I'm trying to understand how Julia sets iterations are done and how those iterations differ from the ones that generate the Mandelbrot set.
Both of them use the following function: $f(z) = z^2 + C$
For the Mandelbrot set, one would just start with an initial value of $z=0$. And iterate every single point (in the boundaries of $-2,2$ and $-2i,2i$ because any other bigger point is graphically useless) in the complex plane using the C variable. Depending if the iteration is bounded or goes to infinite, you draw differently the points.
But, what's the difference in Julia sets? I've read that just by giving $C$ a value and $z$ another value (different from zero, I guess) a Julia Set can be generated/calculated. The value of $C$ is the point in the plane, but what is the value of $z$? is it a random value? a fixed value? how exactly the iteration of a Julia set is done?