I've spent some time pondering various methods of constructing
a physical Turing Machine off and on for a couple years now,
ever since I was introduced to them through mjd's Perl Quiz of
the Week (http://perl.plover.com/qotw/r/024). However, all of my
designs were deliberately non-electronic in nature. Personally,
I find electromagnets, motors, and relays to all be
aesthetically acceptable in this pursuit, but using a
microprocessor to build a physical Turing Machine just somehow
strikes me as... unappealing.
I suspect "mechanical" would be a better word. Microprocessors are mysterious black[1] boxen, whereas relays, etc, are macro-sized and can be made at home by hand.
Interesting fact about TMs - while their computibility is equivalent to computers, the Big-O time for common algorithms is (possibly much) slower. Many O(n) tasks on computers with RAM are O(n^2) on a TM. The only commonality with computers in terms of time complexity is the Polynomial vs. Non-polynomial boundary.
The same is true for any model of computation.
Despite this equivalence, it's orders of magnitude harder to program a TM than the ugliest assembly language you've ever seen. This is one architecture that desperately needs a compiler :)