16 October 2010

R.I.P. Benoît Mandelbrot ~ Fractal Mathematics...

Alas, Benoît Mandelbrot, creator of fractal mathematics has passed away at age 85. Writes Jascha Hoffman in the NYTimes...
"In a seminal book, “The Fractal Geometry of Nature,” published in 1982, Dr. Mandelbrot defended mathematical objects that he said others had dismissed as “monstrous” and “pathological.” Using fractal geometry, he argued, the complex outlines of clouds and coastlines, once considered unmeasurable, could now “be approached in rigorous and vigorous quantitative fashion.” For most of his career, Dr. Mandelbrot had a reputation as an outsider to the mathematical establishment. [...] Dr. Mandelbrot traced his work on fractals to a question he first encountered as a young researcher: how long is the coast of Britain? The answer, he was surprised to discover, depends on how closely one looks. On a map an island may appear smooth, but zooming in will reveal jagged edges that add up to a longer coast. Zooming in further will reveal even more coastline. “Here is a question, a staple of grade-school geometry that, if you think about it, is impossible,” Dr. Mandelbrot told The New York Times earlier this year in an interview. “The length of the coastline, in a sense, is infinite.”
There are endless fractal images, but the Mandelbrot Set remains among the most epic. Here's just one select sampling... And here's a wonderful Zoom!

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