Upon arriving at Logopolis the doctor,Adric and the very confused Tegan encounter Nyssa. The Logopolitans have,for a reason even unknown to them,seem to have created an exact replica of Earth's Pharos Project in order to transmit the vital computational data that is there specialty. Considering they are able to create all matter around them using what they call block transfer calculations rather than machines,the reason for them creating this soon becomes known,also bringing difficult news for Nyssa. The Master has been interfering in the Logopolitans calculations in order for them to facilitate his plans for destroying Earth and the doctor. This also reveals to Nyssa that he commandeered her father's body to accomplish this. He has also used a tissue compression eliminator to kill anyone in his way,one of whom happened to be Tegans aunt as well. What even the Master doesn't know is that Logoplis's block transfer calculations are part of what keeps the entire universe in balance,he has created for himself an entropy effect for the entire universe.
The doctor faces complications of his own as,on Earth he encountered an ivory humanoid Adric refers to as The Watcher,who appears to have told him sound catastrophic end is near. Even after one failed attempt to thrawt the TARDIS after the other,the doctor forges an allience with the Master in order to restore Logopolis to proper function. Since the doctor understands he has to accomplish the next part of his mission with the Master alone,he leaves Nyssa and Adric alone in the TARDIS which,when accidentally thrown out of space time reveals a collapsing universe-including Nyssa's own home world of Traken. Tegan has elected to follow the doctor,in her eyes her key to getting home to Earth whereas the TARDIS set a course their to assist the doctor. He and the Master have arrived at the actual Pharos Project. The doctor soon learns his mission goes beyond saving Logopolis and the universe,but also the Master from taking this opportunity to destroy him and now the universe itself. The Master is forced into escape,at the cost of the doctors own life. When Tegan,Nyssa and Adric arrive at the scene,the doctor informs them his end has been prepared for. Turns out the Watcher was an shadow of the doctors all along,representing his fifth regeneration which than occurs before their eyes.
For Doctor Who this is a very history story as it represents the end of Tom Baker's run as the fourth incarnation of the time lord known as The Doctor. He is still unchallenged in terms of the length of time he played the role. Also of note is the fact that this story in many ways paved the way for the complex writing and fast paced atmosphere of the modern incarnation of Doctor Who. Each of the four parts of this serial is almost a distinct story in and of itself. But aside from the Master's plans and the introduction of Tegan and Nyssa as companions of the doctor,the key theme of this is entropy. First of the TARDIS,then of Logopolis and therefore the entire universe. The idea of a planet able to develop physical structure from a unique form of mathematical calculation was a very forward thinking concept of physics to introduce as a catalyst to this story. As with many of Tom Baker's later stories,it actually finds the doctor seriously concerned for the well being of himself,the TARDIS and his companions. And the stakes are incredibly high. A very spacious,expansive and intelligent story with which to conclude Doctor Who's most acclaimed eras.