Calculation of Julia sets are vey similar to the mandelbrot set (Mset). A single point is taken from an Argand diagram (The Mset) as the value of c. We then take successive points from an Argand diagram as our starting values for X1. We then plot these points in a colour corresponding to the number of iterations made as with the Mset. So, with the Mset the initial value of X is always 0, and c varies according to where we are in the argand diagram. With a Julia set c stays constant and are initial value of X varies according to where we are in the argand diagram. Different Julia sets are produced depending on the complex number chosen for c. (ie. whereabouts we choose c from the mandelbrot set.) The Mset is in fact a catalogue of all possible Julia Sets.

An interesting application I wrote some years ago allowed the user to plot a series of one or more connected lines or curves across the Mset. A sequence of black and white Julia sets would then be generated for a given number of points along these lines, in order to create an animated movie of Julia shapes smoothly evolving new shapes depending on the location in the Mset. Fractint is a popular program for the PC which draws simple Julia set shapes in real time as you move the mouse
across the image of the Mset.