I beg to differ... http://en.wikipedia.org/wiki/Turing_machine THAT is a true computer, if you want to start bandying definitions about. (It doesn't even have to be mechanical) Whether one could build a Turing Machine in DF, I don't know. Any ideas?
If you're able to implement an infinite tape, I'll help with the rest.
However it will be a hell of work to load a program (but then again it can be hard coded).
I'm afraid I'm not even sure if it's possible to implement a
finite tape, except for one possibility: tiles full/empty of water?
i.e.:
1
#######
≈¢≈≈¢≈≈
#######
2
#######
X¢_X¢_X
#######
3
#######
+++++++
#######
¢=hatch, X=floodgate, #=rock/wall, +=floor, _=pressure plate, ≈=water source
In each case, the pressure plate tells us whether it's a 0 or a 1, and the two hatches allow us to 'write 0' and 'write 1' respectively. (1 is >4/7, 0 is <3/7) Cells can be combined in a vertical direction to allow for more than 1-bit. So you can have any finite number of symbols.
The main problem is that you can't move the 'tape'. So what is needed is an 'airlock' arrangement of floodgates (with pumps) so that you can transfer EVERY symbol one cell to the left or right. This is left as an exercise for the reader! :p
Ok, duno, your mission (should you choose to accept it) is to build a Turing Machine to do... erm, something.
(Adding two binary numbers would be a good one to start on)
For testing out Tables of Behaviour, you could download my Finite State Machine emulator at
www.justtotheleftofvenus.tk (click 'downloads', then scroll down). The download contains a few ToBs and one of them is binary addition.