Print Page - Periodic orbits of mandelbulb and mandelbox

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

Welcome to Fractal Forums

Fractal Math, Chaos Theory & Research => Theory => Topic started by: Tater on December 11, 2010, 05:55:18 PM