Examples of logic gates using non-standard models
Picture hanging can realize any monotonone boolean function. 

I.e., you can hang a picture using two pins so that it falls IFF both pins are removed. This is trivial to achieve, and realizes an AND gate.

However, you can also hang it so that it falls IFF either pin is removed. Implementing this OR gate is not so trivial at first.

See the linked paper for nice pictures.