Bad Wolf

"I am the Bad Wolf. I create myself."

- Rose Tyler possessed by the Bad Wolf

After looking into the Heart of the TARDIS, the Time Vortex itself filled Rose Tyler, who then temporarily became the Bad Wolf entity. She scattered the two words throughout time as a sign to herself that she was linked to The Doctor, creating a looped ontological paradox. The Bad Wolf entity appears several times throughout the Doctor Who series afterwards.

Abilities
The Bad Wolf entity was incredibly powerful and could destroy an entire Dalek fleet by dividing all the atoms of the ships and the Daleks themselves. It also had the ability to resurrect already dead beings and make them immortal. It could also form a force field to defend itself from Dalek weapons and spread the words "Bad Wolf" to various points in time and space so that Rose and the Doctor would encounter the words which eventually led Rose to becoming the Bad Wolf in the first place. The Bad Wolf stated, "I create myself", which was a paradox.

Rose Tyler as "Bad Wolf"
Newly empowered, Rose Tyler piloted the TARDIS back to the Ninth Doctor. A nimbus of light surrounded her and shone through her eyes. Rose's natural London accent vanished. She also possessed the destructive and creative powers of a goddess, enabling her to destroy an entire Dalek fleet and have an enormous influence over time and space. While possessed of these gifts, the entity set out to spread the Bad Wolf memethrough many worlds and times. In this way, the Ninth Doctor and Rose's past selves would eventually follow the clues that would enable them to defeat the Daleks, creating an ontological paradox in the process. The Bad Wolf destroyed the Dalek fleet and all the Daleks on Satellite Five, including the Dalek Emperor. She also altered reality to bring back Captain Jack Harkness from the dead (also granting him immortality).

Jack later discovered he could apparently no longer die by any means, and it took him nearly a century and a half of subjective time before he finally learned that she was responsible. As the instigator of Jack's immortality, Bad Wolf was therefore indirectly responsible for the event known as Miracle Day on Earth.

Rose was unable to hold the power permanently without burning up, and the Doctor restored Rose's human self by absorbing the Vortex energy into his own body, a process that would prove destructive to his cellular structure and so prompt the Doctor's next regeneration. Rose subsequently lost most of her memory of her time as the Bad Wolf, saying that the knowledge had been locked like it was "forbidden", and that trying to repeat it could cause the universe to blow up.

The Moment as "Bad Wolf"
When the consciousness of the Moment took form, it selected the form of Rose Tyler as the Bad Wolf entity. When the War Doctor commented that he could kiss her for giving him a way out of the dual-genocide he was prepared to commit, she remarked, "That's definitely gonna happen." The Tenth Doctor was visibly surprised to hear his past self mention the Bad Wolf, as she was only visible and audible to the War Doctor. Due to the timelines rearranging themselves, the War Doctor (and his immediate successor) retained no memory of Bad Wolf.