I've always loved the cool background animation in Jazz 1. I'd like to make something similar because it's just really relaxing to look at, but how exactly does it work? Is it a looping animation, or is an image being warped in real time? I'd love to know.

I think it's a single indexed bitmap of a 'vortex' texture X-Y repeated and moving across the screen. A piece of code then shifts those color entries in a sequence to create the wave effect.

It works more or less the same as the other animations in JJ1 that aren't sprites.

If anyone's more acknoledged on JJ1's internals and I'm utterly wrong here, then feel free to correct me.

I don't think anyone knows much about JJ1's internals. You could take a look at OpenJazz's take on the menu background, but it's definitely not the same effect, just guesswork.