How can I find 3d parametric functions that create unbroken loops that repeat periodically with no breaks?

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I'm learning to make visual effects in Unity's VFX Graph and I want to find a way to make a continuous curve 'cause I think it'd look cool. I did some googling and found some image examples, but no complete equations.

Example:

A parametric function that creates a closed loop

Is there any general strategy I could use to construct/discover 3d parametric functions that create closed loops? Is this a studied topic in mathematics? If so, what keywords should I look for to find more info?