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More about Fractals
Mathematician Benoit Mandelbrot introduced a set of equations in 1975, which impressed artists more than scientists. That's because his equations--called fractals--become amazing geometrical pictures. The Mandelbrot set is a fractal.
Fractals are self-similar structures, containing patterns within patterns. Fractal-like structures are found in nature in clouds, mountain ranges, and coastlines. In fractals, the basic shape occurs infinitely many times in the set, an example of the self-similarity of fractals. If you were to magnify a fractal, it would reveal small-scale details similar to the large-scale characteristics. However, at magnified scales, the small-scale details would
not
be identical to the whole. In fact, the Mandelbrot set is infinitely complex. Yet the process of generating it is based on an extremely simple equation involving complex numbers.
The Mandelbrot set is a mathematical set, a collection of numbers. These numbers are different than the real numbers that you use in everyday life. They are complex numbers. Complex numbers have a real part plus an imaginary part. The real part is an ordinary number, for example, -2. The imaginary part is a real number times a special number called
i
, for example, 3
i
. An example of a complex number would be –2°+°3
i
.
If you would like to read further about complex numbers and how they form the Mandelbrot set, see
“Introduction to the Mandelbrot Set: A Guide for People with Little Math Experience,”
by David Dewey. Portions of the text were reprinted here with permission from Dr. Dewey. Thumbnail">
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