Saturday, October 16, 2010

R.I.P. - Benoit Mandelbrot

Dr. Benoit Mandelbrot, the mathematician who coined the term "fractals", passed away at 85 a couple of days ago (New York Times story).  Mandelbrot didn't really discover fractals (or fractional dimensions), but he brought them to the attention of everyone and showed how they described many natural features such as coastlines (Mandelbrot, B. 1967. How Long is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension. Science 156: 3775: 636-638).  His book, The Fractal Geometry of Nature (1983, W. H. Freeman) brought fractals into the public eye (that's when I learned about them).

Basically, fractals are good for describing self-similar shapes which show complexity at all scales as you zoom in (like a coastline from space, an airplane, on foot, or with a microscope).  A fractal shape can have a finite area bounded by an infinitely long line.

The Mandelbrot set in the complex plane (click to enlarge)

When I first heard about Mandelbrot sets, back in college, I wrote a computer program to display and play around in them (before the web, even before PCs had windows, anyone remember DOS and Turbo Pascal?).  For such a complex figure (you can zoom in forever in any one area to see everchanging views) it's actually quite simple to iteratively calculate.

Here's a slow and deep (sounds dirty, doesn't it?) zoom into the Mandelbrot set.

I'm sure I'll post more about fractals in the future (when it's not 9:50 pm and I'm not so tired).

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