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.
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