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
January 05, 2012, 04:02:14 PM
Dilber MC Theme by HarzeM