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 (1893–1978) 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 Fractory—A ThinkQuest project by David Green, Alex Kulesza, and Keith Bergstresser—where 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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