Left:
Two lissajous figures with different parameters are generated and their coordinates are saved in lists, after which I lerp from one to another. After finishing the animation to the second curve, a new one is generated with, again, different parameters, and the curve then animates to the new one. This process can be repeated indefinitely.
The method produces a lot of shapes in between two lissajous curves, creating a bunch of interesting accidentals. By influencing which curves often follow up on certain curves, I can have the animation show more interesting in-between shapes more often.

Right:
In this shape, the established coordinates from animating the lissajous curves are used as the A and B component of imaginary numbers, and then multiplied with themselves. The result is then used as the X and Y components of a position. This creates entirely new shapes that seem more unpredictable than the lissajous curves they are generated from.