It may be pretty, but I would challenge your claim that it is a Lissajous figure.
A Lissajous pattern is created by two sinusoidal waveforms with a 90 degree phase shift.
This gives various patterns depending on the interaction of the two sine waves and their phase relationship.
A 2 to 1 relationship, for example would result in a figure of eight shape.
Whereas, your project, although interesting, is not going to show this, just a circular pattern that jumps around in an irritating manner.