Logo by Pauldelbrot - Contribute your own Logo!

END OF AN ERA, FRACTALFORUMS.COM IS CONTINUED ON FRACTALFORUMS.ORG

it was a great time but no longer maintainable by c.Kleinhuis contact him for any data retrieval,
thanks and see you perhaps in 10 years again

this forum will stay online for reference
News: Follow us on Twitter
 
*
Welcome, Guest. Please login or register. December 05, 2019, 06:28:28 PM


Login with username, password and session length


The All New FractalForums is now in Public Beta Testing! Visit FractalForums.org and check it out!


Pages: [1]   Go Down
  Print  
Share this topic on DiggShare this topic on FacebookShare this topic on GoogleShare this topic on RedditShare this topic on StumbleUponShare this topic on Twitter
Author Topic: Periodic orbits of mandelbulb and mandelbox  (Read 781 times)
Description: chaotic dynamics on the mandel* sets
0 Members and 1 Guest are viewing this topic.
Tater
Navigator
*****
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
Logged
Pages: [1]   Go Down
  Print  
 
Jump to:  

Related Topics
Subject Started by Replies Views Last post
Period 18 Julia (periodic bailout) UltraFractal Gallery David Makin 3 1423 Last post June 24, 2017, 12:38:40 PM
by Adam Majewski
Periodic Julia patterns Mandelbrot & Julia Set s31415 0 1126 Last post March 31, 2012, 12:02:29 AM
by s31415
a 3D Mandelbulb/Mandelbox gallery on the web 3D Fractal Generation cbuchner1 1 1109 Last post April 07, 2012, 06:58:22 AM
by taurus
Mandelbulb - non-divergent == point or periodic ? Theory David Makin 1 663 Last post August 02, 2012, 10:44:38 AM
by hobold

Powered by MySQL Powered by PHP Powered by SMF 1.1.21 | SMF © 2015, Simple Machines

Valid XHTML 1.0! Valid CSS! Dilber MC Theme by HarzeM
Page created in 0.336 seconds with 29 queries. (Pretty URLs adds 0.007s, 2q)