Logo by Trifox - 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: Check out the originating "3d Mandelbulb" thread here
Welcome, Guest. Please login or register. August 16, 2022, 02:45:29 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
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: Polynomial Menger Sponge  (Read 413 times)
0 Members and 1 Guest are viewing this topic.
Fractal Senior
Posts: 1739

« on: May 11, 2016, 01:52:13 AM »

Polynomial Menger Sponge


Polynomial Menger Sponge
Fractal Senior
Posts: 1739

« Reply #1 on: May 11, 2016, 07:16:14 AM »

Lately for Mandelbulber dev V2.08 we have been exploring Polynomials

    z^2  +  z  +  c;

 or written with some variable parameters added

   newZ =  A * z^2  +  B * z  +  C;

The case, when A = 1 and B = 0, we get      z = z^2 + C ,     mandelbrot julia;

Collatz fractal is  also a  polynomial,  refer:


Each  “z”   can be made conditionally unique by modification,

The polynomial  can be re-written  as:    newZ =  ( Za * Zb)    +   Zc  +  C;

examples of unique "z" conditions:
Za = (VectA + ScaleA * z )   
Zb =  cos( pi * ScaleB * z)
Zc = fabs(z) 
Zd = Box Offset
or infinitely more  complicated,    Ze =  (  Za + Zg + Zp  ……)

however, the more complicated functions,  require  longer render times and can make distance estimation  difficult.

In Mandelbulber dev V2.08  we currently have  a transform, Transf_Pwr2_Polynomial, which is coded as

   newZ =   - (partA * fn(z))   + part B,  where

partA =  Za = (VectA + ScaleA * z )

fn(z) is various z_function options    e.g  Zb =  cos( pi * ScaleB * z) (default = Collatz)

partB  =  Zc + C   =    ScaleC * z + VectC.

Exploration to date, finds the easiest  usage is as a single iteration pre-transform,  and works very well with IFS especially Menger_Sponge, using analytic linear DE.   
Pages: [1]   Go Down
Jump to:  

Related Topics
Subject Started by Replies Views Last post
A Menger Sponge Images Showcase (Rate My Fractal) David Makin 5 3909 Last post April 02, 2007, 03:16:32 AM
by bradorpoints
Menger sponge fly-through 3D Fractal Generation twinbee 10 5171 Last post February 16, 2009, 05:43:21 AM
by twinbee
4D Menger sponge Sierpinski Gasket « 1 2 » makc 27 10975 Last post December 09, 2016, 04:01:39 PM
by knighty
3D menger sponge fly through Movies Showcase (Rate My Movie) DonWebber 0 1987 Last post September 14, 2010, 01:01:18 AM
by DonWebber
Through the Menger Sponge Movies Showcase (Rate My Movie) Michael Scharrer 0 542 Last post October 17, 2015, 05:55:43 PM
by Michael Scharrer

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 0.16 seconds with 29 queries. (Pretty URLs adds 0.005s, 2q)