Compassion

Compassion was a remembrance of a Human who joined the Remote. She traveled with the Doctor, during which time she evolved into a TARDIS.

Biography
Compassion was originally Laura Tobin, a woman residing on the original colony of the planet Anathema. She, like all the colony residents, either was or became sterile. They therefore reproduced using Remembrance Tanks, and over the millennia that the ship that Anathema was based upon took to get to Earth, all the colonists were "remembered" using biomass inside the remembrance tanks. Compassion is the result of this process.

Compassion was a member of the Remote, an offshoot of Faction Paradox. Following her encounter with the Doctor on Earth she chose to travel with him and Fitz (whom she, as Laura Tobin once knew). She also knew Kode, who was the remembered version of Fitz). (EDA: Interference - Book Two)

As Compassion came from a media/signal orientated culture she always wore an ear piece (or receiver). In an attempt to protect her from any 'harmful' signals she might encounter during their travels, the Doctor interfaced her receiver with the TARDIS systems. This interface had unforeseen results, warping her biodata along Block Transfer Computations, culminating in her 'birth' as a sentient TARDIS.

With his own TARDIS having been apparently destroyed in a dimensional rift, and the Time Lords now seeking Compassion to use her as breeding stock to create their own sentient TARDISes, the Doctor and Fitz were forced to use Compassion to go on the run. (EDA: The Shadows of Avalon)

Eventually, however, they were drawn to Gallifrey by the presence of the Edifice just before the Faction Paradox attack and Gallifrey's eventual destruction. After the destruction of Gallifrey, Compassion took the Doctor and the TARDIS- now totally drained of all its energy- to 19th century Earth, subsequently taking Fitz Kreiner to 2001 so that he could meet the Doctor after the TARDIS had repaired itself, and left to explore the Universe with a Gallifreyan technician, Nivet. (EDA: The Ancestor Cell, Escape Velocity).

In an alternate timeline, Compassion was contacted by the embodiment of human technology, they made a deal that resulted in the creation of the City of the Saved. The City existed just beyond the end of the current universe and the creation of the next. (FP: Of the City of the Saved...)

Appearance
Compassion had coppery-red hair and freckles however once she became a TARDIS, her appearance was more a matter of her whims at the time, her freckles were described as being "far too symmetrical to be natural". (FP: Warring States)

Abilities
Since she became a TARDIS, Compassion's senses extended into other dimensions. She could generate a force field around her and could deliver painful electric shocks if attacked. She once accidentally overloaded the brains of four humans by attempting to contact them via her telepathic circuits, temporarily disorientating them. (EDA: The Space Age)

As a TARDIS, Compassion's internal dimensions were mapped to her psychology, full of twisted forests, and dark echoing spaces that she forced the Doctor and Fitz to inhabit. Her console was a black version of the one in the TARDIS she was familiar with but with a crystal spire in the center of it, the controls constantly moved based upon how helpful Compassion felt towards the Doctor at any one time. Compassion used her newly found psychic abilities to influence Fitz's dreams, he admitted to suffering from nightmares when they travelled together, until Fitz and Compassion reached an understanding. (EDA: The Fall of Yquatine)

Behind the scenes

 * Compassion is one of the only ongoing characters from Doctor Who to also appear in the spin-off book series, Faction Paradox.
 * Physically, a fictionalised version of Compassion evidently resembled the actress Nicole Kidman. (EDA: Interference - Book Two). However, she was described as being "gerbil-faced and chubby". This description fluctuated throughout the series with Fitz thinking she's rather plain but with enough "curves" to make her appealing.