The Doctor's poem

The Doctor's deepest essence took the form of an infinite fractal poem, much like chaos equations which corresponded to the dimensions of an individual.

The verse originated from the One-Eyed One's instruction of the First Doctor to connect to the Other. The Doctor fasted for three days and nights (evoking the threefold death) and made supplication to higher powers, proceeding to write a verse which he didn't fully understand. The poem came from deep within his dreams. The Doctor then met with the One-Eyed One at a sarlain and spoke the poetry. Later, the poem would appear inside the Doctor's mind as a Sarlain with fractal petals.

The Doctor would not understand the poem's full significance until later, when he found out all of what he was. As part of the Hermit's game, the Seventh Doctor used his experience with chaos poetry to transfer the Timewyrm's inner poem into Ishtar Hutchings. (PROSE:  Revelation)

The Matrix used fractal technology to preserve Time Lord minds. The Doctor once placed his fractalling essence into a Matrix-like biodata pod to become John Smith. (PROSE: Human Nature)

Behind the scenes

 * The parallels between the Doctor's poem and the Timewyrm's poem in  Revelation suggest that the connection between the Doctor and the Other may be similar to the relation between the Timewyrm and Ishtar Hutchings. The Other is presented as a monstrous creature within a brief flashback in the novel, similar to the monstrous Timewyrm which becomes trapped as a poem inside an infant's mind and eventually, in Happy Endings, allows for a heroic reinvention of the monster's ways.