A lot of mathematical objects can be created with a dependence on a parameter. By making that parameter determined by time (i.e., frame number), you get an animation. This works great for level curves, or parametrically defined curves, etc.

The animated field of cylinders illustrates one possible result of the sum of sinusoidsal functions. The "sphere to cube to sphere" shows superellipsoids, an often not talked about 3d object. The K5 graph animation shows K5.

"Has your software ever glitched out any interesting types of artwork?"

I don't know what you are asking...are you asking have I had a software error ever produce anything interesting? I can't think of any examples...

cheers,

Matt