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Benoit  Mandelbrot

Famed Mathematician Benoit Mandelbrot
Mathematician extraordinare, Benoit Mandelbrot

Crop Circles                                                            Crop Circle Gallery # 2

Crop Circle Gallery # 1                                         Crop Circle Gallery # 4

Benoît B. Mandelbrot (born 20 November 1924) is a French and American mathematician, best known as the father of fractal geometry. He is Sterling Professor of Mathematical Sciences, Emeritus 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 after him.


In 1982, Mandelbrot expanded and updated his ideas in The Fractal Geometry of Nature.[7] This influential work brought fractals into the mainstream of professional and popular mathematics, as well as silencing critics, who had dismissed fractals as "program artifacts"


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 appeared overnight
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 psychic experiences.

(Benoit Mandelbrot biographical data courtesy of WikiMedia Data.)



Gaston Julia

Crop Circle Gallery # 3

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