Mathematician extraordinare, Benoit Mandelbrot
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Crop Circle Gallery # 1
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Benoît B. Mandelbrot (born 20 November 1924) is a French
best known as the father of fractal geometry. He is
Sterling Professor of Mathematical
at Yale University; IBM Fellow
Emeritus at the Thomas J. Watson Research Center;
and Battelle Fellow at the Pacific Northwest National Laboratory.
Mandelbrot was born in Poland. His
family fled to France
when faced with the threat posed by Nazi Germany. He remained in France through
the war to near the end of his college studies. He was born into a family with
a strong academic tradition—his mother was a medical doctor and he was
introduced to mathematics by two uncles. His father made his living trading
clothing. Mandelbrot attended the Lycée Rolin in Paris until the start of World War II. when his family moved to Tulle. In 1944 he returned
to Paris. He
studied at the Lycée du Parc in Lyon and in 1945-47
attended the École Polytechnique, where he studied under Gaston Julia
and Paul Lévy. From 1947 to 1949 he studied at
California Institute of Technology
where he studied aeronautics. Back in France,
he obtained a Ph.D. in Mathematical Sciences at the University of Paris in 1952.
From 1949 to 1958 Mandelbrot was a staff member at the Centre National de la Recherche
Scientifique. During this time he spent a year at the Institute for Advanced Study in Princeton, New Jersey. In 1955 he married
Aliette Kagan and moved to Geneva, Switzerland then Lille, France.
In 1958 the couple moved to the United States where Mandelbrot joined the
research staff at the IBM Thomas J. Watson Research Center
in Yorktown Heights, New York.
He remained at IBM for thirty-two years, becoming an IBM Fellow,
and later Fellow Emeritus.
From 1951 onward, Mandelbrot worked on problems and published papers not
only in mathematics but in applied fields such as information theory, economics,
and fluid dynamics.
Mandelbrot also put his ideas to work in cosmology.
He offered a new theory of the universe, demonstrating that fractal geometry
could be a sufficient, but not necessarily complete adjunct to the Big Bang
theory. He postulated that if the stars in the universe were
fractally distributed, it would not be necessary to rely solely on the Big Bang
theory to explain the universe. His model would not rule out a Big Bang, but
would allow for a universe even if the Big Bang had not occurred.
In 1975, Mandelbrot coined the term fractal to describe these structures,
and published his ideas in Fractals:
Form, Chance and Dimension was published in 1977.
As a Visiting Professor of Mathematics at Harvard University in 1979, Mandelbrot
began to study fractals called Julia sets. Building
on previous work by Gaston Julia,
Mandelbrot used a computer to plot images of the Julia set formulas. While investigating Julia sets, he studied the
Mandelbrot set fractal that is now named
In 1982, Mandelbrot expanded and updated his ideas in The Fractal Geometry of Nature. This influential work brought
fractals into the mainstream of professional and popular mathematics, as well
as silencing critics, who had dismissed fractals as "program
Upon his retirement from IBM
in 1987, Mandelbrot joined the Yale Department of Mathematics. At the time
of his retirement in 2005, he was Sterling Professor of Mathematical Sciences.
His awards include the Wolf Prize for
Physics in 1993, the Lewis Fry
Richardson Prize of the European
Geophysical Society in 2000.
When Mandelbrot set fractals are depicted geometrically,
they result in beautiful and spectacular geometric designs. These designs have frequently
as ‘crop circles’ in ways that suggest they are the work of an alien
intelligence. For this reason they are referred to as ‘Mandelbrot Set’ crop
circles. Flying Saucers and alien beings have been seen in and
around some of these crop circles. While
walking inside these crop circle formations, people frequently have unique
(Benoit Mandelbrot biographical data
courtesy of WikiMedia Data.)
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