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.

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.

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.

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.

A n g l e r 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.

Peter ,

Applications of fractal technology are in use from medicine
where Lyapunov coefficients are applied to irregular heart
beat rhythms,
to geology where stratification of sedimentation as found in hydrology
and the work of Hurst and his exponents
is used in oil exploration.
The Mandelbrot set itself is a 2 dimensional set that has a five fold
type of symmetry
which is useful in ideas of tiling, space filling curves and groups
as applied to fundamental physics. As connected sets in complex analysis
it is pretty much by itself except for it's Feigenbaum dual set
and the Bezier set between them.
The use of the Feigenbaum renormalization technology in particle physics
and biological population dynamics is also well known.

Why do you would want an physical or engineering application?
Complex analysis is applied to electrical circuit analysis
and aircraft wing fluid mechanics.
Acoustical analysis and the design of microwave radar cavities
have also benefited from research into complex analysis.

One fellow just completed a Menger cube out of Lego blocks a yard on
it's sides...
Mostly because it is beautiful Mathematics,
not because he wanted it as a hutch to protect his dog from the rain.

What wash your clothes?
A related area in fuzzy logic has that sort of engineering application.

The first major use of Newton's gravitational equations was to make
artillery fire more accurate.
Napoleon's artillery blew the nose off the sphinx in Egypt.
The first practical use of Einstein's understanding of
energy in fission was the atomic bomb.
Thankfully, no one has made an efficient biological weapon based
on the population dynamics discoveries connected to the
Mandelbrot set yet.
An earthquake weapon based on inversion of Per Bak's
sand box model has been suggested and researched.
Injection wells on faults have been somewhat successful.
The research
that resulted from fractal discoveries can be just as destructively
applied as those of Newton or Einstein.
Roger Bagula

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.)

On Oct 31, 1:02 am, mike3 <mike4...@yahoo.com> wrote:

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.)

There are rational explanations for the shape of the Mandelbrot set
based on an analytical treatment of what is going on. Particularly,
if you ask the question, "What shape must a region have if the points
inside have periodic orbits with a given period?", then the answers
give you the cardioids and the disks/bulbs. Stable points give the
interior and neutrally stable points give the boundaries. Unstable
points give the Misiurewicz points. And realizing that, the larger
the period, the more regions there are, gives rise to the fact that
the midgets and bulbs must get small really quickly to cram an
infinity of them into a finite space. So, there are reasons for the
features, and for me, that enhances its wonder, kinda like knowing how
a rainbow works.

Kerry Mitchell