Logopolis is pretty interesting. Out of the regeneration stories it is certainly unique. I love the sense of foreboding that permeates throughout the story, with the Watcher and Master both instilling this rather constant sense of dread. That works well in building up to the end of the Fourth Doctor, especially with how little we see of the Master at first, only hearing his evil laugh and seeing his victims.

The show makes good use of its sets and props here as well, I really like the layered TARDISes and how we go about the mystery in the first few episodes. Tegan has a pretty decent introduction at first and I think gets nicely brought into this story in a way that works well. Her character isn't lionized like in most companions in the revived series, while her joining the Doctor felt thematically relevant to her job as a flight attendant.

That being said, as the story goes on, once we go to Logopolis, things get a little weaker. It's a really interesting idea of a world dedicated to math yet lacking a ton of technology, and I like that the Doctor is already familiar with this world, as it gives credence to his experience as a being this universe-spanning traveller and makes Logopolis feel like a place of meaning. Where it starts to lose me is the idea that this world is the only thing preventing reality from collapsing. It feels like the Doctor just barely saves the universe and it is now only hanging by a thread. It's a neat idea but doesn't fit as well with the larger franchise and feels like an underplayed idea from even this story.

It's a little awkward, as is some of the other aspects of the writing and acting. For example it feels like Nyssa just appears in this story and it is very abrupt and Sarah Sutton feels a little wooden as a performer here. It's the sort of stuff that makes Logopolis interesting but imperfect. Very important to Doctor Who but not my all time favourite story or even my favourite regeneration event.