Bordering on infinity: focusing on the Mandelbrot set's extraordinary boundary. (Cover Story)

Science News | November 23, 1991| | Copyright

The Mandelbrot set serves as a prime example of how simple mathematical operations can yield astonishingly complex geometric forms. Resembling a hairy snowman, this intricate shape has a convoluted border of loops and curlicues that calls to mind the extravagant ornamentation of baroque designs.

Magnifying the Mandelbrot set's boundary reveals a never-ending array of successively tinier inlets and protrusions. At various positions, the boundary even twists itself into fuzzy, miniature copies of the full Mandelbrot set. In fact, the more you magnify the figure's ...

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