orbit is a point in space for which  v_{n+2} = v_n, and so on.

I am not much of a programmer (I can program in Maple and Matlab but am clumsy with C) so I guess my questions are these -- how does one get access to this information from Mandelbulber or Mandelbulb 3d?  Has anyone looked at this to your knowledge?

Tater
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