Alright we've had our fun. Time for a splash of water: when it comes to applying this stuff to actual paths of motion for physical objects in other coding projects... by all means go ahead, but the motions will be inconsistent with whatever laws of physics the rest of the program uses, supposing you're using any. These kinds of curves typically appear when taking the plot or projection of some kind of harmonic system, or looking at a phase diagram. This means that no projectile, airplane, mosquito, or other flying, gliding, or floating thing will *actually* trace out paths like this. Springy stuff at best like my balloon-laser example from above. Just sayin.