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.
Connected J-set for c1 = -0.71 + 0.1i in the M-set is shown below. The Julia set is the boundary between colored and black regions in the left image. You see too orbit starting at zo = 0 which converges to the attracting fixed point z1 . "Filled" J-set is shown in the right picture (it is marked by "f"). Colors inside connected J-sets show how fast a point goes to attractor. You see attractor and infinit sequence of its preimages f -on(z1).
The left image below is Cantor dust and the right image is connected pure "dendrite".
Now we are ready to a Julia orbit trip (Java).