Re: Mandelbrot and its applications.

On Oct 17, 7:51 am, caos.s...@xxxxxxxxx wrote:
On Oct 11, 5:46 pm, "A n g l e r" <p k o n i u s z @ h o t m a i l . c

o m> wrote:
Hi all.

Been just wondering whether there are any useful applications of
Mandelbrot fractals in image processing/other areas of science (beside
generating nice fractal-based images).

Cheers,
Peter.

I don't see how mandelbrot images could be realted to image processing
at all... They are just images... I guess what you mean is what's the
use of the theory of fractal geometry and/or that of (real or complex)
dynamical systems. Then yeah, a lot, but mostly for other branches of
science, not really on image processing (besides compression and
encripption), there is not obvious reason for them to work fine there.

For me asking what's the use of Mandelbrot fractal images is like
asking what's the use of a picture an electon... the asnwer is "not
much". The usefulness is not on the picture, but the theory behind...
the image can (does!) inspire conjetures and sometimes the creation of
theories of course; then yes, that's what they can be used for.

Which of course inspires all sorts of questions: Why Does The
Mandelbrot Set Look The Way It Does??? WHY, for example, do
spirals and swirls appear at all? What is the nature of the
ornamentation (stuff that attaches to the bulbs)? What does it
represent? Why not just bulbs on bulbs, ad infinitum? Why does
the period of the bulbs seem to correlate with motifs found in the
ornamentation? Why, around midgets, do the ornaments go in
powers of two (it seems related to the "^2" in "z^2 + c", but HOW?)?
See, it's those type of questions that looking at this thing inspires.
I'm quite curious about those questions myself, and I'd like to
know if anyone has any *rational* theories about them and their
answers. (Not crazy, crackpot stuff like the "Integrity Paradigm"
someone dug up googling for a similar question here.)



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