Benoit Mandelbrot was a mathematician by training. He published papers on economics and finance, on turbulence in jet engines (and other environments) and on information technology. He worked at various universities in America and Europe, but he will be most remembered for the work he did while at IBM Research in California.
While at IBM he did work on fractal geometry that would change the way we do computer graphics – so that they are much more realistic when dealing with clouds, mountains, trees, and most other things in nature. The work on fractals impacted a lot of technology and science, but most people will remember only the Mandelbrot set, which bears his name – as a result of his work on fractals. (You can see an example of part of the set in the video below.)
In nature,technology and art the most common form of regularity is repetition: a single element repeated many times, as on a tile floor. But another form is possible, in which smaller and smaller copies of a pattern are successively nested inside each other, so that the same intricate shapes appear no matter how much you “zoom in” to the whole. Fern leaves and Romanesco broccoli are two examples from nature.
One might have thought that such a simple and fundamental form of regularity would have been studied for hundreds, if not thousands, of years. But it was not. In fact, it rose to prominence only over the past 30 or so years—almost entirely through the efforts of one man, the mathematician Benoit Mandelbrot, who died in 2010 just before completing this autobiography. [Stephen Wolfram from The Father of Fractals November 2012]
The work done on fractal geometry by Mandelbrot and others has influenced a large part of science and technology. It is interesting to me that it has impacted several areas of medicine around how surgery is preformed on structures – like the liver – that are fractal in the nature of the veins and arteries that are a part of it. For an hour-long documentary, see The Clouds are Not Spheres.
This video below is a zoom into the Mandelbrot set. It is 5 minutes. There are much longer zooms – some going for hours. You can find those on YouTube by searching. (This zoom at just over 10 minutes is a little better, but twice as long.)
The way the diagrams and videos are coded is that points which are black are IN the set, the other colors denote points that are NOT in the set, and the colors denote how fast the series diverges. (For a description of what the set is, that is easier to understand than the Wikipedia link at the top of the post, see the explanation given by the Numberphile.)