Its definition and name are due to Adrien Douady, in tribute to the mathematician Benoit Mandelbrot.[1] 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 {\displaystyle c} c, whether the sequence {\displaystyle f_{c}(0),f_{c}(f_{c}(0)),\dotsc } {\displaystyle f_{c}(0),f_{c}(f_{c}(0)),\dotsc } goes to infinity (in practice — whether it leaves some predetermined bounded neighborhood of 0 after a predetermined number of iterations).