Logo by KRAFTWERK - Contribute your own Logo!


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 the official fractalforums.com Youtube Channel
Welcome, Guest. Please login or register. February 09, 2023, 09:27:59 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
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: Pure Wrappings / Inflections  (Read 429 times)
0 Members and 1 Guest are viewing this topic.
Fractal Bachius
Posts: 573

« on: February 05, 2017, 02:15:45 PM »

Pure Wrappings / Inflections


Toying with "inflections". As far as I understood them, they are really a wrapping of the complex plane around a given fixed center point. This can ultimately be expressed by a subtraction and a squaring of complex numbers.

In order to visualize a series of such wrappings, I started from a checkerboard pattern on the complex plane. But even when wrapped / inflected, this did not look all that interesting.

Then I layered a reciprocal (i.e. 1/z) on top of the checkerboard, which resulted in a nice, somewhat flower-like, center point around which the checkerboard gets smaller and smaller.

Finally the wrapping / inflection, when layered on top of the above, is nicely visible because it doubles the number of "flowers". So the eight "focal points" in this image are the result of just three wrappings / inflections.

Even without an underlying fractal formula, wrapping / inflection is a nice tool for producing interesting patterns.
Fractal Molossus
Posts: 696

Shapes only exists in our heads.

« Reply #1 on: February 05, 2017, 03:58:29 PM »

Seems the property of period doubling of the embedded julia-shapes in the mandelbrot set can be seen as a more universal property. This is a nice development indeed!

 Repeating Zooming Self-Silimilar Thumb Up, by Craig
Pages: [1]   Go Down
Jump to:  

Related Topics
Subject Started by Replies Views Last post
Pure Evil Vampire Empire Mandelbulb3D Gallery KRAFTWERK 0 271 Last post March 15, 2012, 05:11:43 PM
Raw Fractal Cosmic Friend ( 100% pure fractal ) Wildstyle milo 0 1438 Last post May 07, 2012, 02:08:58 PM
by milo
Raw Fractal Cosmic Child ( 100% pure fractal ) Wildstyle milo 0 1393 Last post May 07, 2012, 02:11:40 PM
by milo
Pure Harlequin Ultrafractal Jimmie 0 612 Last post February 02, 2013, 12:13:51 PM
by Jimmie
Holiday in Hybridia - Pure Poet Tree Mandelbulber Gallery mclarekin 5 412 Last post September 19, 2013, 03:38:20 AM
by mclarekin

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 0.199 seconds with 24 queries. (Pretty URLs adds 0.006s, 2q)