Comment by PaulHoule

Most 'time loops' in science fiction might better be described as time knots.

I think of https://en.wikipedia.org/wiki/Predestination_(film) which is much more complicated than the usual time travel scenario; presumably the protagonist leaves but doesn't really enter since the protagonist is their own mother and father (the matter that makes them up does enter since they eat and breathe the way everybody else does; thinking the story through I'd think if I was going to have such a miraculous and singular existence I'd rather be a fantastic creature of some kind [dragon?] as opposed to a relatively boring intersex person capable of both reproductive roles)

Also https://en.wikipedia.org/wiki/The_End_of_Eternity which tames the complexity of time travel by presupposing 'eternity' has a second time dimension, making large-scale engineering of history practical. 'Eternity' itself owes it's existence to a time loop which is ultimately broken by the protagonist.