Let it run all the way through once, then feel free to watch it multiple times.
Made in Mandelbulb 3D. I somehow managed to go backwards from using presets! This fractal (in the first frame) is, I believe, the very first thing that loads up when you open the program. I did the usual parameter-fidgeting and then messed a bit with the colors (making everything lower-contrast and such). Also, the pixelated noise stuff in the end (or middle, depending on how you view the frames) appears to be because I didn't set some settings to high enough detail, but it would have taken a lot longer if I had done so, so I didn't, as this is mainly just a test.