The Julia set is associated with those points z = x + iy on the complex plane for which the series zn+1 = zn2 + c does not tend to infinity. c is a complex constant, one gets a different Julia set for each c. The initial value z0 for the series is each point in the image plane.
The well known Mandelbrot set forms a kind of index into the Julia set. A Julia set is either connected or disconnected, values of c chosen from within the Mandelbrot set are connected while those from the outside of the Mandelbrot set are disconnected. The disconnected sets are often called “dust”, they consist of individual points no matter what resolution they are viewed at.
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