Representability of a finite relation algebra A is determined by playing a certain two player game G(A) over `atomic A-networks'. It can be shown that the second player in this game has a winning strategy if and only if A is representable.
Let T be a finite set of square tiles, where each edge of each tile has a colour. Suppose T includes a special tile whose four edges are all the same colour, a colour not used by any other tile. The tiling problem we use is this: is it the case that for each tile t in T there is a tiling of the plane Z x Z (Z being the integers) in which edge colours of adjacent tiles match and with t placed at (0,0)? It is not hard to show that this problem is undecidable.
From an instance of this tiling problem T we construct a finite relation algebra RA(T) and show that the second player has a winning strategy in G(RA(T)) if and only if T is a yes-instance. This reduces the tiling problem to the representation problem and proves the latter's undecidability.