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Fractal Inventor:  Mandelbrot

[fractal information page]

See also: Wikipedia entry honoring Benoit Mandelbrot

A natural selection


(Original publication: April 22, 2003 [http://www.thejournalnews.com/newsroom/042203/d01w22mandelbrot.html])

YORKTOWN HEIGHTS — When Benoit B. Mandelbrot coined the term "fractal" in the 1960s, he was a rebel. Today, he's revered for inventing a new geometry. For someone who has spent his life shocking the mathematical establishment, Mandelbrot is taking the accolades well.


On Friday, Mandelbrot will receive the prestigious Japan Prize in Tokyo.


The 78-year-old native of Poland has lived to see his geometric theories excite new generations of mathematicians.


"The things I did 20 years ago, 30 years ago — then reviewed as crazy, wild, ridiculous, insane — now every kid knows them in high school," Mandelbrot said on a recent afternoon at IBM's Thomas J. Watson Research Center in Yorktown Heights, where he's a Fellow emeritus.


For the uninitiated, think of fractal geometry as a way to measure the rough and tumble real world. Nature abounds with complex shapes, from trees to snowflakes to mountains.


What Mandelbrot discovered is that these geometric shapes look the same when you break them into their smaller components. Consider the cauliflower, whose smaller and smaller buds mirror the whole bunch.


"There are many shapes in the mathematical world that are like that," Mandelbrot said. "What I did was to put them together. I invented a new geometry, the purpose of which is to study these shapes."


Shapes in nature had been largely ignored by mathematicians, who were daunted by their complexity.


"As a physicist, I was trying to find ways of representing the messiness of nature. How many flat things do we see in nature? Maybe a lake when there is no breeze and no fish, but not many more," Mandelbrot said. "How many flat things do we see in industry? Everything! This cabinet, the wall, and so on. So industry took some very basic shapes which are rare in nature and made them everywhere."


Mandelbrot tapped the Latin word "fractus," which means fragmented and irregular, for his theories, many of which he honed during his years as an IBM researcher in Yorktown Heights. Today, the Westchester County resident is also a mathematics professor at Yale.


He's also the closest thing to a rock star that the mathematics world has. A search of the Web for "Mandelbrot" using Google yields 125,000 results.

Mandelbrot's work was revolutionary, said science writer John Briggs, author of "Fractals: The Patterns of Chaos" and a professor at Western Connecticut State University.


Traditional Euclidian geometry of lines, points and planes doesn't work well in nature. "Until Mandelbrot, most nature was viewed as disorderly," Briggs said.

Imagine a sheet of paper is the surface of the earth. Now crumple it and imagine those wrinkles are mountains. Fractal geometry provides a way to describe those shapes. Mandelbrot's work harkens back to a centuries-old view of mathematics as an expression of the wonder of nature, Briggs said.


Today, people are more inclined to regard math as the logic of nature. "Mandelbrot brings us back to the sense of the wonder of things, without giving up the logic," Briggs said.


People respond to the idea of natural fractals because they are easy to understand, but there's also a purely mathematical aspect to Mandelbrot's work.


Plotting certain mathematical equations on an axis and assigning colors to the results yields those colorful images people think about when they hear the term "fractals."


The "Mandelbrot Set" is a group of fractal images derived from a particular set of equations.


Mandelbrot's work has even spawned a new school of artists who call themselves "Fractalists" and create computer-assisted art.

Fractal equations are being applied not only to art, but to engineering, to medicine to economics and to computer animation.


"His work has spread and impacted so many fields that there's nobody in the world who is broad enough to appreciate the full impact," said Thomas Theis, director of physical sciences at IBM Research and Mandelbrot's twice-weekly lunch companion.


Mandelbrot's mix of gall and genius gave him license to ask the questions no one else did, Theis said. "In science and mathematics, it's impolite to proclaim the significance of your work, but it just never occurs to him whether it's polite or not," Theis said. "One of the reasons he was able to have an impact on so many fields is that it doesn't occur to him that he shouldn't."


The Japan Prize is validation of a life's work. Second only to the Nobel Prize, it's awarded each year by the Science and Technology Foundation of Japan to scientists whose work has "advanced the frontiers of knowledge and served the cause of peace and prosperity for mankind."


Past winners have included Robert Gallo, who co-discovered the HIV virus; Timothy Berners-Lee, inventor of the World Wide Web; and Johns Hopkins' Donald Henderson, who helped eradicate smallpox.

Mandelbrot is sharing the 2003 Japan Prize, and an accompanying $400,000, with University of Maryland Professor James Yorke, who created the related mathematical field of chaos theory.


That a butterfly flapping its wings in China can cause a tornado in Kansas is Yorke's metaphor for the unpredictable nature of complex systems such as the weather. Both fractal geometry and chaos theory attempt to explain the real world, which isn't bound by the confines of the classroom or laboratory.

In between his ongoing mathematics work, Mandelbrot is collecting his papers and writing a memoir of his life.


Born in Warsaw to a family with a strong academic background, Mandelbrot emigrated to France in 1936 to flee the growing German threat.


He was deeply influenced by an uncle who was professor of mathematics at the College de France in Paris, but his formal schooling was interrupted by the war. His family fled Paris for Lyon, where poverty and fear of the German boss of the city — who was later revealed to be Klaus Barbie — forced him to lay low.


"I have had a very adventurous life," Mandelbrot said. "I almost perished a number of times in my youth. I survived all kinds of complications. In the war in France I was almost killed by Germans or French police. I was 19 at the time. At 20 I was a war-hardened veteran, even though I had never seen military action, because I happened to have survived."


Though traumatic, those experiences gave him the strength to buck convention and become a champion of geometry in a world dominated by algebra.


"Life is full of risks, and most people avoid the risks, because risks are never nice. Had I not gone through the war, I might have been like everybody else. But I had no choice," he said.


Practical fractals

Here are a few examples of the ways fractals have affected myriad fields:

Hollywood's computer artists can create more realistic landscapes using fractal equations, which "iterate," or repeat, to generate complex images without taking up much data storage space.

Doctors can measure the irregular shape of red blood cells to determine how to make medicines that will adhere to the molecules better.

Antennas shaped like fractals are small enough to fit inside a cell phone while still carrying a strong signal.

Fractal equations are well-suited to the wildly random world of financial trading, where price flucuations have been resistant to traditional mathematical models.

Fractals are complex shapes generated by relatively simple equations. Forecasters are researching equations that can predict the most complex system of all, the weather.