TARDIS coral

TARDIS coral was the organic substance of which the Doctor's TARDIS was composed. The vessels were grown, not built. (TV: The Impossible Planet) The interior of the War Doctor, (TV: The Day of the Doctor) Ninth Doctor, (TV: Rose) Tenth Doctor, (TV: The Christmas Invasion) and Eleventh Doctor's TARDIS had a coral-like appearance; there were several pillars that seemed more like trees or vines than structural support, and a coral-like substance around portions of the structure. (TV: The Eleventh Hour)

However, when briefly merged with his tenth incarnation's TARDIS, the Doctor's fifth incarnation noted that the coral structures could be part of the current TARDIS' "desktop theme." He also suggested that it was worse than the "leopard skin" appearance. (TV: Time Crash)

The tertiary console room of the Seventh Doctor's TARDIS had a similar organic rock-like appearance. (PROSE: Nightshade)

TARDIS coral began growing around the tribophysical waveform macro-kinetic extrapolator after it was integrated with the TARDIS long enough. (TV: The Runaway Bride)

The Black Archive contained a piece of TARDIS coral. (TV: The Day of the Doctor)

Behind the scenes
Cwrel TARDIS
 * Part of the Bad Wolf Bay scene at the end of Journey's End was removed. In it, the Tenth Doctor gave the Meta-Crisis Tenth Doctor and Rose a piece of TARDIS coral, and Donna told them how to increase the rate of growth by a factor of 59. (This scene was removed due to complicating Rose's departure, but was included in the DVD box set. Russell T Davies says it can still be considered canon despite its omission.)
 * According to the deleted scene a piece of TARDIS coral, which appeared to be roughly the size of a mouse, would take thousands of years to grow a TARDIS.
 * The 28 October 2006 Radio Times, in an image of the Torchwood Three headquarters, identified a piece of large coral on Captain Jack Harkness's desk as the beginnings of a TARDIS. John Barrowman confirmed that "Jack's growing a TARDIS... It's probably been there for 30 years. I suppose in 500 years he'll be able to begin the carving process."