Logo by Trifox - 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 the official fractalforums.com Youtube Channel
 
*
Welcome, Guest. Please login or register. January 30, 2023, 06:09:40 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: IFS and Minkowski Dimension  (Read 2883 times)
Description: How to calculate Minkowski Dimension from image and IFS
0 Members and 1 Guest are viewing this topic.
Crucifixio
Guest
« on: February 11, 2009, 09:04:11 PM »

I'm writing program to generate fractals using IFS and caluclating Minkowski dimension. I've got question how to calculate Minkowski dimension from Image (2d fractals) using box counting with some Epsilon (size of the box) and how to calculate exact dimension from IFS to find error between count-box dimension and exact dimension from IFS ?
Logged
David Makin
Global Moderator
Fractal Senior
******
Posts: 2286



Makin' Magic Fractals
WWW
« Reply #1 on: February 11, 2009, 10:21:24 PM »

I haven't looked into using box counting to get the fractal dimension but I did search a lot on the internet a while ago for documents on finding the "correct" fractal dimension of a given affine IFS from the transformations and I found:

"A Multifractal Analysis of IFSP Invariant Measures With Application to Fractal Image Generation" by J.M. Gutierrez and A. Iglesias and M.A. Rodrıguez

I found it on the web as "fractals96.pdf".

I highly recommend it as a read (if your maths is up to it) but basically it concludes that for a given IFS:

log(p0)/log(s0) = log(p1)/log(s1) = log(p2)/log(s2) =.... = Constant

where the pn are the (correct) probabilities for the scales sn and Constant is basically the fractal dimension. Normally it's used to get the correct probabilities for a given set of transforms.

The only problem with this is how you decide the scale value to use for transforms that have non-uniform scales.
I basically used the determinant values but other methods may yield better results in some situations (from a rendering point of view) e.g. min or max scale along any one axis.

If you want the document but can't find it then just drop me a line at makinmagic@tiscali.co.uk
Logged

The meaning and purpose of life is to give life purpose and meaning.

http://www.fractalgallery.co.uk/
"Makin' Magic Music" on Jango
David Makin
Global Moderator
Fractal Senior
******
Posts: 2286



Makin' Magic Fractals
WWW
« Reply #2 on: March 29, 2009, 12:42:13 AM »

<snip>
...basically it concludes that for a given IFS:

log(p0)/log(s0) = log(p1)/log(s1) = log(p2)/log(s2) =.... = Constant

where the pn are the (correct) probabilities for the scales sn and Constant is basically the fractal dimension. Normally it's used to get the correct probabilities for a given set of transforms.
<snip>

Something interesting just struck me about this - the standard "Measure Theory" version of fractal dimension is dimension=log(new length)/log(old length) so in fact here the probablity is analagous to "new length" and/if the scale is analagous to "old length".
Logged

The meaning and purpose of life is to give life purpose and meaning.

http://www.fractalgallery.co.uk/
"Makin' Magic Music" on Jango
paxinum
Guest
« Reply #3 on: July 08, 2010, 05:31:03 PM »

You mean Hausdorff dimension?

Minkowski developed the 4-dimensional 3-space + time used by Einstein in relativity theory...
Logged
Pages: [1]   Go Down
  Print  
 
Jump to:  

Related Topics
Subject Started by Replies Views Last post
The Fractal Dimension of ZIP Codes Fractal News across the World bib 0 2363 Last post January 05, 2012, 04:02:14 PM
by bib
Higer dimension modulus or something odd (new) Theories & Research Alef 2 440 Last post July 25, 2012, 05:38:20 PM
by Alef
ABSOLIENS: gÚnÚralisation naturelle des nombres complexes Ó toute dimension ? franšais Yannis 1 2581 Last post January 01, 2013, 06:49:05 PM
by Yannis
Help me with the fractal dimension Help & Support kna007 0 314 Last post October 11, 2012, 09:08:30 AM
by kna007
hausdorff dimension of PI ???!?! General Discussion « 1 2 » cKleinhuis 16 2249 Last post January 09, 2013, 12:43:15 AM
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 0.133 seconds with 25 queries. (Pretty URLs adds 0.005s, 2q)