I.M. Foreman's Travelling Show

I.M. Foreman's One-Species Nongenetically Engineered Travelling Show was a complex space-time event. It was similar to, although not like, a TARDIS.

Piloting and Travel
I.M. Foreman programmed the show's course by meditating and communicating telepathically with it.

It was a space-time vessel but it had no extra-dimensional connections. It moved through space and time by retroactively building a site and disguising itself before/during/as it moved there. This process took years.

It was not designed for instantaneous (or even fast) travel, unlike a TARDIS. Unlike most TARDISes, the show could (and did) travel back into the Dark Time. (EDA: Interference - Book One, Interference - Book Two)

Effects the show has on space time
A byproduct of this was that it sometimes knocked dents in space-time, luring other space-time travellers to the site. It brought Faction Paradox, the Remote and the Third Doctor and Sarah Jane Smith to the planet Dust. It is thought that it may have brought the First Doctor and Susan to Earth, 76 Totter's Lane, 1963.