Benoît Mandelbrot

Benoît B. Mandelbrot (born November 20, 1924) is a Polish-born French mathematician and leading proponent of fractal geometry. He is Sterling Professor of Mathematical Sciences, Emeritus at Yale University and IBM Fellow Emeritus at the Thomas J. Watson Research Center.

Mandelbrot and fractals

Although Mandelbrot invented the word fractal, many of the objects featured in The Fractal Geometry of Nature had been previously described by other mathematicians (the Mandelbrot set being a notable exception). However, they had been regarded as isolated curiosities with unnatural and non-intuitive properties. Mandelbrot brought these objects together for the first time and highlighted their common properties, such as self-similarity (sometimes partial or statistical), scale invariance and (usually) non-integer Hausdorff dimension.

Related Topics:
Scale invariance - Hausdorff dimension

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He also emphasised the use of fractals as realistic and useful models of many natural phenomena, including the shape of coastlines and river basins; the structure of plants, blood vessels and lungs; the clustering of galaxies; Brownian motion; and stock market prices. Far from being unnatural, Mandelbrot held the view that fractals were, in many ways, more intuitive and natural than the artificially smooth objects of traditional Euclidean geometry. As he says in the Introduction to The Fractal Geometry of Nature:

Related Topics:
Coastline - Blood vessel - Lung - Galaxies - Brownian motion - Stock market - Euclidean geometry

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:Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.

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Mandelbrot's informal and passionate style of writing and his emphasis on visual and geometric intuition (supported by the inclusion of numerous illustrations) made The Fractal Geometry of Nature accessible to non-specialists. It sparked a widespread popular interest in fractals as well as contributing to new fields of science such as chaos theory.

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