Hi. My name is Veronica and I'm an art major at Western Michigan University.
Lately I've been trying to get into projection, and projection mapping to
render projections onto 3D objects.
Greetings, and Welcome to this particular Forum !!!

I would love to create some 3D animations of fractals and I was
wondering if it was possible to manipulate the speed and view of
the camera around one so that it could go to music (i.e. zooming in
and out to a tempo). ....... If anyone has any suggestions where
I start I'm all ears. I've never created my own fractal....
There are hundreds of applications available for creating fractal images:
http://www.fractalforums.com/fractal-related-links/finding-fractal-related-software/ But as most people in this forum will attest to, it is a very time consuming process. That is if you render each image as a frame of the animation and continue that process to get enough frames to make a lengthy video.
Another process is to use one of the more specialized fractal programs that are capable of producing 3-D objects (meshes), which can then be saved/exported for importing into a 3-D rendering application (i.e. Maya, Bryce, 3DSMax, etc.). From there you could do fly-bys, rotations, various textures and backgrounds, and much more.