A cellular automata dynamic is usually based on a one or two dimensional spatial pattern. But when this method is utilized to analyze the urban spatial dynamic, it is difficult to include important parameters, such as variation of density and the mix of land use. Although this obstacle can be overcome by using a set of continuous variables related to the cell (Semboloni, 1999), the current paper proposes a different approach based on a 3-D spatial pattern. This approach has already been used to study "game of life" in a 3-D spatial pattern (Bays, 1988). In the current situation, the rules proposed by White, Engelen and Uljee (1997) will be adapted to a 3-D spatial pattern.
When the third dimension is included, it is possible to vary density while maintaining discrete variables. A varying density produces results that are quite different from those obtained with constant density. To demonstrate these differences, the paper includes the results of the model and a comparison of clusters that occur when using 2 or 3-D spatial patterns.