Lissajous curve is the graph of a system of following parametric equations which describe complex harmonic motion.
x = Asin(at + ϕ), y = Bsin(bt)
It was studied by Nathaniel Bowditch, an American mathematician in 1815 and later in detail by Jules Antoine Lissajous, a French physicist in 1857.
Simulator : https://monkeyscript.github.io/lissajous-curve/
Wiki : https://en.wikipedia.org/wiki/Lissajous_curve
All the parameters can be tuned and the simulator plots 100 points per second with varying t value.