Benoit Mandelbrot, mathematician, scientist, troublemaker, passed away today at the age of 86. One of my greatest inspirations as a child, he had the courage and insight to look for new laws and new forms of organization in the messiest areas of human endeavor from map-making to the stock prices of cotton. Almost single-handedly, Mandelbrot established fractal geometry, a revolutionary new paradigm, which has opened up new vistas upon the Universe.
Countless students, scientist and programmers can likely recount their first encounter with the structure that epitomizes his work and bears his name – the Mandelbrot Set.
An object of seemingly infinite beauty – as can be seen by zooming in deeper and deeper on its porous boundary, this is just one member of a huge family of mathematical structures known as Iterated Fractal Systems (IFS). Among other fields, fractal geometry is now understood as being the central organizing principle in plant and animal anatomy, the structure of large-scale networks – be they of roads or information technology, and even the structure of the universe from the largest to the smallest scales.