Points on complex z plane (dynamical or variable space) which under iterations fc for fixed c go to an attractor (attracting fixed point, periodic orbit or infinity) form the Fatou set. The Julia set (J) is its complement. Therefore the Julia set includes all repelling fixed points, periodic orbits and their preimages.
The Mandelbrot set is the black region on this image.
Points outside the M-set are colored according to how many
iterations n were completed before |zn| > 2
(see also the Distance Estimator algorithm).
Each point c in the Mandelbrot set specifies the geometric structure of the corresponding Julia set. If c is in the M-set, the J-set is connected. If c is not in the M-set, the J-set is a Cantor dust.
This is the famous "Douady's rabbit".
The "white" triangle shows orbit star of attracting period-3
orbit f: z1 -> z2 -> z3 -> z1 .
This cycle lies in n = 3 components of
the interior of the J-set. Moreover, these n components are joined
together at one point. The attracting cycle hops among these n
components as fc is iterated.
The left image below is Cantor dust and the right image is connected pure "dendrite".
Now we are ready to a Julia orbit trip.