Quad tesseral addressing is an alternative method of defining points in two-dimensional Euclidean space which has some significant advantages over the Cartesian approach. An important feature of Tesseral addressing is the ability to map every part of the spatial domain onto a one-dimensional sequence, and when stored with attributes in a database, each address can act as a single key to data. Tesseral addressing is hierarchical, the place system being used to indicate hierarchical depth, and each full tesseral address associated with a tile is unique. Furthermore, tesseral addressing can be extended to three or four dimensions using additional symbols (Diaz 1986, Grunbaum, 1987), and there are arithmetics which support tesseral addressing. for example, addition is tile translation.
Tesseral addresses are generated by quartering the positive quadrant of Cartesian space to yield parent tiles labeled as shown in Figure 1, which illustrates one explanation of quad tesseral addressing. We can continue this process of hierarchical division, with new tesseral addresses generated by always appending to the right of the parent tesseral address, until some required depth is reached.
Figure 1: Basic Tesseral addressing