The Mandelbrot Fractal

The Mandelbrot Fractal

Nassim Nicholas Taleb mentions Benoît Mandelbrot in his latest book, ‘The Black Swan’. I was surprised to learn that Mandelbrot has worked in a number of different fields in addition to mathematics. He is, however, best known as a mathematician and the ‘father of fractal geometry.’ Maybe the best known fractal of all is the Mandelbrot fractal. (A fractal, by the way, is, loosely speaking, a mathematical structure that is self-similar on all scales; they are often products of iterative procedures.) The Mandelbrot Fractal is generated from the very simple iterative equation

Mandelbrot Equation

I won’t go into the details, but the equation above illustrates the simplicity, and it is almost magical how such a simple equation can generate such complexity one finds in the Mandelbrot Fractal. (If you are interested in the details, go to the Mathworld page from the link above.) The pictures of the Mandelbrot Fractal in this post are all stolen from Wikipedia (sorry!), and they say more than a thousand words; the Mandelbrot is magical!

A zoom on the Mandelbrot

I once wrote a small program that drew the Mandelbrot set (okay, I got some help with the programming, and due to limited computing power it had to be an approximation; it looked good though). It was written in Delphi‘s implementation of the Object Pascal programming language. The program is currently trapped in an old, unconnected hard-drive, but I’ll upload it whenever I get around to it. In the meantime, you should google for Mandelbrot images and post links to the most beautful ones in the comment section!

UPDATE: I had to add another image and link to the Wikipedia page dedicated to the Mandelbrot itself. Check out the zoom animations; truly amazing!



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