Named after Benoit Mandelbrot
The co-ordinates (a, b) of each point in the diagram represents a different complex number c where
For the iterative process defined by z0=0 + 0i, zr+1=zr2 + c:
If the sequence z0, z1, z2.....
remains bounded then the point representing this value of c is in the Mandelbrot Set, which is the unshaded part in the centre of the diagram.
The colours surrounding the set correspond roughly to the rate at which the sequence tends to infinity.
In fact they correspond to the number of iterations (n) needed before |zn|>2, and the colours can be chosen arbitrarily by the programmer writing the software to produce the diagrams.
The programmer has no control over the shape of the Mandelbrot Set!!!