Re: Definition of a fractal

From: Lewis L. Smith (mmbtupr_at_aol.com)
Date: 08/07/04

  • Next message: Lewis L. Smith: "Re: Definition of a fractal" 
    Date: 6 Aug 2004 22:57:44 -0700

    "Roger L. Bagula" <rlbtftn@netscape.net> wrote in message news:<40EDABB6.3090809@netscape.net>...
    > Dear Dr. Edgar,
    > Well, then we should change the FAQ.
    > I was going on my conversation with him
    > and the lecture he gave a UC Riverside
    > while he was visiting Dr. Lapidus.
    > He was unaware how popular a movement he had started
    > and felt isolated Mathematically from popular thought.
    > He also thought that no one Mathematical method was
    > worthy of being a basis for early education as fractals had been
    > in some places used in high schools to begin student in Mathematics.
    > Mostly he thought that fractals were being misused
    > and abused by some people in their publications.
    >
    > I can't afford two copies of books... I usually stick with the older
    > version.
    > I wish I had had enough to buy your book on fractals and differential
    > processes. Mandelbrot maintains there is no connection of fractal
    > behavior and fractional differential processes like the allometric
    > process of Ludwig von Bertalanffy in General System Theory.

    The sender is a semi-retired energy economist,
    participant in the Complex-M discussion group
    and author of several papers on the relationshiop between
    economics, management and complex systems.

    Thanks to participants for the interesting historical information.

    Suggest the following working definition of a fractal —

    A fractal is a line which looks just as wiggly to a hermit crab
    as it does to a satellite.

    Good example is the coast of the US state of Maine,
    the coast of Norway and the coast of the United Kingdom.

    If the pattern is exactly reproduced at all scales,
    the fractal is "self-similar", as would be the case for the output
    of a deterministic, iterable function with no stochastic component.
    Otherwise the fractal is "affine".

    Notwithstanding it is possible to speak of a fractal surface
     in the following manner.

    Imagine a system [such as a weather system] whose track
    [orbit, trajectory] is an affine fractal. It moves between and within
    two, three dimensional attractors. Given enough time, from
    any arbitrary starting point, the "virtual bag" of each attractor
    will become almost [but never] "full" and so densely packed that
    each attactor will appear to have a fractal surface.

    End

  • Next message: Lewis L. Smith: "Re: Definition of a fractal"

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