In the positive quadrant, the numbering of tesseral addresses follows an ordering known as the Morton sequence (Morton 1966) illustrated below in Figure 2. The Morton number of a tile is its index in this sequence, and is related to the tesseral address at the level of its binary representation (Diaz 1986).
The importance of the Morton sequence is that we are able to linearize space - imagine space to be a packed ribbon which can be unraveled - and this in turn enables us to apply one-dimensional reasoning techniques. Moreover, the linearization extends to three, four and higher dimensions, applying the same technique and avoiding the combinatorial explosion of relations (see section 4).
