Process

The Process, known in the Pythian Book of Future Legends as the Amphisbaena, was a parasitic life form which the Seventh Doctor speculated to be a datavore, a creature which consumed information.

The Process resembled a slimy worm or leech, but with lamprey-like mouths at each end. It moved by cartwheeling itself end over end, leaving a slime trail behind. It had clawed fins and red-brown skin which turned grey with age. It was able to cocoon individuals in silk and could also feed on the mental energy of people.

In the early 1990s, the creature tried to get inside the TARDIS while it was in Perivale. The ship warned Ace and the Doctor of the danger and they returned to the ship, which the creature was trying to leech of its power. Scrabbling to get inside, it became stuck between the "inside" and "outside" of the TARDIS; it had breached the dimensions of the TARDIS, including time, so that when the Doctor went to consult the TARDIS manual, it had already been eaten with a slime trail leading away into a gap in the ship's interior dimensions, even though the leech still hadn't gotten inside.

The Doctor went into the ship to deal with it while the TARDIS dematerialised. Before he could find a way to fight off the leech, the TARDIS collided with the Time Scaphe, an experimental time vessel from ancient Gallifrey. This activated the Banshee Circuits and the TARDIS reconfigured itself into a multi-dimensional city (which the Doctor called a SARDIT). The creature, now a hundred times larger and calling itself the Process, encountered the Doctor and presumably killed him in its attempt to regain the "Future" which the Doctor had "stolen."

Due to the fluidity of time within the city, there were three zones separated by mercury streams: Past, Present, and Future. The Process created insectoid guards from the different versions of the Scaphe crew in the different zones and resided in a tower where it made itself ruler of the city, using Vael, who betrayed the crew, as an enforcer in addition to the Guard Captain. It made the crew search the city for the Future in exchange for food.

Ace's presence in the city, however, disrupted the Process' timeline. An older Process addressed its younger self in an attempt to correct events as its memory of its Past did not match what was occurring in the Present. The Doctor, slowly recovering and using Architectural Configuration, trapped the older Process. The younger Process would not listen to it and even fought with its older self as it sought to create a new world to rule. It summoned the egg from which it had hatched, intending to ensure its Future and the creation of a new world by supervising its own birth. However, Vael, intending to kill the Doctor, accidentally turned the full force of his pseudo-pyrokinetic mind against the egg, incinerating it and preventing the Process and its timeline from coming into being. (PROSE: Cat's Cradle: Time's Crucible)

The damage the Process inflicted on the TARDIS included its link with the Eye of Harmony. (PROSE: Cat's Cradle: Witch Mark)

Behind the scenes
Doctor Who Magazine #183 showed Andy Lambert's idea of what the Process would look like, before Peter Elson's design was used.