*These fractals were generated by the program, ChaosPro*
(© Martin Pfingstl), then graphically modified.
**About Fractals**The fractal
pictures on this site are images were generated*, captured, and
graphically manipulated by Aaron Cohen.**
Fractals: ***the simple explanation . . .*In your
study of geometry, was there ever a way to describe or construct a
picture of a coastline, mountain, or lightening?The
development of fractals has enabled this, as well as producing
breathtaking illustrations and magical, mystical "journeys."These
journeys occur when a computer program generates a fractal and
then provides the opportunity to zoom in to it.What one
finds is an opportunity to zoom infinitely into the intricate
detail, finding smaller copies of the whole.Three
dimension fractal geometry has been used in the entertainment and
animation industries to generate real-looking landscapes.A fractal
is a mathematically-generated object that mimics, describes and
mathematically replicates many real-world objects that do not have
simple geometric shapes — such as clouds, mountains, turbulence,
coastlines, snowflakes, lightening . . .**For the
more curious . . . ***a more complex definition:*A fractal
is a mathematically-generated object that, possesses infinite
detail, and can be "broken up" and subdivided in parts, each of
which, at different levels of magnification, is approximately a
smaller copy of the whole.Thus, with
the assistance of fractal-generating computer programs, you can
keep zooming in — literally forever — to small areas of detail in
the fractal. And you will find repetitions of the original.This is
similar to holograms: if you cut a hologram into pieces, each
contains a copy of the whole image.The
discovery of fractals, and their rough or fragmented geometric
shape, provided mathematics — for the first time — with a way to
describe and mathematically replicate many real-world objects that
do not have simple geometric shapes, such as clouds, mountains,
turbulence, coastlines, snowflakes, lightening . . . These
shapes are rough or irregular on all scales of length, and so
appear to be 'broken up' in a radical way.
"The oldest standard example is a coastline ("How
long is the coast of Britain?"), which when measured one kilometer
at a time might turn out to be 5000 kilometers long, but when
measured one meter at a time comes out to be, say, 12000
kilometers."
(http://www.mrob.com/pub/muency/fractaldefinitionof.html)
Fractals
describe "many situations which cannot be explained easily by
classical geometry, and has often been applied in science,
technology, and computer-generated art. The conceptual roots of
fractals can be traced to attempts to measure the size of objects
for which traditional definitions based on Euclidean geometry or
calculus fail." **The term
fractal was coined in 1975 by Benoît Mandelbrot, author of The
Fractal Geometry of Nature" from the Latin, *fractus*,
broken. The conceptual roots of fractals can be traced to attempts
to measure the size of objects for which traditional definitions
based on Euclidean geometry or calculus fail.Several
definitions have been created over the years as mathematicians
struggled with the complex properties of fractals.
** For
further information:
http://en.wikipedia.org/wiki/Fractal
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