The Mandelbrot set is a two-dimensional set with a relatively simple definition that exhibits great complexity, especially as it is magnified. It is popular for its aesthetic appeal and fractal structures. The set is defined in the complex plane as the complex numbers for which the function does not diverge to infinity when iterated starting at , i.e., for which the sequence , , etc., remains bounded in absolute value.
The Mandelbrot set within a continuously colored environment
Start. Mandelbrot set with continuously colored environment.
Gap between the "head" and the "body", also called the "seahorse valley"
Double-spirals on the left, "seahorses" on the right
Benoit B. Mandelbrot was a Polish-born French-American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of physical phenomena and "the uncontrolled element in life". He referred to himself as a "fractalist" and is recognized for his contribution to the field of fractal geometry, which included coining the word "fractal", as well as developing a theory of "roughness and self-similarity" in nature.
Mandelbrot at a TED conference in 2010
Benoit Mandelbrot
Mandelbrot speaking about the Mandelbrot set, during his acceptance speech for the Légion d'honneur in 2006
A Mandelbrot set
