For some classes of tilings on a regular grid in two dimensions, it is possible to define a height function associating an integer to the vertices of the grid. For instance, draw a chessboard, fix a node A 0 with height 0, then for any node there is a path from A 0 to it. On this path define the height of each node A n + 1 (i.e. corners of the squares) to be the height of the previous node A n plus one if the square on the right of the path from A n to A n + 1 is black, and minus one otherwise.