Post by Unkle John on Oct 18, 2010 15:27:51 GMT -5
Benoit Mandelbrot, Father of Fractals, Dies at 85
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 École 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.
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 École 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.