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In article <78299@hydra.gatech.EDU>, jgostin@mal-s1.gatech.edu (Jill Gostin) writes:
> 
> Can anyone tell me how wavelets and fractals relate to each other,
> or point me to a good reference? I don't know much about wavelets
> at all.                             
> 
> Thanks,
> Jill
> -- 
> Jill Butterfield Gostin                EMAIL: jgostin@mal-s1.gatech.edu
> Georgia Institute of Technology, GTRI Modeling and Analysis Lab
> "Happiness is excitement that has found a settling down place..."
> -E.L. Konigsburg, _From the Mixed-up Files of Mrs. Basil E. Frankweiler_

Hi, I found one paper connecting the two subjects:

GC Freeland and TS Durrani, ``IFS Fractals and the Wavelet Transform,''
  Proc. ICASSP '90, New Mexiko, pp 2345--2348.

and it refers to a few others:

A Arneodo, G Grasseau and M Holschneider, ``Wavelet transform of
  Multi-fractals,'' Physical Review Letters, Vol 61, pp 2281--2284, 1988.

F Argoul et al, ``Wavelet Transform of Fractal Aggregates,'' Physics
  Letters, A, Vol 135, No 6/7 pp 327--336, 1989.


I suppose it depends on what you mean by `fractals.' If you take
it to mean some set which is (deterministically or randomly) self-similar
or self-affine over a wide range of scales, then multi-resolution 
analysis is appropriate.

Wavelets is a framework bringing together many approaches to
such analysis, inter alia subband coding, quadrature mirror 
filters and pyramidal coding.

A nice introduction to wavelets is given in the IEEE Signal Processing
Magazine of October 1991 (Oliver Rioul and Martin Vetterli, ``Wavelets
and Signal Processing,'' pp 14--38) with *many* references.

They compare the wavelet transform to the short time Fourier transform
via the general *Wigner distribution.*

So at least wavelets may be used to analyse fractals, and maybe to
generate a few new ones. The emphasis in wavelets is generally
to get a complete set of orthonormal (or at least biorthogonal) wavelets.
A new set may be needed for each application.

Hendrik
-- 
                         Hendrik F.V. Boshoff                              
    Dept E&E Ingenieurswese             Dept E&E Engineering               
    Universiteit van Stellenbosch       University of Stellenbosch         
    SUID-AFRIKA                         SOUTH AFRICA                       
                      email boshoff@firga.sun.ac.za