Considering the organic curved walls (and the angles of the straight ones) I might have gone with a hex grid instead of a square grid.
That would have been my first choice too. But D&D 4.0 loves its stupid squares. Wolfgang included a square grid in his original (and markedly excellent!) drawings, so I followed his lead.
We don't stop playing because we grow old; we grow old because we stop playing.
-George Bernard Shaw