Mandelbrot set

Fractal named after mathematician Benoit Mandelbrot

The Mandelbrot set is a two-dimensional set. It is defined in the complex plane as the complex numbers c {\displaystyle c} for which the function f c ( z) = z 2 + c {\displaystyle f_{c}(z)=z^{2}+c} does not diverge to infinity when iterated starting at z = 0 {\displaystyle z=0} . In other words, it is the set of c {\displaystyle c} for which the sequence f c ( 0) {\displaystyle f_{c}(0)} , f c ( f c ( 0)) {\displaystyle f_{c}(f_{c}(0))} , and so on, remains bounded in absolute value.

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