It can be shown that once the modulus of z is larger than 2 (in [cartesian form]?, when x2+y2>22) the point c will tend to infinity. This value, known as the Bailout value enables a large number of iterations to be skipped when calculating points outside the Mandelbrot set. Whilst it is of no mathematical importance, most fractal rendering programs display points outside of the Mandelbrot set depending on the number of iterations before it bailed out, creating concentric shapes, each a better approximation to the Mandelbrot set.
The Mandelbrot set was created by [Bendroit Mandelbrot]? as an index to the Julia? Sets: each point in the complex plane corresponds to a different Julia set.
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Why not provide some links to freeware programs that compute fractals?