*3.2. Changes in Interrelationships among Local Spaces*

We further explore the changes in the specific relationship of 'temple-residence-garden' in the process of spatio–temporal changes in the temple heritage to summarize some

highlighted findings. A quantitative estimate of the MD values is calculated by Formula (1) given in Section 2.2. in the DepthMap software. In 1962, the MD values of the West Garden (5.25–17.67), Pingshan Hall (5.26–8.95), and the Main Hall (4.75–6.26) were lower than the average value of the global MD. The global influence effect of the West Garden is not significant, while the MD value of the West Garden fluctuates, which may indicate that variations in accessibility are noticeable in hierarchical orders [31]. The MD values of both knee level and eye level in 1973 were lower than those observed in the 1962 model, but the hierarchical relationship of the topological space system did not occur in qualitative variations.

For the knee-level layer in 2022, the MD value of the Main Hall (4.20–5.51) approximates the MD of the global spatial system (4.23–5.42). The accessibility of the Main Hall is decreasing year by year; otherwise, the MD value of Pingshan Hall (4.93–7.78) is still remarkably higher than that of the Main Hall. The MD value of the West Garden (4.33–16.84) is higher than that of the global MD, indicating that the hierarchical order of accessibility in the West Garden is weakened. At eye level, the accessibility of the West Garden and Pingshan Hall is also approximate, and the accessibility of religious space and architecture (i.e., the Main Hall) is higher than that of these areas dominated by semi-natural landscapes (i.e., the West Garden and Pingshan Hall).

#### *3.3. Changes in Spatial Connectivity*

The 'connectivity' index in the VGA model can reflect visitors' recognition of the space. By the analysis of the eye-level connectivity in 1962 (Figure 6), values of the mean con. of Mahavira Hall (502.59), Pingshan Hall (228.56), and Guling Hall are calculated, whereas the mean con. of The West Garden (3570.83) is much higher than the global average value. As for the knee-level connectivity, the mean con. values of the West Garden (247.08) were less different from those of other architectures in 1962. In 2022, both knee-level and eye-level connectivity of the new-built East District were noticeably higher than elsewhere; however, the relationship between existing spaces has not changed. Compared with the changes in spatial connectivity among the three periods, the perception of the spaces surrounding the architecture and garden was very close before the redesign and reconstruction of the East District, while the visual perception of the architecture is relatively closed. The visual space permeability of the West Garden is the highest, with visions of higher openness.

#### *3.4. Changes in Spatial Intelligibility*

After the redesign and construction of the East District since the 2000s, the form and configuration of the global space have observed to undergone certain changes, which may affect the activities of visitors. In the space syntax theory, 'intelligibility' is a parameter for the evaluation of difficulties the visitor will suffer in understanding geographical positions in the global space, and the complexity of spaces can be calculated based on the MD value of the local and global spaces [32]. Results attained in the former steps are used for regressive calculation of the intelligibility, with connectivity as the x-variable and NAIN as the y-variable (Table 2). By a Python program developed with the package matplotlib for quantitative statistics, the goodness-of-fit (R2) parameter is calculated. R2 has a value range of [0–1]. The closer R<sup>2</sup> to 1, the higher the intelligibility, and vice versa. It is seen that the global 'intelligibility' values are consistently low, which indicates that the probability of getting lost in the space is higher for visitors, which can be explained by its unique 'temple–residence–garden' spatial structure.

**Table 2.** Values of intelligibility in different periods.


Quantitative estimation of the MD values in the VGA model is calculated by Formula (1) in the DepthMap software (Table 3). The higher the MD value, the higher the average number of turns it would take visitors to pass through the space; in other words, the space is relatively more complex. We observed that the visual-spatial structure of the temple heritage in different periods keeps relatively simple. On average, at least two turns of the visitor's movement can enable them to take a global visual perception of almost all spaces in the study site. The reason for changes in visitors' paths is explained as follows. The structure of accessible space distribution is found to be of high complexity, requiring visitors to make at least six turns to pass through the heritage space in both 1962 and 1973. However, after the reconstruction of the East District, the scale of the Daming Temple increased. There are at least four turns needed for visitors to pass through the temple in 2022. making it easier for visitors to perceive the global structure of the space, which is likely to be effective for the revitalization of the temple as well as the development of tourism [33]. Simultaneously, with the expansion of the East District, the scale of the temple has been increased, making it more efficient and encouraging visitors to perceive the global topological structure of attractive spaces. Therefore, it has a certain positive significance for the heritage revitalization and tourism development of the temple.

**Table 3.** Values of global MD in different periods.

