The Mandelbrot set is the set of complex numbers c for which the function f{c}(z)=z2+c does not diverge when iterated from z=0 , i.e., for which the sequence f c(0), f c(f c(0)) , etc., remains bounded in absolute value. Its definition is credited to Adrien Douady who named it in tribute to the mathematician Benoit Mandelbrot,a pioneer of fractal geometry.