Path: utzoo!attcan!uunet!aplcen!ktc
From: ktc@aplcen.apl.jhu.edu (Kim Constantikes)
Newsgroups: comp.theory.dynamic-sys
Subject: Re: Computing Fractal Dimension
Message-ID: <5910@aplcen.apl.jhu.edu>
Date: 9 Jul 90 12:27:05 GMT
References: <81951@tut.cis.ohio-state.edu>
Reply-To: ktc@aplcen (Kim Constantikes)
Organization: Johns Hopkins University
Lines: 12

The boxcounting dimension (and algorithm) is an approximation to the rigorous
Hausdorff dimension, which is usually accepted as the "Fractal dimension". 
There are a multitude of other dimensions as well, such as information
dimension, simularity dimension, cluster dimension, etc.  These dimensions
usually, but not always, agree.  Note that boxcounting is a particularly
poor choice for estimation of the dimension of experimental data.  For a 
rigorous treatment of these subjects, see Falconer, "The Geometry of Fractal
Sets".  See Feder, "Fractals", for a good introduction, or the AMS collection
on fractals for a more rigorous but succinct treatment.

My own experience is that estimation of the Hurst exponent via range scaling
analysis is the best first approach.