The Mandelbrot set is a set of points, a distinctive and easily recognisable two-dimensional fractal shape. It arises from the repeated application of the deceptively simple equation z_{n+1} = z_{n}^{2}+ C.
Any complex number C, is in the Mandelbrot set if, when starting with z_{0} = 0 and applying the iteration repeatedly, the absolute value of z_{n} does not head out to infinity.