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Mandelbrot, Father of Fractals ~ RIP

October 18, 2010

Benoît B. Mandelbrot, father of fractals and the amazing, incredible (to mathemeticians, artists and normal people too) mandelbrot set, died last week.

From Wikipedia:

Mandelbrot worked on a wide range of mathematical problems, including mathematical physics and quantitative finance, but is best known as the father of fractal geometry. He coined the term fractal and described the Mandelbrot set. Mandelbrot extensively popularized his work, writing books and giving lectures aimed at the general public.

Mandelbrot died in a hospice in Cambridge, Massachusetts, on 14 October 2010 from pancreatic cancer, at the age of 85. Reacting to news of his death, mathematician Heinz-Otto Peitgen said “if we talk about impact inside mathematics, and applications in the sciences, he is one of the most important figures of the last 50 years.”  Chris Anderson described Mandelbrot as “an icon who changed how we see the world.”  French PresidentNicolas Sarkozy said Mandelbrot had “a powerful, original mind that never shied away from innovating and shattering preconceived notions”.  Sarkozy also added, “His work, developed entirely outside mainstream research, led to modern information theory.”

Views of the Mandelbrot set. Each successive image is a magnification of the previous image.

The Mandelbrot set is a mathematical set of points in the complex plane, the boundary of which forms a fractal. The Mandelbrot set is the set of complex values of c for which the orbit of 0 under iteration of the complex quadratic polynomialzn+1 = zn2 + c remains bounded.[1] That is, a complex number, c, is in the Mandelbrot set if, when starting with z0 = 0 and applying the iteration repeatedly, the absolute value of zn never exceeds a certain number (that number depends on c) however large n gets. The Mandelbrot set is named after Benoît Mandelbrot, who studied it.

For example, letting c = 1 gives the sequence 0, 1, 2, 5, 26,…, which tends to infinity. As this sequence is unbounded, 1 is not an element of the Mandelbrot set.

On the other hand, c = i (where i is defined as i2 = −1) gives the sequence 0, i, (−1 + i), −i, (−1 + i), −i, …, which is bounded and so i belongs to the Mandelbrot set.

When computed and graphed on the complex plane the Mandelbrot set is seen to have an elaborate boundary which, being a fractal, does not simplify at any given magnification.

Just so you know. 😉

Fractal Zoom (HD) to 6.066 e228 (2^760) Mandelbrot – (Last Lights On)

Deep Zoom into Mandelbrot Set (“Mathematical Porn”) by Team Fresh.  Read more about this astonishing animation here.

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