Monday, October 18, 2010

Benoit B. Mandelbrot, Fractal Geometry: Math, Art, and Science

"Benoit Mandelbrot, Father of Fractal Geometry, Dies at 85" (October 17, 2010)

"Benoit Mandelbrot, the father of fractal geometry, has died at the age of 85, the AFP reports. The French-American mathematician discovered mathematical shapes called "fractals," and developed a geometry that was used to analyze naturally occurring shapes that were previously thought unmeasurable.

" '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.'

"Fractals are said to be infinitely complex and can be found in things like clouds, snowflakes, and mountain ranges. Physics, geometry, and finance are a few of the many areas to which Mandelbrot applied the theory. According to an article in the U.K.'s Telegraph, Mandelbrot's book 'The Fractal Geometry of Nature' has sold more copies than any other book on advanced mathematics.

"Mandelbrot first started studying the concept while working as a research fellow at IBM in the 1950s, and it revolutionized the field...."

Fractal equations and computers' number-crunching capacity also brought mathematics and art together. That image displays a Mandelbrot set: created by Wolfgang Beyer with the program Ultra Fractal 3. (Beyer uploaded it to Wikimedia Commons - click the picture to see a larger version.)

At least, the Lemming thinks that's art - since it's got aesthetic appeal and was made with a human instrumentality.

There's more about Mandelbrot in the news:
"Benoit Mandelbrot" (October 17, 2010)

"Benoit Mandelbrot, who died on October 14 aged 85, was largely responsible for developing the discipline of fractal geometry – the study of rough or fragmented geometric shapes or processes that have similar properties at all levels of magnification or across all times.

"Before Mandelbrot, mathematicians believed that most of the patterns of nature were far too complex, irregular, fragmented and amorphous to be described mathematically. Euclidian geometry was concerned with abstract perfection almost non-existent in the real world. Mandelbrot's achievement was to conceive and develop a way of describing mathematically the most amorphous natural forms – such as the shape of clouds, mountains, coastlines or trees – and measuring them. His work has become the foundation of Chaos theory – the mathematics of non-linear, dynamic systems.

"In the 1960s Mandelbrot, a research fellow with IBM, began a mathematical analysis of electronic 'noise' which was sometimes interfering with IBM electronic transmissions, causing errors. Although the nature of these errors was not understood, IBM scientists noted that the blips occurred in clusters; a period of no errors would be followed by a period with many.

"Examining these clusters, Mandelbrot noticed that they formed a pattern and that the closer they were examined, the more complex the pattern seemed to become...." described Mandelbrot as a "French-American," but there's a little than that involved. As put it:

"...Benoit B Mandelbrot (he awarded himself a middle initial, although it stood for nothing) was born on November 20 1924 in Warsaw, Poland, into a family of Lithuanian Jewish extraction. His father made his living selling clothes while his mother was a doctor, but the family had a strong academic tradition and, as a boy, Mandelbrot was introduced to mathematics by two uncles...."

The Lemming thinks it'd be easier to say that Benoit B. Mandelbrot is from Earth, and leave it at that.

Aside from making nifty pictures, Mandelbrot's fractal math has helped solve problems - like figuring out why Earth didn't freeze, a couple billion years back. (June 6, 2010)

More about Mandelbrot:

No comments:

Unique, innovative candles

Visit us online:
Spiral Light CandleFind a Retailer
Spiral Light Candle online store

Pinterest: From the Man Behind the Lemming

Top 10 Most-Viewed Posts

Today's News! Some of it, anyway

Actually, some of yesterday's news may be here. Or maybe last week's.
The software and science stuff might still be interesting, though. Or not.
The Lemming thinks it's interesting: Your experience may vary.
("Following" list moved here, after Blogger changed formats)

Who Follows the Lemming?


Family Blogs - Blog Catalog Blog Directory