Professor Benoit Mandelbrot
YALE AND PACIFIC NORTHWEST NATIONAL LABORATORY
Fractional Roughness: Beautiful, Damn Hard, and Suprisingly Useful
Some fractals imitate mountains, clouds, stock markets, and many other aspects of nature and culture. Others yield wild and wonderful new patterns that a child can draw but great masters struggle or fail to understand. All are shapes that look the same from any distance, far away or close by. Since time immemorial, some have been used by great artists. A hundred years ago, mathematicians called them monsters and an excuse to split from physics. Now—especially since my 1975 term fractal—they help heal this split. Fractal geometry helps mathematics and the sciences to cross a long avoided boundary between the smooth and the rough. Partial differential equations must allow very rough solutions. Man's basic sensation of roughness can now be measured intrinsically by fractal dimension, first step to being mastered. An introduction to fractal geometry with updates on some current developments including finance.