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'Father of Fractals' takes on the stock market

Seeing a snowflake pattern in the NASDAQ
Partial view of the Mandelbrot set fractal.
Partial view of the Mandelbrot set fractal.
Image / Wolfgang Beyer
Benoit B. Mandelbrot
Benoit B. Mandelbrot
Photo courtesy / Yale Mathematics Department

Benoit Mandelbrot is world-famous for making mathematical sense of irregular shapes--clouds that are not round, mountains that are not cones, coastlines that are not smooth, and now, stock markets that are not as simple as previously thought.

Mandelbrot, known as the "father of fractal geometry," spoke Nov. 8 to a crowd of more than 200 people in Room 10-250. His talk was the first in a series sponsored by the MIT Molecular Frontiers Club. Molecular Frontiers is a new international alliance of scientists, including several at MIT, intended to inspire young people to get involved in science. The title of Mandelbrot's lecture was "The Mandelbrot Set and Fractals in Finance."

Mandelbrot coined the term "fractals" in 1975 to describe shapes that appear similar at all levels of magnification and are also called "infinitely complex." Examples of fractal-like structures in nature include snowflakes, rivers, broccoli flowers and systems of blood vessels.

"Fractals and chaos theory are particularly good at engaging young minds because of the images involved," said Andreas Mershin, a postdoctoral associate at MIT's Center for Biomedical Engineering, who introduced the 86-year-old Mandelbrot, who is the Sterling Professor of Mathematical Sciences, Emeritus at Yale University and lives in Scarsdale, N.Y.

Mandelbrot, who sometimes drifted into anecdotes about former colleagues and students, described the long process of his work. "I have been working on this subject all my life. My Ph.D. was finished in 1952, and I never realized until recently what I was actually doing. Only later did I realize that everything I was working on had the property of roughness."

In the middle of World War II, Mandelbrot was a young man studying in the south of France. "The conditions were as grim as possible, and somehow I found I had this gift for seeing shapes in complicated structures instantly," he said. After continuing his studies in Paris, Mandelbrot left France for Caltech in 1947 to study aeronautics.

He returned to France to get a Ph.D. in mathematical sciences from the University of Paris and then worked in the United States and Europe throughout the 1950s. In 1958, Mandelbrot settled with his wife, Aliette, in Yorktown, N.Y., where he joined the research staff at the IBM Thomas J. Watson Research Center. He went on to devote his academic life to seeing the truth in the roughness of geometrical shapes.

After working on the general properties of fractals, he moved on to examine more specific and complex examples, focusing on what came to be known as the Mandelbrot Set. An unusual type of fractal that comes from a simple equation, the Mandelbrot Set is popular outside of mathematics because of its aesthetic appeal and its complicated structure. No one has been able to prove the Mandelbrot Set is true, according to Mandelbrot. "But no one has been able to prove it's not true, either," he said, as large pictures of fractals filled the screen behind him.

Mandelbrot recently began to apply his knowledge of fractals to explain stock markets. "Markets, like oceans, have turbulence," he said. "Some days the change in markets is very small, and some days it moves in a huge leap. Only fractals can explain this kind of random change." He and a journalist, Richard Hudson, have co-written a book on the thorny subject to explain the complex gyrations of stock prices and exchange rates.

Molecular Frontiers, a new nonprofit based in Cambridge, is the brainchild of Swedish physical chemist Bengt Nordén, former chair of the Nobel committee for chemistry.

Mandelbrot is an IBM Fellow Emeritus at the Thomas J. Watson Research Center and a Battelle Fellow at the Pacific Northwest National Laboratory.

Katharine Stoel Gammon is a student in MIT's Graduate Program in Science Writing.

A version of this article appeared in MIT Tech Talk on November 22, 2006 (download PDF).

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