Height Functions
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 nodes of the grid. For instance, draw a chessboard, fix a node with height 0, then for any node there is a path from to it. On this path define the height of each node (i.e. corners of the squares) to be the height of the previous node plus one if the square on the right of the path from to is black, and minus one otherwise.
More details can be found in Kenyon & Okounkov (2005).
Read more about this topic: Domino Tiling
Famous quotes containing the words height and/or functions:
“It’s the height of folly to want to be the only wise one.”
—François, Duc De La Rochefoucauld (1613–1680)
“When Western people train the mind, the focus is generally on the left hemisphere of the cortex, which is the portion of the brain that is concerned with words and numbers. We enhance the logical, bounded, linear functions of the mind. In the East, exercises of this sort are for the purpose of getting in tune with the unconscious—to get rid of boundaries, not to create them.”
—Edward T. Hall (b. 1914)