I spent an hour trying to implement a 2d Turing Machine.
http://www.puzzlescript.net/play.html?p=6863139
So far, it is unsatisfactory because I do not know how to emulate an infinite playfield, and I cannot figure out how to put a delay between applications of the rules (so you cannot see it running).
That said, with a little tinkering, a Turing machine is possible.