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.
|
