The whole begining sequence that follows directly on from logopolis is really fun, and I think you get a good feel of each character. especially tegan, i love how she just drove off in the van! i love adrics silly little monologue about being from the stars. i like that all three characters' backstories are remaining relevant, like adric's maths skills and leaving e-space, nyssa's scientific competency (tbh i dont think she had much in keeper of traken but its a good trait to give her and expand upon) and tegan being very pushy, more physical i guess? more brawny? and just having a strong forceful personality. yeah they're all really fun together. and a lot of this episode is tegan and nyssa centric, with adric mainly being damseled! a nice change. the doctor remembering adric without needing reminding is a good relationship moment for the two of them. people say that this tardis team is like 5 and his children but i dont like that and i did not really get those vibes from this. i like them more as equals, friends, yknow? and they're all adults, adric and tegan for sure do not need a father, i think maybe nyssa does though. again on being equals - they dismiss tegan piloting the tardis in that adric gave her the instructions to do so - but she must have still had a hand in it, otherwise the tardis would not have landed like that. and how is following adric's instructions different to following instructions that were programmed into the tardis? so i think it counts. strange that classic is so much more willing for the companions to be allowed to pilot the tardis than nuwho. the 4th part is very exciting!! the zero room is so funny. they're so much more willing to explore the tardis from full circle onwards, which continues into the majority of 5's era i believe. i wish that was more of a thing in nuwho - i would kill to see companion or doctor rooms! or idk maybe like an area of the console room decorated to a companion, some trinkets. and then it would be sad in  later seasons after they leave..
the evidence of fans taking over the show is evident in this episode - with the referencing to old companions.