Some ideas are:
- You branch off into another timeline and your actions make no difference to the previous timeline
- You’ve already taken said actions but just didn’t know about it so nothing changes
- Actions taken can have an effect (so you could suddenly erase yourself if you killed your parents)
- Only “nexus” or fixed events really matter, the timeline will sort itself out for minor changes
- something else entirely
I have always been a fan of stable time loops so I guess option 2 is the best one for me.
One trope I’d like to see more of is loops which are not stable themselves, but are stable as a group. Eg a 2-loop has loop A in which someone goes back in time and changes history leading to a new timeline loop B. Someone in loop B later goes back in time and changes history in a way that turns the timeline back into loop A.
My headcanon is that your option 3 is basically an n-loop that we only see the first few loops of.