Benoit Mandelbrot, a mathematician at IBM, is an expert in processes with unusual statistical properties, such as those in which a random variable's average or its variance is infinite. His early work in the 1950's and 1960's suggested that the variations in stock market prices, the probabilities of words in English, and the fluctuations in turbulent fluids, might be modeled by such strange processes.
Later he came to study the geometric features of these processes and realized that one unifying aspect was their self-similarity. In the mid-1970s he coined the word "fractal" as a label for the underlying objects, since they had fractional dimensions. Fractals are shapes or behaviors that have similar properties at all levels of magnification or across all times. Just as the sphere is a concept that unites raindrops, basketballs, and Mars, so fractals are a concept that unites clouds, coastlines, plants, and chaotic attractors.
© The Exploratorium, 1996