Logo by mclarekin - 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: Visit us on facebook
 
*
Welcome, Guest. Please login or register. March 29, 2024, 02:05:11 AM


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: Lattès Julia sets  (Read 1608 times)
0 Members and 1 Guest are viewing this topic.
s31415
Conqueror
*******
Posts: 110



WWW
« on: April 28, 2013, 10:32:22 PM »

Hi,

I finally wrote a blog post about a class of dense Julia sets I've been exploring lately:
http://algorithmic-worlds.net/blog/blog.php?Post=20130428
Julia sets are associated to conformal maps of the sphere to itself. Very roughly, a point belong to the Julia set if its iterations under the conformal map behaves in a chaotic way. It happens that certain Julia sets cover the whole plane, i.e. all the orbits are chaotic. This does not occur for the familiar Julia sets z -> z^2 + c, but does occur for more general rational maps. Dense Julia sets produce dense fractal patterns, just like the Ducks-Kaliset type algorithms, which I find much more appealing than usual 2d fractals. See my galleries for many examples of such patterns:
http://algorithmic-worlds.net/expo/expo.php

One way to construct maps whose Julia set is dense is to use the fact that the sphere admits branched coverings by a torus. The maps of the sphere which are covered by "affine expanding maps" of the torus are called Lattès map, and they necessarily have dense Julia sets. The blog post provides more explanations. Here is a reference for the mathematically inclined:
http://arxiv.org/abs/math/0402147

You can check many pictures of Lattès Julia sets in this collection:
http://algorithmic-worlds.net/expo/expo.php?Collection=Lattes&CollSearch=0
Under each picture, you can find the formula of the corresponding conformal map.

Best,

Sam
Logged

Pauldelbrot
Fractal Senior
******
Posts: 2592



pderbyshire2
« Reply #1 on: April 29, 2013, 12:33:52 AM »

Repeating Zooming Self-Silimilar Thumb Up, by Craig
Logged

Pages: [1]   Go Down
  Print  
 
Jump to:  

Related Topics
Subject Started by Replies Views Last post
Virtual investigation to Mandelbrot sets and Julia sets Mandelbrot & Julia Set Jules Ruis 0 5752 Last post October 19, 2006, 06:36:54 PM
by Jules Ruis
3D Julia sets 3D Fractal Generation kronikel 0 3315 Last post August 06, 2011, 10:35:30 PM
by kronikel
3D Julia Sets Mandelbrot & Julia Set hgjf2 3 2547 Last post October 25, 2012, 07:01:17 PM
by hgjf2
fractal dimension of Julia sets Mandelbrot & Julia Set claude 12 4891 Last post July 26, 2016, 03:35:34 AM
by valera_rozuvan
Frog and bunny-shaped quaternion Julia sets Mandelbrot & Julia Set tkim 4 2369 Last post July 31, 2015, 08:51:50 PM
by kram1032

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 0.158 seconds with 24 queries. (Pretty URLs adds 0.01s, 2q)