You can customize your sprite paths as well, just make a group of codes and the conditions with the formulas.
All of that paths can be done by this way.
Start doing simple paths like circles, updating the path every tick, and keep it doing ellipses, etc.
The formulas you said you have. So, post a formula here and, if necessary, I can help you doing a sample.
Oh, and also, if it's not your problem, Yeah, it'll be great.