This was built using only the built-in plugins in After Effects. It uses an evolving fractal noise source comp to "paint in" a 3D fractal, using multiple staggered and offset 3D layers.
The project file is available to download and use (under free CC license) from the Digital Distortion web site: digitaldistortion.net/rsrc_3dFractalCloud.html
It's a pretty cool effect, unfortunately it's limited by the nature of how it works. As it's using stacked layers in a 3D space, if you position the camera too low, you'll see visual artifacts. Also, as you get closer in, you see the separation between the layers (creating an unpleasant "scanline" effect to it). I experimented with some techniques to try and reduce this, including adding a high frequency oscillation to blur the gaps between layers using motion blur, but nothing really solved the issue adequately. Render times and memory usage are quite steep too. This animation took 3 hours to render on my 2008 mac pro with 20GB RAM.
If anyone else can work out a better way to reduce the stacking artifacts, then please share it :)
Soundtrack: "Daughter (for Sara)" by Conelrad