Castrovalva

Castrovalva, also called the Dwellings of Simplicity, was a city created with block transfer computation by the Master and the power of an enslaved Adric's mathematical skill. It appeared to be a town located on a cliffside of what Nyssa believed was the planet Andromeda.

When the Fifth Doctor needed a place to recover from the effects of his recent regeneration, Nyssa and Tegan brought him to Castrovalva, because of a fictional entry placed in the TARDIS Index File by Adric. Indeed, the Master intimated that there was never a "real" Castrovalva. Thus, statements from the Index File, such as the "fact" that it was on a planet in the Andromedan Phylox Series", were simply untrue.

The Master's hope was that he could lure the Doctor into a fictional world, then destroy him by "imploding" that world. However, because the Doctor was able to make some of the Castrovalvans self-aware, the plan failed. One of them, Shardovan, threw himself into the apparatus enslaving Adric, which brought an unplanned end to the city. The Doctor and his companions escaped just as Castrovalva fell in on itself. (DW: Castrovalva) The Master escaped as well. (DW: Time-Flight) Andromeda, which was real — even though it was by no means certainly called "Andromeda" —  also survived the "implosion" of Castrovalva.

Characteristics
Castrovalva seemed to have an extensive history, its library holding books of information from twelve hundred years ago to the present day. The Castrovalan people did very little except read, but encouraged new ideas. They began hunting for sport at the time of the Doctor's arrival.

Behind the scenes
According to writer Christopher H. Bidmead, director Fiona Cumming and actor Peter Davison, the name of the planet on which Castrovalva is located is not called Castrovalva. (DCOM: Castrovalva) This is seemingly confirmed in-narrative by the episode 2 close-up of the TARDIS Index File entry on Castrovalva, and by a later exchange between the Doctor and Nyssa who says, "[Castrovalva] is in Andromeda, a small planet of the Phylox Series."