The Mandelbrot set is the set of complex numbers for which some function does not diverge when iterated from z=0. Zooming into the Mandelbrot set Its definition is credited to Adrien Douady who named it in tribute to the mathematician Benoit Mandelbrot. The set is connected to a Julia set, and related Julia sets produce similarly complex fractal shapes. Mandelbrot set images may be created by sampling the complex numbers and testing, for each sample point.