Logo by teamfresh - 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
 
Home Help Search Gallery Downloads Login Register
*
Welcome, Guest. Please login or register. November 29, 2025, 05:44:02 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!


Welcome to Fractal Forums > Fractal Software > 3D Fractal Generation > DE calculation for "compound" fractals ?
Pages: [1]   Go Down
« previous next »
  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: DE calculation for "compound" fractals ?  (Read 3304 times)
0 Members and 1 Guest are viewing this topic.
David Makin
Global Moderator
Fractal Senior
******
Posts: 2286



Makin' Magic Fractals
WWW
« on: May 03, 2010, 10:28:53 PM »
Hi all,

Here's a compound fractal, (on each iteration) the standard Mandelbox (without constant) followed by standard ^8 -sine White/Nylander Mandelbulb:



This was rendered with correct scaling of the running derivative in the Mandelbox calculation and correct adjustment of it in the Mandelbulb calculations with the final DE value calculated based on the normal Mandelbulb method.

My question is - what should have been done as the final DE calculation ? Should it actually be different due to the use of the Mandelbox ?
If the Mandelbulb had been done first followed by the Mandelbox then should the DE calculation use the Mandelbox DE calculation insted of the Mandelbulb one ?
« Last Edit: May 03, 2010, 10:58:36 PM by David Makin » Logged
The meaning and purpose of life is to give life purpose and meaning.

http://www.fractalgallery.co.uk/
"Makin' Magic Music" on Jango
reesej2
Guest
« Reply #1 on: May 04, 2010, 12:02:23 AM »
The use of the Mandelbox should change it somehow, but I haven't a clue how to work it out... I'd be fascinated to see it.
Logged
Jesse
Download Section
Fractal Schemer
*
Posts: 1013
« Reply #2 on: May 04, 2010, 12:27:44 AM »
That is very promising, good work.
Just wonder if there is already a common way to calculate the derivative and a DE based on it for general formulas?
Logged
David Makin
Global Moderator
Fractal Senior
******
Posts: 2286



Makin' Magic Fractals
WWW
« Reply #3 on: May 04, 2010, 12:49:38 AM »
Quote from: Jesse on May 04, 2010, 12:27:44 AM
That is very promising, good work.
Just wonder if there is already a common way to calculate the derivative and a DE based on it for general formulas?

Well there is, in that in this case any of the delta DE methods should work OK, it's just that in my experience so far the analytical method produces the best results when you consider quality of image and render speed together so I was hoping if maybe someone had ideas on how to turn the running derivative and final z into a DE value correctly for compound fractals like this one.
The method I have used here, simply using the DE formula for the Mandelbulb, works OK but I'm sure (based on the render speed) that it's not producing very linear distance estimation i.e. its a lot slower at rendering to a given quality than using the analytical method for either a pure Mandelbox or a pure Mandelbulb.
Logged
The meaning and purpose of life is to give life purpose and meaning.

http://www.fractalgallery.co.uk/
"Makin' Magic Music" on Jango
knighty
Fractal Iambus
***
Posts: 819
« Reply #4 on: May 04, 2010, 03:03:22 PM »
Honeslty, I don't know but I suspect it is related to the asymptotic behaviour of the orbits, the phi function and the fact that the DE formula for the mandelbox doesn't involve log(r). If I remember well, phi(z)=z when z->infinity. for the mandelbox we should have something like phi(z)=z/scale^i (which gives DE=|z|/|dz|).
« Last Edit: May 05, 2010, 02:40:42 PM by knighty, Reason: Corrected very stupid mistakes. Sorry. » Logged
knighty
Fractal Iambus
***
Posts: 819
« Reply #5 on: May 05, 2010, 10:03:22 PM »
I have given it a try with DE=0.5*r*log(r)/dr/DEfactor. It works very well and is near optimal when not adding 1 to DEfactor. If not, it is up to 3 times smaller.
Logged
David Makin
Global Moderator
Fractal Senior
******
Posts: 2286



Makin' Magic Fractals
WWW
« Reply #6 on: May 06, 2010, 12:02:57 AM »
Quote from: knighty on May 05, 2010, 10:03:22 PM
I have given it a try with DE=0.5*r*log(r)/dr/DEfactor. It works very well and is near optimal when not adding 1 to DEfactor. If not, it is up to 3 times smaller.

Do you mean the same thing I did, i.e. Mandelbox(without constant) followed by Mandelbulb, or did you actually try Mandelbulb(without constant) followed by Mandelbox ?
Logged
The meaning and purpose of life is to give life purpose and meaning.

http://www.fractalgallery.co.uk/
"Makin' Magic Music" on Jango
knighty
Fractal Iambus
***
Posts: 819
« Reply #7 on: May 06, 2010, 04:26:57 PM »
I did Mandelbox without constant followed by mandelbulb this way:
DEfactor=1.
dr=1.
iterate begin:
box fold.
sphere fold (including update ofEfactor).
scale without adding constant and including update of DEfactor without adding 1.
Mandelbulb including update of dr.
iteration end.
DE=0.5*r*log(r)/dr/DEfactor.

(I have separated DEfacor and dr just for convenience)
Haven't yet tried the other case.
Logged
visual.bermarte
Fractal Fertilizer
*****
Posts: 355
« Reply #8 on: July 19, 2010, 10:54:35 PM »
compound fractals: tests
super.fatty


land.of.confusion
Logged
visual.bermarte
Fractal Fertilizer
*****
Posts: 355
« Reply #9 on: July 20, 2010, 03:03:47 AM »
K.tests grin
Logged
matsoljare
Fractal Lover
**
Posts: 215



WWW
« Reply #10 on: July 20, 2010, 05:44:07 PM »
Can we have some higher resolution versions of those?
Logged
Pages: [1]   Go Down
« previous next »
  Print  
« previous next »
 
Jump to:  

Related Topics
Subject Started by Replies Views Last post
How are B&W images from "Beauty of Fractals" created? Mandelbrot & Julia Set « 1 2 » Duncan C 29 23063 Last post January 11, 2008, 06:49:23 PM
by Duncan C
My friend "max" and Pacman made it into the world of fractals Fractal Humor Dinkydau 4 6654 Last post November 16, 2009, 10:43:02 PM
by Dinkydau
complex compound /w new coloring z^2 looks like a 3d Mandelbrot. "Wolf, Wolf!!" Images Showcase (Rate My Fractal) M Benesi 8 2256 Last post July 22, 2010, 08:29:36 AM
by M Benesi
New book: "Alt.Fractals: A visual guide to fractal geometry and design" Commercial Corner ErkDemon 4 9815 Last post September 26, 2014, 02:57:18 PM
by LMarkoya
"Fractals!" at Fulldome UK 2011 Fractal News across the World bib 2 4382 Last post March 02, 2011, 06:43:50 PM
by Madman

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 0.707 seconds with 27 queries. (Pretty URLs adds 0.013s, 2q)