Sunday, October 17, 2010

The fractals are orphans: Benoït Mandelbrot has died

Benoît B. Mandelbrot (20 November 1924 – 14 October 2010) was a Franco-American mathematician. Born in Poland, his family moved to France when he was a child. Mandelbrot spent much of his life living and working in the United States, acquiring dual French and American citizenship.

"Gold Nugget" Front cover of Benoît Mandelbrot's master piece "hazard & finance" Flammarion publisher (in french)

"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 polynomial zn+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..."

Fractal Zoom Mandelbrot Corner

A fractal zoom on a mandelbrot set, finishing on a dendrite area.
Made using XaoS (freeware program)

Search Google: Mandelbrot fractals
Search Google: Mandelbrot Wallpaper

Search Google: Mandelbrot 3D

Mandelbrot Applet

"This is the start page for the Mandelbrot Applet. The Mandelbrot Set is one type of fractal, and besides it's mathematical value it can be aesthetically pleasing. One of the interesting properties of the Mandelbrot Set is that it can be arbirtrarily magnified, and while some elements will look similar to other areas of the Set no part will be exactly the same. In practice however there is a maximum magnification caused by the limited precision of the computer - increasing the precision further would be considerably slower. Please note that Java must be installed for the Applet to work (and apparently it is installed in your browser)."

Mandelbrot Exporer

"Mandelbrot Explorer runs on Windows PCs (2000, XP, 2003 Server, Vista, 2008 Server, Windows 7), and needs the Microsoft .NET Framework (version 2.0 or later) to run. The .NET Framework is part of Windows Vista, 2008 Server and Windows 7; those running Windows 2000, XP or 2003 Server will need to install it separately (if you haven't done so already)."

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