The Near Edge of Chaos (Dennis Aubrey)


Benoît Mandelbrot is dead.

Benoît B. Mandelbrot (20 November 1924 – 14 October 2010) was a Polish-born French mathematician and leading proponent of fractal geometry. He was Sterling Professor of Mathematical Sciences, Emeritus at Yale University and IBM Fellow Emeritus at the Thomas J. Watson Research Center. He was the founding father of fractal geometry – the branch of mathematics that perceives the hidden order in nature. That is the official description of him, but it falls so short of describing who Mandelbrot really was or what he accomplished.

Benoît Mandelbrot (20 November 1924 – 14 October 2010)

In a prior life of mine, I founded and ran a software company called Altamira Group, which specialized in graphic applications using fractal geometry for high resolution imagery. We developed the “Genuine Fractals” applications in 1995-1997 and released the first version at the end of 1997. I am proud to say that the products are still on the market and are still useful to graphics artists world-wide. In that context, the work of Michael Barnsley and Benoît Mandelbrot were key to our success. Both men were visionaries and powerful intellects who could change the way one perceived the world. They certainly did for me.

“In the whole of science, the whole of mathematics, smoothness was everything,” Mandelbrot says in “Hunting the Hidden Dimension.” “What I did was open up roughness for investigation.”

Fractal image created by Pascal Agneray

The National Academy of Sciences described his work as follows: “Seeks a measure of order in physical, mathematical or social phenomena that are characterized by abundant data but extreme sample variability. The surprising esthetic value of many of his discoveries and their unexpected usefulness in teaching have made him an eloquent spokesman for the ‘unity of knowing and feeling.'”

There could be worse obituaries than that.

If you are interested, please see “Hunting the Hidden Dimension,” a PBS Nova special on fractals.

Here is a video from TED – Ideas Worth Spreading called Benoit Mandelbrot: Fractals and the Art of Roughness

And finally, here is a link to a fine article in the Economist on Mandelbrot’s passing (courtesy of my friend Dave McDonell, who knows a good thing or two when he sees them).

Fractal image created by Pascal Agneray

I close this post with a toast to Mandelbrot and ponder how the human mind is capable of looking at the infinite complexity of the world and seeing pattern and an inner order. Like the great spiritual thinkers of the past, Mandelbrot was able to connect the seemingly dissimilar and to perceive the fundamental unity of the universe. The difference between Mandelbrot and these spiritual explorers, however, was his ability to communicate that pattern and order mathematically – to demonstrate them. To me, this is a great thing and I believe that the cathedral of Mandelbrot’s mind is as inspiring as Chartres or Reims and as full of beauty and nobility as those great medieval landmarks.

The two fractal images in this post were created by Pascal Agneray, a good friend from France who lives in Chicago.

2 responses to “The Near Edge of Chaos (Dennis Aubrey)

  1. Very interesting, Dennis. I never thought of art as mathematics. I really like the blue one but the yellow one is beautiful and vibrant, too.

  2. Barbara, it might be more accurate to describe mathematics as art. In this particular case, the complex images are generated from ridiculously small equations that iterate. The result from the calculation is fed back into the equation over and over again. The plotting of those values results in these amazing images, which have unique properties. Great stuff, and thanks for commenting.

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