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A Julia set is "black" (and connected) when the c point is inside the Mandelbrot set, and like dust (disconnected, a.k.a "Fatou dust") when the c point is outside the Mandelbrot set. You probably have read already that several times, but the Mandelbrot set is the map of all Julia sets. It become more evident when you see this kind of animation (which is spoiled by weird artifacts unfortunately)
<a href="http://www.youtube.com/v/H603qZfhTNM&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/H603qZfhTNM&rel=1&fs=1&hd=1</a>

Also, a "traditional" property of the Julia sets which you can see in the above animation, is that is has similarities in shape with the corresponding c point in the Mandebrot set. For example a Julia set near the west tip looks like the west tip, a Julia set in the seahorse valley looks like a seahorse, etc...

When your Julia set goes from what you call "Julia" to black, it means that the c point crosses the Mandelbrot set border from the exterior to the interior.

What I really find incredible is that Julia and Fatou, French mathematicians in the beginning of the 20th century, had mathematically calculated these properties (connected or not, and many more) without having computers to visualize these sets. Mandelbrot "only" re-used their work and was the first one to draw these sets with a computer.

disconnect = dust. It is either in one part (Julia set, which can be very convoluted if near the border of the Mandelbrot set, but still on the interior), or in an infinity of infinitely small parts (Fatou dust)

This one was done with Fractal Explorer.

Polinomial julia/param animation
C°=Z°: Z2=Fn1(Z); Z=Sin(Z)-C; C=1/(50*Z2)
Function- CASinh
Filter-Stalks-2(v)
Bailout 2


<a href="http://www.youtube.com/v/penRUQcTdv4&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/penRUQcTdv4&rel=1&fs=1&hd=1</a>

I hate it when that happens!  But I cannot resist personalizing my videos.  I German woman in my Movie Making group complained of same thing.  Do they still "gooose Step" there? 
Ok now this one you'll be able to see, being that they could not grab Beetoven!

<a href="http://www.youtube.com/v/48-a21ckOLc&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/48-a21ckOLc&rel=1&fs=1&hd=1</a>

Another FE julia/params.

<a href="http://www.youtube.com/v/umBdxdzq5Kc&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/umBdxdzq5Kc&rel=1&fs=1&hd=1</a>