## 4 Experimental Application of the Model
### Spatial Meta-Pattern Description and Identification  
For the experiment, a basic spatial meta-pattern and its values were described using the instances of UML classes and explanatory attributes of the general SP and meta-pattern model from Section 3, as presented in Table 3.  
Figure 10: Spatial structure of Star8 (Visuality Graph, DepthmapX). Figure 9: Idealized spatial entity Star8 (AutoCAD drawing, Autodesk AutoCAD). The structures of basic geometrical meta-pattern values were drawn and analyzed with the aim to select working VGA measures and to test if they can be used for the identification of real SP. VGA measures (listed in Table 4) were selected using these rules: (1) evaluating them by the meaning: what the measure defines or shows on the map; (2) taking those measures that can hypothetically define the shape of the visual field, e.g., the geometrical form of the selected spatial area which are used for SP identification (class Form); (3) testing measures in the VGA spatial meta-pattern description and identification experiment (described in this section); and, finally; (4) evaluating the values of the measures and deciding which measures can be used to define the physical and the functional form of spatial meta-pattern value and which of them can be normalized for later use. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**Instance\_Name: Measure**} \\ \hline
**Name** & **Formula** & **Component** & **Description** \\ \hline ‘k’ & ‘MAP VARIABLE’ & NULL & ‘number of cells in system’ \\ \hline ‘d\({}_{\text{xy}}\)’ & ‘MAP VARIABLE’ & NULL & ‘distance from cell x to y’ \\ \hline ‘v’; ‘N’ & ‘MAP VARIABLE’ & NULL & ‘cell of the grid’; ‘neighborhood’ \\ \hline ‘e’; ‘E’ & ‘MAP VARIABLE’ & NULL & ‘pair of mutually visible cells’; ‘edge’ \\ \hline ‘g’; ‘c’ & ‘MAP VARIABLE’ & NULL & ‘generating point’; ‘center of gravity of polygon’ \\ \hline ‘A’; ‘TI’ & ‘MAP VARIABLE’ & NULL & ‘isovist area’; ‘isovist perimeter’ \\ \hline ‘TD’ & ‘\(\sum_{y}MIN\,d_{xy}\)’ & ‘d\({}_{\text{xy}}\)’ & ‘total depth of system’ \\ \hline ‘Visual Mean Depth & ‘\(\frac{TD}{(k-1)}\)’ & ‘TD, k’ & ‘average number of visual steps to reach every other cell in system’ \\ \hline ‘RA’ & ‘\(\frac{2\times k\text{MD}}{k-2}\)’ & ‘MD, k’ & ‘relative asymmetry’ \\ \hline ‘D’ & \(\frac{2(k(\log_{2}(k+2)/3-1))}{(k-1)(k-2)}\)’ & ‘k’ & ‘idealized diamond system’ \\ \hline ‘RRA’ & ‘\(\frac{RA}{D}\)’ & ‘RA, D’ & real relative asymmetry \\ \hline ‘Point First Moment’ & ‘\(\sum_{v_{i}\in\,N\,(v_{i})}d\big{(}v_{i},v_{j}\big{)}\)’ & ‘v, N, d’ & ‘isovist potentialto spin around’ \\ \hline ‘Through Vision’ & (found in DepthmapX) & ‘e, E’ & ‘amount of visibility lines that pass through location’ \\ \hline \hline \end{tabular}
\end{table} 
Table 4: VGA measures for basic meta-pattern values identification (measures are taken from Reference [9]). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Instance\_Name:** & **Instance\_Name: PatternValue** & **Type:** & **Configuration:** \\
**Pattern** & & **PAAttribute** & **PAAttribute** \\ \hline Name & Name & Image & Value & Value \\ \hline  & ‘Line’ & & ‘Meta-pattern’ & NULL \\  & ‘Star4’ & & ‘Meta-pattern’ & NULL \\ ‘Basic Meta-pattern’ & & & ‘Meta-pattern’ & NULL \\  & ‘Sector’ & & ‘Meta-pattern’ & NULL \\  & ‘Labirinth’ & & ‘Meta-pattern’ & NULL \\  & ‘Circle’ & & ‘Meta-pattern’ & NULL \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Description of basic spatial meta-pattern. For the basic meta-pattern identification, Space Syntax method was defined by the class Method, and the VGA measures used were defined by the class Measure, as presented in Table 5. In addition, the instances of the classes Form and Structure with corresponding instances of the class FormMeasure were described. For the structure with the attribute Structure.Type = \"Visuality Graph', the VGA measures from Table 4 were used to identify the values of basic spatial meta-pattern values.