Let there be a series of complex numbers z, starting with for example z_0:=0.

Going from element to element shall be defined as:

z_{i+1}=z_i²+c

(were c is a complex number, too).

Then you plot the complex plane of c, for each point:

If either the real or the imaginary part of z with that c goes outside (i.e. diverges, does not converge) with a finite number of steps, you put a white pixel, and otherwise you put a black pixel.

Then you get the Mandelbrot plot, a beautiful fractal image.