My Homeboy: Dr. Benoît Mandelbrot

Dr. Mandelbrot

Dr. Mandelbrot hugging on Torben

Dr. Benoît Mandelbrot is one of my main homeboys. He was born on 20 November 1924 and died this past weekend 14, October 2010. He was 85 years old.

Dr. Mandelbrot moved around a lot when he was younger, initially to avoid the Nazis (he was jewish) and later to find better educational opportunities. (He is pictured to the right hugging on the duck, Torben).

He was 51 when he coined the term fractal and started the branch of mathematics that it defined. It has come to affect many aspects of science.

Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.
—Mandelbrot, in his introduction to The Fractal Geometry of Nature

It was my junior year in high school when I learned how to compute the mathematical image that is named after him: The Mandelbrot Set. A friend of mine and I used to spend days (because it sometimes took that long on the machines of the time) waiting for the output from our computers to show us some interesting area of it. The math behind it is simple. If Z and C are numbers in the complex plane, iterate on the following formula: Z_{x+1}=Z_{x}+C. If the pythagorean distance of Z from 0 goes above a certain number (I used 1) then it is not in the set, move on the the next point. Color the pixel in the complex plane with something representing how many iterations the pixel took to escape. Some will never escape, others will fly out into infinity in only a couple of iterations.

I always thought the set looked like a fat guy, surrounded by a nimbus of self-similar fat guys, sitting on the john.

Mandelbrot Set

I'll be out in a minute!

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