Well, of course he didn't! :) Doctor Who is a fictional (albeit awesome) television show - however, a recent discovery of a previously lost Van Gogh painting does provide a striking image of what looks like the TARDIS!
The Van Gogh Museum identified a long-lost Vincent Van Gogh painting (pictured-right) that spent years in a Norwegian attic because it was thought not to be authentic. It is the first full-size canvas by the Dutch master discovered since 1928.
"Sunset at Montmajour" depicts a dry landscape of oak trees, bushes and sky, painted with Van Gogh's familiar thick brush strokes. It can be dated to the exact day it was painted because Vincent described it in a letter to his brother, Theo, and said he painted it the previous day - 4th July 1888. He said the painting was done "on a stony heath where small twisted oaks grow."
A brief glance to the upper-left side of the painting shows what appears to be a blue box complete with light box, but on closer inspection is actually a house with a chimney.
The great thing about art, however, is that it is down to the individual to decipher its meaning - and we see a TARDIS! :)
[Source: The Van Gogh Museum]