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What's the name of the curve you get from changing the x or y frequency on what was previously a path around an ellipse?

The equation would be:

f(t) = (Acos(ut), Bsin(vt))

And it looks like a wavy line instead of an ellipse.

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Do you perhaps mean Lissajous curves?

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Previously means when $ u = v$ ?

Lissajou figures. If $ u/v = 2 , 3 $ , ie multiple arguments, Lissajous close after $ u v $ LCM waves ..

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