Here's one that uses an electric motor to power it - but no electronics:
http://hackaday.com/2011/03/25/mechanical-turing-machine-can...
Comments on Reddit suggest this is also a fully-mechanical Lego Turing Machine (including electric motor), but I haven't watched the full video to make sure there's no Mindstorms CPU kit:
It looks quite small? Given that it is an universal computer, I guess that is quite a feat.
That's mine. It's a physical implementation of a 5-symbol, 2-state Turing machine which was shown to be universal by Wolfram. If it were perfectly reliable (it isn't) and had an infinite tape (it doesn't) then it would be universal. Going to the extremes of low symbols and states makes it extremely inefficient in terms of code density, if you can apply that term to a Turing machine. The shortest program I've been able to write for it, doing unary subtraction of 3 and 2 would take about 60 hours and need a tape three times longer than I have.
Thanks for the correction - I doubted if such a relatively simple device could be universal (see comment below), but it's fascinating to learn that it is! :-)
Still, I am not sure how big other physical computers are (do any even exist)? I think it's cool :-)
Is there a compiler for it? :-)
It calculates a cellular automata called Rule 110 (http://en.wikipedia.org/wiki/Rule_110) which is very difficult to code for. I've seen a paper which shows a method for coding any Turing machine into rule 110, but most of it is beyond my mathematical ability at the moment. So far as I know nothing resembling a normal compiler exists for it.
It's actually much simpler to make a mechanical implementation of rule 110 directly, but Turing machines are more widely recognised.
As I said there, I'm always deeply disappointed (less deeply as time goes by, I'm coming to expect it) when something like this in Lego is actually just a peripheral for a program running in silicon somewhere.
I no longer have any of my Lego, but I remember building most of a completely mechanical Turing Machine way back in the early 1970s. So satisfying seeing it work purely mechanically, and I'm sure someone with more creativity and skill than I had, or indeed have, could do it.
Please?