Logo by reallybigname - 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: Support us via Flattr FLATTR Link
 
*
Welcome, Guest. Please login or register. March 28, 2024, 08:19:43 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 Julia patterns  (Read 1737 times)
0 Members and 1 Guest are viewing this topic.
s31415
Conqueror
*******
Posts: 110



WWW
« on: March 31, 2012, 12:02:29 AM »

Hi,

Just to offer some update about Dense Julia patterns. It turns out they have very cool invarance properties under conformal transformations. Under such a transformation, while the details of the pattern change, its general look stays invariant. Some examples in pictures can be found here.

Even cooler, these properties can be used to create periodic Julia patterns on the plane. The construction involves the geometrical concept of covering. The dense Julia sets live on the sphere, as I explained in a previous post. On the other hand, a periodic pattern can be seen as a decoration of a torus. The existence of a covering of the sphere by a torus allows to pull-back the Julia pattern from the sphere conformally and create a periodic pattern. More details and pictures can be found in this blog post.

This last post also exemplifies why non conformal transformations are aesthetically much less interesting than conformal ones, as far as Mandelbrot/Julia-type fractals are concerned.

Attached are two pictures of dense Julia patterns. Check the blog post for higher resolution pictures.

Sam


* 20120330-20110808-Weierstrass.jpg (128.04 KB, 500x500 - viewed 411 times.)

* 20120330-20111029-invj24.jpg (218.3 KB, 500x500 - viewed 426 times.)
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 7949 Last post June 24, 2017, 12:38:40 PM
by Adam Majewski
Periodic orbits of mandelbulb and mandelbox Theory Tater 0 1218 Last post December 11, 2010, 05:55:18 PM
by Tater
Fractals using periodic boundaries 3D Fractal Generation msltoe 2 4380 Last post December 21, 2010, 07:09:19 AM
by fractower
An animation of periodic dense Julia patterns Movies Showcase (Rate My Movie) s31415 0 1212 Last post June 26, 2012, 10:54:48 PM
by s31415
Mandelbulb - non-divergent == point or periodic ? Theory David Makin 1 4189 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 0.216 seconds with 24 queries. (Pretty URLs adds 0.01s, 2q)