Any cellular automata has a corresponding set of Wang tiles. Wang tiles can be physically instantiated, for example in funny shaped plastic blocks. Conway's game of life is a cellular automata. Therefore, it is possible to construct a set of cheap plastic blocks that play Conway's Game of Life.

Coming soon to a toy store near you.

Imagine it, you lay out some interesting pattern, like an R-pentomino, then start layering up iterations one on top of the other. The blocks are shaped so that the only way you can build it up is to follow the rules of the cellular automata. A three year old could play this game.

Another cute thing: you don't have to do it a layer at a time. You can do part of a layer, then a smaller part of the next layer on top of that, and so on. You can build *light cones*. You can physically feel how information moves through the structure. You can perform a relativistic transformation and start building the thing in a diagonal plane. It's a hands on lesson in special relativity.

Here's a more mundane example, binary addition:

#0 #0 #1 #1 #1 0# 0# 0# 1# 1# -# - -# #-# #- #0 #1 #1 #0 #1 ... etc ...

Just line up the appropriate blocks. The sides are shaped so to transmit whether there was a carry or not.

Decimal addition done this way would need 200 types of blocks, but it's probably possible to split it down into less blocks. Have numbers with protruding sticks of appropriate lengths, and the sticks from two inputs have to fit an appropriate hole in an output (possibly with a carry prod in there as well).

Multiplication is harder, but possible. Wang tiles can implement Turing machines (simple proof: Wang tiles can implement Conway's Game of Life, the Game of Life can implement a Turing machine), so they can implement anything. The question is whether it can be done reasonably simply... may require some ingenuity.

Wouldn't it be the coolest teaching aid ever?