We are saddened by the passing of Benoit Mandelbrot, a mathematician who not only spurred a remarkable advance in science, he also captured the general imagination. Mandelbrot realized that the length one finds for a crinkly curve like a coastline depends on the tool used to measure it. A shorter ruler can catch more of the twists and folds of the curve, making the total observed length longer. In principle, Mandelbrot saw, an infinitely crinkly coastline could pack an infinite perimeter into a finite area of space. Such a curve, characterized not by its length but rather by its roughness, Mandelbrot called a fractal.
An idealized fractal shape looks the same whether seen from a distance or close up: each part resembles the whole. No matter how much one zooms in on a piece of a fractal, one finds the same kind of irregular shape, never a smooth curve. This failure to obtain smoothness undermines basic assumptions of calculus and thus forces scientists to turn to new mathematical tools. The idea behind abstract fractals had been discussed before, but Mandelbrot brought fractals into the study of the real world.
Mandelbrot was born in Warsaw in 1924. His family fled Poland to escape the rising Nazi threat, and he was educated in France. His most famous work took place while he was employed on IBM's research staff. Mandelbrot died on 14 October 2010 of pancreatic cancer, in Cambridge, Massachusetts.
Benoit's concept of fractals is fundamental to the science of complex systems. He was a giant---his height is difficult to measure.
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