Nice try ;) but the rational-ratio Lissajous is a closed figure that retraces.

To complete the retrace, oil would have to get back down to around $15. Even without all that "liquidity" being injected by our freaked-out Fed...no.

I said that it retraces, but not exactly. Explain why as the price comes back down it is starting to retrace. I agree that it may never go back completely, but very similar to chaotic nonlinear systems a potential duty cycle limit may exist.

In any case, the pattern does give an indication of how you could get a closed-form and analytical expression for the empirical behavior that is seen.
Something like:
x=A*sin(t)+B
y=K*sin(3t+C)

the variable t is similar to time but it could creep along, speed up, or reverse itself as it creates the pattern.

Hey, I don't necessarily believe in this, just that it fits a pattern. At least as well as that stupid Logistic does for Hubbert curves :) :) :) You can probably guess by now that I was just waiting for that punchline.