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In article <1488@srtp.UUCP> bernard@srt-poste.fr writes:

> I'm looking for references of methods for calculating an estimation of
> fractal dimension of data sets
>	B. Lemarie

Edgar E. Peters, <Chaos and Order in the Capital Markets.  A New View
     of Cycles , Prices, and Market Volatility>, New York, John Wiley
     & Sons, Inc., ISBN 0-471-53372-6 (1991).

The section entitled "The Fractal Dimension" (pp. 155-157, in Chapter
12, "The Dynamical Analysis of Time Series") describes the correlation
integral, which the author describes as "A similar, more practical
method [than estimating the fractal dimension graphically by covering
the contour with circles and computing the fractal dimension D as

     D = log(N) / log(1/R), where
     N = number of circles of diameter R.]

"The correlation integral Cm(R) is the probability that a pair of
points in the attractor [Peters is discussing the measurement of the
fractal dimension of an attractor in a phase space of a chaotic
system] is within a distance R of one another."

Peters also discusses the Hurst dimension, which is the reciprocal of
the fractal dimension, and shows how to determine it using a different
graphical procedure.

Finally, Peters gives several listings of short computer programs for
various kinds of nonlinear analyses, all in the BASIC language.  One
of them calculates Cm(R) from a data series of up to 2,000 values.

Peters' book is also the best I've found so far on nonlinear dynamics
applied to analysis of financial time series.

Another excellent book on nonlinear topics is:

Manfred Schroeder, <Fractals, Chos, Power Laws.  Minutes from an
     Infinite paradise>, U.S.A., W. H. Freeman and Company, 
     ISBN 0-7167-2136-8 (1991).

Schroeder discusses fractal dimensions in at least nine different
places in this book.  The treatments are very brief in comparison to
Peters' book, but is a much broader work that shows the relationships
of such concepts from the point of view of a polymath who is
comfortable in physics, mathematics, engineering, and biology.

Bill Park
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Grandpaw Bill's High Technology Consulting & Live Bait, Inc.