# Analysis of Urban Spatial Accessibility of Museums within the Scope of Seoul
## 2 Space Syntax and Research Method  
### Space Syntax  
Space syntax is a methodology for analyzing spatial layouts and configurations conceived by [PERSON] and [PERSON] [38]. Space syntax generally uses convex and axial maps to analyze a given space [39; 40]. Segment maps allow us to represent space by improving axial maps by introducing the concept of angle and distance based on conventional axial maps [41]. Here, convex space defines the unit of space with the closed spatial area, which can be seen as a polygon with all interior angles not exceeding 180\({}^{\circ}\). As opposed to the convex space, when humans recognize a space, the axial map can express it with lines connecting the visual maximum points of the connected spaces, and the convex space and the axial map define the number of spaces that are passed from a specific space to another as spatial depth [16; 42]. In other words, when moving from a space A to the nearby D connected to A, the spatial depth between A and D is 1, and the graph that arranges the connection of several spaces by spatial depth expressing the connecting relation is called a J-Graph (Figure 1). Calculated from such a concept of spatial depth is the Total Spatial Depth (TSD) [16]. Furthermore, in the design of the convex space as shown in Figure 2, all interior angles of space A do not exceed 180\({}^{\circ}\). Thus, the convex can be designed by referring to the space, but in space B, the interior angles do exceed 180\({}^{\circ}\). Hence, space B should be segmented into B-1 and B-2 and regarded as two spaces in the process of analyzing spatial structure. The axial map also conforms to similar design criteria, and if a space is shown in a bent form, the axial lines should be separated so that each axial line can recognize the space at once. Generally, the analysis based on an axial map stresses the dynamic aspects and is often used in analyzing external spaces, whereas the convex space is more useful in reflecting static spatial characteristics and is used mainly in analyzing internal spaces [16; 43]. In space syntax (Table 1), integration indicators are generally classified into global and local integration. These indicators have proven relevant to space use patterns and social, cultural, economic, and political phenomena [44]. In addition, the intelligibility index was used because of the need to recognize urban structure to analyze the accessibility of museums in Seoul, which is calculated using Equations (1)-(3) below. Table 2 shows the definitions of the symbols in the equations [29]. Local integration allows us to track the accessibility and density of use of a specified space by considering up to three spatial depths adjacent to the space [45]. Intelligibility can be explained by the R2 correlation coefficient calculated by the correlation between the global and local integration [46]. The closer the value is to 1, the more systematic and recognizable the space [47]. \[MD=\frac{TSD_{i}=\sum_{s=1}^{m}S\times K_{s}}{K-1} \tag{1}\]  
\[D_{n}=\frac{2\big{\{}n\big{[}log_{2}\big{(}\frac{n+2}{3}\big{)}-1\big{]}+1 \big{\}}}{(n-1)(n-2)} \tag{2}\]  
\[I_{(i)}=\frac{D_{n}}{\frac{2}{n-2}\big{(}\frac{\sum_{s=1}^{n}d(i,k)}{n-1}-1 \big{)}} \tag{3}\]  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{2}{c}{**Indicator**} & \multicolumn{2}{c}{**Interpretation**} \\ \hline \multirow{3}{*}{Integration} & \multirow{3}{*}{Global integration} & A region with high integration means that movement is relatively easy among the overall regions to be analyzed. \\ \cline{2-3}  & & Local integration & Calculated by considering only a few space depths from each space, generally three space depths. \\ \hline \multirow{3}{*}{Intelligibility} & \multirow{3}{*}{The systematicity of the space is evaluated using an index derived from the correlation between the global and local integration.}