How can the shape in this picture be descibed mathematically?

Question

I'm reading an article on Boltzmann that contains the following figure:

It is obviously related to harmonic oscillators (since the article says so), but how could I describe this figure mathematically? I've seen it somewhere before, but have no recollection of where.

Answer 1

Lissajous figure with $x = \sin (4 t)$ and $y = \sin (7 t)$.

Count the number of extrema along the top and along the side to get the ratio of frequencies.