Logopolis was a planet of mathematicians, the Logopolitans, who utilised Block Transfer Computations, with the Monitor as their representative. However, Logopolis was also highly instrumental in keeping the fabric of the universe known as N-Space from falling apart.
History
The Logopolitans had set up an exact replica of the Pharos Project dish to send Block Transfer Computations out into the universe to maintain the CVEs which, by removing entropy from the universe, enabled it to survive.
The Fourth Doctor visited Logopolis in 1981 to ask the Logopolitans to help restore the chameleon circuit of his TARDIS. The Watcher also arrived there at the same time as the Doctor with Nyssa, whom the Doctor and Adric had last met on Traken.
The arrival of the Tremas Master fatally disrupted life there. He killed Logopolitans at random with his Tissue Compression Eliminator. Eventually, because the Logopolitans' Block Transfer Computations no longer worked, the planet itself began to crumble and lose coherence, as did the inhabitants, including the Monitor due to a build up of entropy that quickly formed an entropy wave. The wave was soon stopped by the Fourth Doctor. (TV: Logopolis)
References
The Sixth Doctor believed that Bletchley Park almost put Logopolis to shame. (AUDIO: Criss-Cross)
The artist Zhe Ikiyuyu was said to be trained on Logopolis. (COMIC: The Arts in Space)