Mandelbrot set exploration

The Mandelbrot set is the set of complex numbers c for which the function does not diverge when iterated from z=0, Images of the Mandelbrot set exhibit an elaborate and infinitely complicated boundary that reveals progressively ever-finer recursive detail at increasing magnifications, making the boundary of the Mandelbrot set a fractal curve. The «style» of this repeating detail depends on the region of the set being examined. Mandelbrot set images may be created by sampling the complex numbers and testing, for each sample point c, whether the sequence fc(0), fc(fc(0)), fc(fc(fc(0))),... goes to infinity. Credited to Adrien Douady who named it in tribute to Benoit Mandelbrot. Song : S.T.A.Y by Hans Zimmer #math