Eleanor
Milne's far-reaching intellectual interests include fractals. Fractal
geometry has produced some breathtaking and beautiful pictures; a tribute
to the artistry of the engineers and physicists who discover and invent
them. Fractals are irregular geometric shapes that repeat in the large
pattern the shape of the smallest components that make up the whole. Computers
are necessary to work out fractal equations that can be relatively simple
but require a huge number of calculations to explore solutions and variations.
Although
they are often spoken of in the same breath, fractals and chaos theory
are not the same. Chaos theory describes the fact that tiny variations
in initial conditions yield enormously differing results. For example,
Edward N. Lorenz's Butterfly Effect (mentioned in the movie Jurassic
Park) proposes that the flap of a butterfly's wings in Brazil can
set off a tornado In Texas.
Fractal
configurations include the Julia set (shown here), Mandelbrot set, Cantor
dust, Ushikis' Phoenix, the Seahorse valley and Elephant valley. The
first two are named in honour of Gaston Julia (18931978) and Benoit B.
Mandelbrot (b. 1924). Julia's 1918 mathematics paper inspired Mandelbrot
who coined the word fractal to describe his computer generated visualizations
at IBM's T. J. Watson Research Center in New York in the late 1970s.
You
can download freeware for making fractal images from a website maintained
by Noel Giffin at the TRIUMF project on the University of British Columbia
Campus in Vancouver, B.C.: http://spanky.triumf.ca/www/fractint/fractint.html
More
EXTERNAL LINKS:
http://library.advanced.org/3288/
The FractoryA ThinkQuest project by David Green, Alex Kulesza, and
Keith Bergstresserwhere you can learn about and make your own fractals.
http://www.fractalus.com/ifl/
The Infinite Fractal Loop (IFL) started by Douglas Cootey in 1997 and
now maintained by Damien Jones to showcase "the finest fractal art on
the net."
http://www.fractalus.com/ifl/list.htm
is IFL's directory of fractal art galleries. With over 100 fractal examples
it takes a while to load, so you could choose instead
http://www.fractalus.com/cgi-bin/theway?list&ring=fractals,
a text-only list of fractal art galleries.
Sprott's Fractal
Gallery Two examples of Sprott's "fractal of the day" illustrate this page.
Strange Attractors: Creating Patterns in Chaos.
Jewel
Box image A beautiful image created when Rollo Silver zoomed in on
the Seahorse valley of the Mandelbrot set.
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