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Differences between 2 and 3-D

In order to consider the effects of three-dimensional parameters, $F_{k,q}$ has been varied by multiplying it by a coefficient $f$ ranging 0.5-2.5. If this coefficient is higher than 2.5, only cells with $k=1$ are built and, in essence, the resulting cluster will be two-dimensional. If the coefficient is lower than 0.5, cells with $k=10$ are built.

To adequately examine this problem, the coefficient $f$, from 0.5 to 2.5., has been varied during a set of one hundred experiments. The resulting clusters have been evaluated by using three indicators:

  1. number of built cells;
  2. standard deviation of the location of cells around its centroid;
  3. concentration of activities calculated by using the average number of the cells having the same activity of the central cell and located in the eight bordering cells.

The results of these experiments, in relation to the established indicators, are shown in figure 4. By increasing the coefficient $f$, it is possible to increase both the number of built cells and the standard deviation. In such conditions, the activities tend to be more and more dispersed unless industrial activity, because its related cost ($F_{k,q}$) increases sensibly when $k>1$ (see table 1). On the other hand, the concentration of activities decreases with the increasing of the coefficient.

Figure: The variation of indicator Y axis, as a function of the variation of coefficient $f$ Y axis. Graph A, built cells; graph B, standard deviation; graph C, average number of cells having the same activity of the central cell and located in the eight bordering cell.
\begin{figure}
\begin{center}
\par\resizebox {8cm}{!}{\includegraphics*{grafvarx.eps}}\end{center}\begin{footnotesize}
\end{footnotesize}\end{figure}

Clearly, important differences exist in the resulting clusters. These differences depend on the variation of density that are obtained by using the third dimension. Thus, it can be stated that the third-dimension modifies crucial characteristics of the clusters.

         

Further developments

The model can be upgraded by introducing a further cost characteristic - urban code - in the equation 1. By introducing this element, it is possible to to establish an interaction between the user and the model, and to experiment with a possible evolution path of the cluster in relation to urban plans.

         


next up previous contents
Next: Conclusions Up: The dynamic of an Previous: Results of experiments   Contents
ferdinando semboloni
2000-11-06