Benoit Mandelbrot (11/20/1924—10/14/2010) popularized the description and construction of 2D and 3D sets of fractional (non-integer) dimension.  He called them fractals.  I won’t use the word “invent” because such sets were studied as far back as the 1800s.  Of course, to say fractional (or “fractal” or non-integer) dimension, one has to redefine dimension a wee bit—Haussdorf, a 19^th century mathematician did that.  (The famous Cantor set, always a subset of the real numbers between zero and one, can be constructed to have any Haussdorf dimension between zero and one—no wonder Cantor went crazy.)  Just about everything Mandelbrot described and constructed still must exist in a space of integer (1, 2, 3, …) dimensions.  The construction of a fractal is often based on self-similarity, tacking on more and more similar but smaller pieces, ad infinitum (or taking them out).

Fractals represent ultimate geekiness because they have found many applications in computer graphics, including artsy stuff like landscapes and seascapes.  There was also a time, though, when just about every other paper in solid state physics used fractals, fractional dimensions, and self-similarity to describe complex systems—they’re ubiquitous in nature.  Today that fad has passed, but fractals still remain (sounds like a line in Paul Simon’s “Sounds of Silence,” doesn’t it?  It appeared 12 years before Mandelbrot’s The Fractal Geometry of Nature).

Mandelbrot spoke once at Clark University in Worcester, MA.  There was a cocktail hour before, befitting a famous VIP visiting from IBM, followed by a lecture—Mandelbrot seemed to enjoy himself at both.  He didn’t discuss the history of fractals much—to paraphrase Newton, Mandelbrot had stood on the shoulders of mathematical giants—but Benoit certainly sold his product well.  I’ll have to admit that his book is a work of art and probably helped popularize the subject even more—maybe a large number of applied mathematicians nowadays owe their geekiness to that book and its applications to computer graphics.

Today fractals are just another useful tool in the applied mathematician’s bag of tricks.  I even remember an image compression scheme based on fractals (JPEG is a more popular one).  Applied to sonic data (like MPEG), it could probably find useful applications today in compressing Senate filibusters—it was a lossy compression scheme, but the public wouldn’t care about that when dealing with filibusters.  No problem with candidates on the stump, of course, because they never spout more than fifteen-second soundbites.

And so it goes….

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