Founder of Fractal Geometry Dies
On October 19, the world remembered a visionary mathematician who helped to redefine the world as we now see it: Benoît B. Mandelbrot (he gave himself the middle initial) died in Cambridge, MA at the age of 85.
For nearly seven decades Mandelbrot contributed pioneering work to the fields of geometry, geology, medicine, cosmology, and engineering. He is best known for developing the field of fractal mathematics and for coining the term "fractal" to refer to a new class of irregular mathematical shapes. Previously, the standard Euclidean geometry of straight lines and perfect squares limited mathematical descriptions of reality to approximations, but Mandelbrot's introduction of "fractal dimension" allowed complex objects like clouds and coastlines to be measured with precision. He was also one of the first people to use computer graphics to study the Mandelbrot set, which was named in his honor.
Although the far-reaching significance of the discovery and naming of fractals is not discussed in his obituary, Mandelbrot's chief insight came when he noticed that the Mandelbrot set and other fractals exhibited "self-similarity," which means that a portion of an object looks like the whole; a typical example is of branches as miniature trees that make up a larger tree. In part because of this realization, we have since come to understand that the natural world is built of fractal forms and exhibits self-similarity on cosmic scales, from atoms to galaxies.
Mandelbrot's work in fractal geometry allowed him to influence a wide range of disciplines, and his numerous publications include information on "how galaxies cluster, how wheat prices change over time and how mammalian brains fold as they grow, among other phenomena." He saw patterns and trends in data sets where others only saw static haze and opened up vast domains of inquiry that we have only just begun to explore.
"Benoit Mandelbrot" by Steve Jurvetson on Flickr courtesy of Creative Commons Licensing.