French-American mathematician Benoit Mandelbrot discovered fractal mathematics, the study of measuring and simulating irregular shapes found in nature.
Mathematician Benoit Mandelbrot, the father of fractals, died of pancreatic
cancer on Oct. 14, AFP reported. He was 85
years old.
His work on fractals has become a foundation of the Chaos theory and is
critical to many applications and systems, ranging from digital compression on
computers, modeling turbulence on aircraft wing designs, and texturing medical
images.
Most people know fractals as the
weird, colorful patterns
drawn by computers. The word "fractals" was coined by Mandelbrot to
refer to rough or fragmented geometric shapes or processes that have similar
properties at all levels of magnification or across all times. There are
mathematical shapes with uneven contours that mimic irregularities found in
nature, such as clouds and trees, and can be measured and simulated, Mandelbrot
discovered.
Up until then, mathematicians believed that most of the patterns of nature
were too complex and irregular to be described mathematically.
"Fractals are easy to explain, it's like a romanesco cauliflower, which
is to say that each small part of it is exactly the same as the entire
cauliflower itself," Catherine Hill, a Gustave Roussy Institute
statistician, told the AFP. "It's a curve
that reproduces itself to infinity. Every time you zoom in further, you find
the same curve."
In his 1982 book, "
The
Fractal Geometry of Nature," Mandelbrot said complex outlines of
clouds and coastlines, once considered unmeasurable, could "be approached
in rigorous and vigorous quantitative fashion" with fractal geometry. With
fractals, it is possible to create models of coastlines, cell growth and other
processes that look like the real thing.
He even applied the theory to the financial market, predicting and warning
about the global financial meltdown in his 2005 book
"The (Mis)Behaviour of Markets." He cited the huge risks being
taken by traders who tend to act as if the market is predictable, comparing
them to "
mariners
who heed no weather warnings."
Mandelbrot was analyzing electronic noise that was interfering with IBM
electronic emissions as an
IBM research fellow in the 1960s. The scientists had noted the blips
occurred in clusters, with a period of no errors followed by a period of many.
Mandelbrot noticed a pattern to these error clusters. He found an hour where
there were no errors, and the next hour had many errors. When he divided the
error period into a smaller interval, he found the ratio of errors and no errors
remained the same. In other words, carving up the hour into 20-minute sections
resulted in 20 minutes with no errors followed by 20 minutes with many errors.
Regardless of the interval size, Mandelbrot found the ratio of error-free
periods and error-filled periods remained the same. He called the property "self
similarity."
After retiring from IBM, Mandelbrot
became a professor of mathematical sciences at Yale, and later held
appointments as professor of the practice of mathematics at Harvard
University, professor of engineering
at Yale, professor of mathematics at the ??½cole Polytechnique in France, professor
of economics at Harvard, and professor of physiology at the Einstein College of
Medicine.
He was awarded the Wolf Prize for Physics in 1993 and in 2003 the Japan
Prize for Science and Technology. In 2006 he was knighted by the French. He
even has an asteroid named after him: 27500 Mandelbrot.
Born in Poland,
he was educated in France
before joining IBM in the 1950s.
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