The Lissajous projection conjecture

A knot has a Lissajous projection if its projection to the $x$-$y$ plane arises from a second-order Lissajous parametrization, with coordinates of the form

$$x(t)=\cos(n_1t+\phi_1),\qquad y(t)=\cos(n_2t+\phi_2),$$

for integer frequencies $n_1,n_2$ and real phase shifts $\phi_1,\phi_2$. The Lissajous projection conjecture. Every knot has a Lissajous projection. The source motivates this by observing that sufficiently large frequencies may produce the required projections; whether every knot admits one remains open in the supplied text.