JULIA ANIMATION

[Bent-Winged Angel]

This is a series of 5 , 5 second clips.  all julia.. I was fascinated with the self similarity of each.  Also how they slowly went back, in black to julia.  Can anyone explain the theory behind all this?  I know I can make a pretty image, but now I want to know the how & why!  Hope I explained it alright. 

<a href="http://www.youtube.com/v/juK9TpC3Rvw&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/juK9TpC3Rvw&rel=1&fs=1&hd=1</a>

[bib]

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.

[Bent-Winged Angel]

Thanks bib!  I did know that julia sets could be, connected disconected Or dust.  I was surprised that the "black" was soo consistant.  Also the "morphing of the black back to julia was much slower than the colored part. Ahh you put all the julia types together in the brot.  cool!

[bib]

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)

[Bent-Winged Angel]

bib thanks for clearing up the connnected VS disconnected issue for me. I stayed away from the center of brot to get this.

<a href="http://www.youtube.com/v/Q7-ifrdy4mE&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/Q7-ifrdy4mE&rel=1&fs=1&hd=1</a>

[Bent-Winged Angel]

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>

[trafassel]

I cannot see you video in my country (Germany) because it contains some content of f*** Sony Music Entertainment.

[Bent-Winged Angel]

I cannot see you video in my country (Germany) because it contains some content of f*** Sony Music Entertainment.

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>

[Bent-Winged Angel]

This was done with Fractal Explorer. (julia/params)  Had difficulty with the numbers & getting it smooth.
Burst of movement made it difficult to find the "right" audio.
<a href="http://www.youtube.com/v/lsPsN3WbOv4&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/lsPsN3WbOv4&rel=1&fs=1&hd=1</a>

[Bent-Winged Angel]

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>