http://library.wolfram.com/explorations/explorer/images/mandelbrotdefault.gif

The Mandelbrot set is one of the most widely recognized fractal patterns, generated by an IterativeFunctionSystem on ComplexNumbers on the complex plane.

A complex point ''C'' is in the set if the iterated function http://mathworld.wolfram.com/images/equations/MandelbrotSet/equation1.gif, where http://mathworld.wolfram.com/images/equations/MandelbrotSet/inline1.gif, does not tend to infinity.

Put another way, each iteration on the plane is a Julia Set. The Mandelbrot is the set of all connected Julia Sets, and the colors outside the Brot measure how disconnected the remaining Julia Sets are.

The Mandelbrot set is an example of MisallocatedCredit, wherein Brooks and Matelski discovered and analysed it much earlier, but Mandelbrot used the new-fangled computer technology to popularise it.
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A simple Java viewer for Mandelbrot and Julia sets:  http://home.houston.rr.com/casmco/Mandelbrot.jar -- EricHodges

''A Buddhabrot:''

http://www.superliminal.com/fractals/bbrot/half_res_rgb.gif

''And an Eulogy:''

http://boingboing.net/images/brot.jpg

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see also DecemberZeroFive; MandelBug

CategoryMath