Study on the Spatial Morphology of Ando Tibetan Traditional Villages in China: A Case of Traditional Villages in Huangnan Prefecture

Abstract

Traditional villages (TVs) are physical manifestations of traditional culture, and their spatial structure embodies the essence of regional culture. The spatial form of TVs in the Ando Tibetan area can be used to understand the historical evolution, turnover, and inheritance of traditional culture in the region. This study uses four typical TVs in the Huangnan Prefecture (HNP). Using the fractal theory, spatial syntax theory, GIS, and geomorphological statistical analysis, this study analyses the spatial morphology structure of TVs of the Huangnan Tibetans. Analyses are conducted from the perspectives of external morphology and internal structure. A quantitative system of spatial morphology of TVs is constructed. This study found that three out of the four sample villages in the HNP have high fractal values (>1.5046) and belong to the strongly structured agglomeration morphology regarding overall morphological characteristics. Furthermore, the public space patches exhibit a more complex spatial morphology and typical fractal characteristics. The morphological characteristics of the village boundaries in the four sample villages exhibit band-like, mass-like, and point-like characteristics. The types of belt and mass tend to point to Muhesha (MHS), JaJia (JJ), and Shuangpengxi (SPX), while Tufang (TF) does not exhibit a clear tendency. The over-spatial permeability of the village is poor, making it hard to perceive the overall space. The average depth, degree of integration, and village selection are concentrated in the central area and the primary and secondary roads. The geometrical center is the core of the village’s degree of integration. This study presents traditional Ando Tibetan villages’ complex and diverse spatial morphology, providing scientific references for their protection, development, and utilization.

1. Introduction

As a branch of urban morphology research and development, the spatial cognition of traditional village morphology is not a new topic. As early as 1841, J. G. Kohl analyzed the relationship between settlement form and topography [1]. Moreover, in 1895, A. Meitzen conducted a field study of agricultural settlements in northern Germany and classified these settlement forms [2]. However, the research in this period focused on the description of the phenomenon. After the 1960s, as computer technology developed, a combination of quantitative and qualitative methods was gradually adopted, and human behavior and psychological factors were introduced into the studies of rural settlements [3,4,5,6].

By promoting the living heritage of traditional culture, traditional villages (TVs) can contribute to rural sustainable development and the revitalization of villages [7,8]. By preserving TVs and their cultural heritage, the spatial form of TVs acts as a vessel for regional culture [9,10]. A traditional village’s spatial form is formed by its overall space, its architectural space, and its street space [10,11,12]. Spatial morphology is the premise and foundation of the protection and development planning of TVs [13]. A previous study on the morphology of TVs mainly focused on description [11], generalization, and interpretation [12,13,14]. In this qualitative method, the complex spatial laws of the village cannot be fully understood [9,14]. For researchers, revealing the essence of the spatial pattern of TVs through quantitative analysis has become an urgent problem.

In recent years, the research on village boundary patterns has emerged [15]. The boundary patterns of TVs are part of their overall patterns, reflecting the results of their adaptive growth and development [16,17,18]. They consist of the physical boundaries of the architectural parts at the edge and the virtual boundaries of the gaps between the adjacent buildings [19]. The boundary pattern of rural settlements is complex, ambiguous, and uncertain [20]. The study of village boundaries has significant implications for identifying settlements, understanding their growth patterns, and preserving and developing villages in the future [18,21]. One of the most notable studies on village boundary morphology is that of Jiang et al. [22], who used three different virtual boundary scales (100 m, 30 m, and 7 m) to create a planar closed graph of settlement boundaries. The results show that the 30 m scale is better suited to reflect the complexity of the village boundary, without being too general or too detailed. It can accurately represent the concave and convex changes in and internal spatial structure of the village boundary [23,24]. Therefore, in this study, we defined the external boundaries of TVs based on a 30 m scale.

Meanwhile, spatial syntax has been widely used as a theoretical tool to quantify space and explore the underlying laws of spatial patterns [15,25,26]. It has been extensively applied to the study of TVs [8,27,28,29]. The concept involves analyzing the spatial patterns of a city in different historical periods and summarizing the laws of spatial evolution through various structural features [10,30,31,32]. By comparing the spatial form characteristics of different cities horizontally [29,33], they analyzed similarities and differences and suggested the direction of spatial optimization [33,34,35]. Almost all studies on the spatial morphological features of villages are based on an individual village analysis, not a comparative analysis of villages or regions [18,35,36]. In addition, more studies have been conducted in North China and fewer in other regions, particularly in Northeast China and the Tibetan Plateau [18,37,38]. Studies on the predictive and adaptive strategies for village development are scarce, as is the application of evolutionary laws to village development [19,21,39].

Currently, there is a lack of multi-level quantitative research on the spatial morphology of TVs in the HNP that combines multi-level analyses from outside to inside and from whole to local [40,41]. A comprehensive quantitative system for analyzing the spatial morphology features of TVs is constructed with remote sensing and ArcGIS Pro 3.0 spatial analysis techniques, as well as the fractal theory and spatial syntax. This study has three sub-objectives, including (1) comparing the spatial morphology of TVs in the HNP from three perspectives (regional characteristics, boundary morphology, and road network structure); (2) exploring the total space, linear space, and point space of each village, and comparing the spatial morphology of the different villages; and (3) describing the common and unique features of the spatial morphology of the HNP villages to gain a comprehensive understanding of the spatial characteristics of TVs. The findings of this study could provide guidance for the protection, inheritance, development, and utilization of TVs in the HNP.

2. Materials and Methods

2.1. Study Area

The HNP is located in the southeastern part of Qinghai province in China (Figure 1), between 100°34′~102°23′ E and 34°03′~36°10′ N. It is named after its location on the south bank of the Yellow River. The region has a continental climate on the plateau and its terrain is high in the south and low in the north. It mostly comprises Tibetan villages, with a small number of Hui, Tu, and Han villagers. These settlements are all distributed in Tongren and Jianzha counties. The concentration of cultivated land in the river hinterland and the terraces surrounding the alpine mountains in the HNP have formed a rich agricultural landscape area and a unique regional culture. For this study, representative villages were selected for horizontal comparative analysis. From the 30 TVs in the HNP, we chose MHS, SPX, JJ, and TF.

2.2. Data Sources and Processing

In this study, aerial high-resolution images (AHIs) of the sample villages and planning drawings were used. The aerial high-resolution images were captured by an unmanned aerial system. An equal-scale CAD map, boundary map, and axis map of the villages were digitized using CAD 2022 and ArcMap Pro 3.0 platforms. A 2D planar closed graphic was created by connecting the endpoints of each adjacent building to form the village boundary. To enhance the accuracy of the village shape, the boundary was digitized using the 30 m scale based on Pucci’s method. The axial maps were generated using CAD 2022 software and then imported into DepthMap 1.0. The axial map was then used to extract streets and lanes in the complex village. To understand the overall texture and spatial morphology feature of TVs in the HNP, a quantitative analysis will be conducted, as shown in Figure 2.

2.3. Methods

2.3.1. Fractal Model

A fractal model is an important tool for analyzing irregular entities in nature. It reveals the growth and evolution mechanisms of urban morphology, such as spatial form, boundaries, and structure [19,30,42]. This study used the fractal model to quantify the settlement pattern of the TVs to reflect the complexity of the village public space, which can be calculated using Equation (1).

$$D={\displaystyle \frac{\left[2\lg \left(P/4\right)\right]}{logA}}$$

(1)

where D is the number of dimensions that characterize the degree of spatial fragmentation, and P and A stand for the perimeter and the area of the public space patch, respectively. According to Pu, a 1.3794 threshold value represents a weak type of structured rural settlement, a 1.5046 threshold value reflects a moderate-type settlement, and a > 1.5046 threshold represents a strong type of settlement. The fractal intensity of TVs in the HNP was represented based on this interval division method [43].

2.3.2. Shape Index

The boundary shape of each sample village was analyzed quantitatively using the shape index, S, which expresses the degree of concavity and convexity of the village, and has been widely used to study irregular boundaries, such as town boundaries, village boundaries, etc. [32,43]. S is calculated with Equation (2).

$$S={\displaystyle \frac{P}{\left(1.5\lambda -\sqrt{\lambda }+1.5\right)}}\sqrt{{\displaystyle \frac{\lambda }{A\pi }}}$$

(2)

where P and λ are the perimeter and the ratio of the length to width of the village boundary, respectively, and A is the area of the entire boundary. According to the criteria of Pu et al. (2013) [43], fingerprint clusters are defined as clusters with λ ≥ 2, while globular clusters are defined as clusters with λ ˂ 1.5, and clusters with 1.5 ≤ λ ≤ 2 are without a clear direction (

Table 1. Quantitative criteria for aspect ratios and shape index.

λ Worth	Morphological Types	S Worth	λ Worth	Segmentation by Type
λ ≥ 2	Fingerprint	S ≥ 2	λ < 1.5	Fingerprints with doughnut tendencies
			1.5 ≤ λ < 2	Indications of no clear preference
1.5 ≤ λ < 2	No clear direction		λ ≥ 2	Fingerprints with a tendency of banding
		S ≤ 2	λ < 1.5	Globular
λ < 1.5	Globular		1.5 ≤ λ < 2	Clusters with banding tendencies
			λ ≥ 2	Ribbon

).

2.4. Spatial Syntax Model and Parameter Setting

Bill Hillier [44] proposed the theory of spatial syntax to explain the relationship between the spatial layout of cities, settlements, buildings, and human society. From an intuitive perspective, space bridges the material city, economy, and society [10]. In addition to space, spatial syntax also describes economy and society [45,46]. Space serves as a bridge between the physical city economy and society from an objective standpoint. Space syntax describes space and how space economy and society interacts [41]. Li et al. 2022 [10], presented spatial form as an association between space and space. Li et al. (2023) [46] define spatial syntax as the network system of streets and the additional spaces it generates in urban–rural spaces. Spatial syntax relies on the analysis of the street network’s composition since movement patterns are determined by its structure [47]. Spatial grammar translates space into a graphic that represents it quantitatively [16,21].

(1) Intelligibility index. Gong [48] defines intelligence as the degree of correlation between local and overall variables in space and the degree to which local spatial features facilitate the construction of overall spatial system structural features. In the comprehensibility map, the horizontal and vertical axes represent the global ID and local ID, respectively. According to Nie et al., 2022 [11], each point on the map represents an axis, and the distribution of scattered points determines its comprehensibility value. The comprehensibility of the corresponding axis is higher if the scattered points are linearly distributed and relatively concentrated [19]. It facilitates a good interaction between local and global spaces when the comprehensibility is high. On the other hand, low comprehensibility makes it difficult for local spaces to perceive the whole space [49]. Comprehensibility is categorized as low when R² < 0.2, medium when 0.2 < R² < 0.4, and high when R² > 0.4, which can be calculated with Equation (3).

$$R^2={\displaystyle \frac{\sum \left(I_{\left(3\right)}-I_{\left(3\right)}^{\prime }\right)\left(I_{\left(n\right)}-I_{\left(n\right)}^{\prime }\right)}{\sum {\left(I_{\left(3\right)}-I_{\left(3\right)}^{\prime }\right)}^2\sum {\left(I_{\left(n\right)}-I_{\left(n\right)}^{\prime }\right)}^2}}$$

(3)

where $I_{\left(3\right)}$ is the local integration value at step n = 3, $I_{\left(3\right)}^{\prime }$ is the average of the 3-step integration, $I_{\left(n\right)}$ is the global integration value, and $I_{\left(n\right)}^{\prime }$ is the average of the global integration.

(2) Selectivity index. The degree of selection, also known as the degree of penetration, is the frequency of elements in a spatial system, as the shortest topological distance between two nodes [18,23]. Spatial units have the advantage of being the shortest travel path, indicating the possibility of penetrated space. The higher the degree of selection, the higher the probability that the crowd will pass through the space [45,46], which can be calculated as Equation (4).

$$C={\displaystyle \frac{lo{g}_2\left[\frac{1}{\left(n-1\right)\left(n-2\right)}{\sum }_{i=1}^n{\sum }_{j=1}^n{\sigma }_{\left(i,x,j\right)}+1\right]}{lo{g}_2\left[{\sum }_{i=1}^{n}d\left(x,i\right)+3\right]}}$$

(4)

where C is the degree of spatial selectivity of TVs, I ≠ x ≠ j, d(x, j) stands for the shortest distance from space x to i, and σ ((i, x, j)) is the shortest topological path of the TV area i from x to j, which can be calculated as Equation (5).

$${\sigma }_{\left(i,x,j\right)}\{\begin{array}{c}1, x is the shortest path from i to j;\\ {\displaystyle \frac{1}{2}}, x\ne i \ne j or x\ne i\ne j;\\ {\displaystyle \frac{1}{3}}, x=i=j;\\ 0, else.\end{array}$$

(5)

(3) Average depth index. The depth value is the shortest distance between all the spaces, where highly accessible nodes are called integrated zones and less accessible nodes discrete zones [17,30]. The mean depth (MD_i) is the sum of the topological distance of a node space i from all other nodes in the system (Equation (6)).

$$M{D}_i={\sum }_{j=1,j\ne i}^n{d}_{ij}/\left(n-1\right)$$

(6)

where $d_{ij}$ is the topology cost from the i-node space to j-node space.

(4) Integration index. This is known as the degree of integration, which refers to the level of discretization between nodes in a spatial system, including global and local integration [10]. The global degree of integration refers to the closeness of the connection between a node and all nodes in the system, and the local degree of integration refers to the closeness of the connection between a node and the nodes within a few steps of the node, which is usually used in the range of three steps and five steps [50]. We chose a local integration degree of 3 in this paper since the 3-step range corresponds closest to the human walking distance [15]. In general, when the integration degree exceeds 1, there is a large amount of aggregation in the range of 0.4 to 0.6. The ID can be calculated with Equation (7).

$$I={\displaystyle \frac{2\left(D_v-1\right)}{n-2}}$$

(7)

where n is the total number of axes or nodes in the traditional village space, $D_v$ stands for the average depth, and $D_v$ can be calculated with Equation (8).

$$D_v={\displaystyle \frac{1}{n-1}}{\sum }_{i=1}^n{d}_i{N}_d$$

(8)

where $d_i$ is the minimum number of connections from one axis to any other axis in the network of axes, and $N_d$ is the number of connected axes.

3. Results

3.1. Qualitative Analysis of the Spatial Morphology of TVs in the HNP

(1)

Overall spatial pattern of TVs

The geomorphological environment and natural ecological conditions of the HNP provide basic living conditions for the villages, but they also constrain the development of village space. Plateaus, slopes, terraces, and mountain valleys are the most common places to find TVs. The HNP has four types of TVs, including belt, block, group, and scatter. The internal morphology of each type of village differs clearly.

(i)

Best Layout

The results show that the village layout of MHS follows a stem-and-branch structure, which is typical of belt-shaped layout villages (Figure 3). MHS is situated in MHS Gully on the west bank of Longwu River in a shallow mountainous river valley area characterized by interlocking mountains and gullies. The village’s layout cleverly utilizes the mountain topography, arranged along sloping terraces, backed by mountains, and facing the water. This fully combines with the surrounding natural ecological environment to form a living environment suitable for the traditional way of life. The result is a comfortable and highly distinctive humanistic landscape of the village. The topography surrounding the village is undulating, gradually ascending on both sides of the Longwu River, displaying a terrain pattern of a river valley, followed by Chuanshui, and a shallow mountain.

(ii)

Block Layout

SPX is a block layout village (Figure 3). It is situated on a hillside surrounded by Arokang Mountain, Beishan Mountain, and Danxia Mountain. The Langjia River meanders through the middle of the village, providing water sources and fertile land. The village’s unique layout is characterized by its large size, covering an area of approximately one square kilometer. It is situated in the middle of sloping land, with open surroundings. To defend against foreign enemies, the village is surrounded by mountains at its back, the Langga River and SPX in front, and two deep ditches on either side, creating a terrain that is easy to defend and difficult to attack.

(iii)

Group Layout

The layout of JJ is shown in Figure 3. The village is surrounded on three sides by mountains, and the terrain is relatively flat. The Sangzhuo River flows from the village to the east, and the Luowo Forest lies to the southeast of the village. The village layout is relatively compact, with higher elevations in the south and lower in the north. The village as a whole has a rectangular shape and a high and attractive terrain. Additionally, the Audubon Mountain Range is located close to the Yellow River.

(iv)

Scattered Layout

TF has a scattered layout, as shown in Figure 3. The village is primarily located along the Yangtze River and the southern side of the mountain terrace, with buildings scattered throughout the hillside. The village has a small scale and a scattered spatial form, with a ‘zigzag’ road connecting the scattered buildings. The buildings are mostly located near the sloping cultivated land, and the basic village is not located on the ‘zigzag’ road. The village’s buildings are mostly situated near the sloping cultivated land, with little to no level ground available. The spatial arrangement of the village follows a sequence of buildings, courtyards, and settlements occupied by the villagers.

(2)

Linear space of TVs

A lane is not only the primary public space of the village but also the backbone of the village’s spatial form. The street space in TVs in the HNP is divided into three levels. The primary road is the main point of contact and traffic organization for each functional area. It has a width of 4–6 m and serves as the main location for communication and activities between neighbors. Typically, trees and buildings surround both sides of the road. The secondary road’s second level is the alleyway between residential clusters, with a width of approximately 3–4 m. The space within the alleyway is rich and has a certain sense of rhythm, providing a gathering place for daily communication among villagers. The third level consists of inter-house roads, which are usually 1–2 m wide. These roads have a complex and narrow form, low traversability, and are manifested as a closed alleyway in the village with a relatively dense architectural layout. In contrast, a goat’s lane with no enclosure on any side is in the village with a relatively sparse architectural layout. The formation of the street pattern is closely related to natural factors, such as the village’s topography and water system. The layout of the streets can be divided into four types: fishbone, central, checkerboard, and zigzag.

(i)

Fishbone-type streets and alleys

Fishbone-type streets and alleys are commonly found in villages with a belt-shaped layout pattern. Their ‘skeleton’ typically consists of 1–2 main streets, with main streets and branch alleys crossing longitudinally, creating clear axial connections and distinct levels of streets and alleys. The layout usually adopts a T-shaped or cross character. The T shape or cross shape is commonly used to connect streets, improving the traffic flow and reducing visual obstacles for pedestrians. In this type of street, branch and side alleys run parallel to each other and are not connected. Residents’ daily activities are often directly connected to the main street. MHS has a typical fishbone-type street layout. The village’s structure consists of a main street that runs along the MHS ditch due to the river flowing through the village. The village’s branch alleys and main street are mostly perpendicular to each other, and the residents’ residences are mostly constructed along the contour of the layers (Figure 4a).

(ii)

Central-type streets and alleys

Our results show that, in TVs with a central-type street layout, the streets and lanes extend outward from the core functional buildings or squares, creating a village centered around the streets and lanes. The village center is an important location for villagers to engage in activities, social exchange, and is the hub of their daily lives. The street pattern in SPX exhibits significant cohesive characteristics, with streets expanding from the center to the periphery and showing a tendency to extend and disperse outward from the inside. The village takes the main street in the center as the core and expands outward, and its street spatial morphology has typical core-type characteristics (Figure 4b).

(iii)

Checkerboard-type streets and lanes

In TVs of the checkerboard-type, the streets and lanes are typically arranged in a checkerboard pattern, allowing for easy transportation throughout the area. The chosen sites are primarily situated in open and flat areas, such as flatlands or mountain basins, and are less affected by the topography compared to mountain villages. The street layout of flatland villages is more relaxed and informal, with more evident natural growth characteristics, and usually lacks prominent main streets, similar to the hutongs in Beijing. JJ has two main streets that connect the three clusters, each of which has a checkerboard shape. Among the checkerboard-style streets, those with high accessibility are typically in the form of a cross or T shape or five-way intersections. This design can facilitate pedestrian communication and encourage gathering at connecting nodes (Figure 4c).

(iv)

Zigzag-type streets

Most of the zigzag streets and alleys create scattered villages. This type of village always has streets and lanes following the contour lines in a zigzag pattern. The linear structure is significant, and the plan layout gradually changes to follow the trend of the mountain. The space layout climbs up step by step, following the difference in heights of the terraces. TF has two main streets that connect the three clusters. Each cluster is linearly distributed along the contour (Figure 4d).

(3)

Point-like space of TVs

TVs have a spatial form that includes a planar overall layout environment, linear roads and alleys, and point-like characteristics. Public activity spaces in these villages are flexible and serve as places for villagers to engage in daily activities and to communicate with the outside world. These spaces not only express the lifestyle of villagers but also reflect their sense of identity and belonging to traditional village spaces. Public spaces typically rely on other elements, such as water, trees, buildings, streets, and alleys, which serve as both components and carriers of their interconnection and interaction. Increasing public activity spaces has enhanced the spatial form of TVs (Figure 5).

3.2. Quantitative Analysis of the External Spatial Morphology of TVs in the HNP

3.2.1. Overall Spatial Morphology of TVs

Based on Figure 6 and

Table 2. Fractal dimension values of HNP villages.

Village Name	Area of Public Space A (m2)	Perimeter of Public Space P (m)	Sub Dimensional Value D	Histomorphic Type
MHS	119,976.904	27,385.158	1.5103	Strongly Structured
SPX	113,988.59	26,209.8285	1.5094	Strongly Structured
JJ	165,099.494	37,975.2952	1.5246	Strongly Structured
TF	82,497.0098	14,375.7026	1.4464	Medium Structured

, it is evident that the fractal dimension values of the four sample villages are relatively high, greater than 1.5046, and their grouping morphology belongs to the strongly structured settlement type. The high-fractal-dimension villages exhibit developed and advanced street and courtyard systems, clear and varied spatial directionality, and a strong sense of space. The external space of TVs in the HNP displays complex morphological characteristics. This is because TVs typically develop in response to changes in the topography and geomorphology, resulting in planar boundaries that are often zigzagging and complex, with typical fractal characteristics.

3.2.2. The Boundary Morphology of TVs

The results show that the aspect ratios (λ) of MHS, SPX, JJ, and TF are 2.206, 1.036, 1.162, and 1.691, and the shape indexes (S) are 6.942, 1.306, 8.397, and 4.905, respectively (Figure 7 and

Table 3. External morphological characteristics of TVs.

Name of TV	Area of Public Space A (m2)	Perimeter of Public Space P (m)	Sub-Dimensional Value D	Histomorphic Type
MHS	119,976.904	27,385.158	1.5103	Strongly structured
SPX	113,988.590	26,209.829	1.5094	Strongly structured
JJ	165,099.494	37,975.295	1.5246	Strongly structured
TF	82,497.009	14,375.703	1.4464	Medium structured colonies

). The external boundary morphology characteristics of TVs indicate that the subdivision of the boundary morphology in the HNP is dominated by pointing. This includes band tendency pointing in the MHS, mass tendency pointing in JJ and SPX, and no clear tendency pointing in TF. The villages are arranged according to the topography, spreading out along the contour lines. Gently sloping areas are used for agricultural cultivation due to the constraints of the topography and geomorphology.

3.3. Quantitative Analysis of the Internal Spatial Morphology of TVs in the HNP

3.3.1. Overall Spatial Pattern Analysis

The slopes of the fitted regression line for the four villages, in terms of global and local integration, are small. Additionally, their R² values fall within the range of 0.1–0.3, and their comprehensibility values are in the lower category. The comprehensibility values for MHS, JJ, SPX, and TF Villages are 0.16, 0.12, 0.24, and 0.022, respectively. These values suggest that the local space of these villages does not provide a good representation of the overall space. This also reflects the TVs’ poor overall spatial permeability in the HNP (Figure 8 and

Table 4. Comprehensibility of TVs.

Name	Integration [HH] R3	Integration [HH]	Scatter Plot Correlation Coefficient	Comprehensibility
MHS	0.956	0.214	2.167	0.167
SPX	0.957	0.384	1.956	0.246
JJ	0.959	0.275	1.833	0.122
TF	0.907	0.142	1.669	0.022

).

3.3.2. Quantitative Analysis of Street Morphology

(1)

Selectivity

Figure 9 and

Table 5. Statistics for village selectivity, average depth, and degree of integration.

Name of TV		Choice		Average Depth		Degree of Integration
	Minimum	Average	Maximum	Mean Depth	Mean Depth R3	Integration [HH] (Average)	Integration [HH] R3 (Average)
MHS	0	0.153	1.068	31.608	2.108	0.214	0.956
SPX	0	0.109	1.094	16.341	2.128	0.384	0.957
JJ	0	0.12	1.265	24.319	2.135	0.275	0.959
TF	0	0.271	1.066	42.552	2.087	0.142	0.907

illustrate that MHS, SPX, and TF have chosen to build their villages in a mountainous area. The center of these villages has a flat topography, forming a distinct main street. This street has good selectivity and permeability. The village’s central area has the highest connectivity value in the entire village, resulting in better connectivity and permeability than the surrounding areas. As a result, the axial color transitions from warm to cold as one moves from the central area to the periphery. JJ was chosen as the site for a plateau village due to its less restrictive topography during the village layout process. The buildings in JJ are denser than those in mountainous villages due to the influence of the concept of living in clans, resulting in a more varied spatial form for the streets and lanes. The buildings in clustered living areas are denser than those in mountain villages, resulting in a greater number of axes and a higher density of streets and lanes, as shown in the axial map. The warmest color on the map, red, represents streets and lanes with the highest spatial connectivity value and best permeability. The streets and lanes with the highest permeability are primarily the main lanes that form the village’s backbone and serve as the village’s center.

(2)

Mean depth

Figure 10 and Table 5 show that the average depth is minimized in MHS, SPX, JJ, and TF villages. This is mainly concentrated in the leaf-vein space formed by the main traffic road and its surrounding roads in the village. This type of street space has strong structural stability, which enables it to quickly accommodate the high population flow in the village and avoid traffic congestion. Therefore, in the village, the main roads connect to various branch roads, facilitating the flow of people from areas with high depth values to those with low depth values and high accessibility. Externally, the village’s main roads connect to roads leading to nearby towns and cities, directing the flow of people from the village outward to achieve population diversion.

(3)

Integration degree

Figure 11 and Table 5 illustrate the global and R3 local integration degrees of MHS, SPX, JJ, and TF villages. The street spaces of these four TVs exhibit a gradual decrease in integration degree from the village center to the edge. The data suggest that the village’s central area experiences high levels of both pedestrian and vehicular traffic, making it the distribution hub for both modes of transportation. Additionally, this area is the most densely populated part of the village. Furthermore, the decreasing level of integration from the village center to the outskirts also suggests that traffic and pedestrian flow follow a similar pattern. In summary, the degree of selection, average depth, and integration of TVs in the HNP are concentrated in the main and secondary roads and village center area.

3.3.3. Quantitative Analysis of Public Space

The axis value of the ‘integration core’ represents the gathering capacity at the village’s topological core [14]. This linkage connects the ‘integration core’ to the public activity space in the traditional village area [43]. Therefore, studying the village’s main public space is transformed into studying the village’s integration core [41]. The integration core refers to accumulating integration values for all axes and sorting all elements based on their integration values in ascending order [30]. The integration values of the selected elements are then added until the total value reaches 10%, and the resulting collection of elements is known as the ‘integration core’.

The integration core axes of MHS, SPX, JJ, and TF villages are located at the topological center of the entire axial map (Figure 11). The visual regularity of the integration core axes suggests that there is a pattern in the self-organized development of TVs in the HNP. TVs do not grow randomly, but rather in a self-organized manner.

The intersection of Wangjiasi’s and Manikang’s streets (Figure 12) is the global integration core of the MHS. It has the warmest axis color and the highest integration degree of 0.318 (Table 3), indicating that it is the most accessible area in the village. Meanwhile, based on the core map of the R3 local integration degree in the MHS, the highest value is still concentrated in the Manikang, with a value of 2.252 (

Table 6. Statistics of global integration (I) and R3 local integration (I) in villages.

Name of TVs	Global Integration (I)			R3 Local Integration (I)
	Average	Minimum	Maximum	Average	Minimum	Maximum
MHS	0.214	0.103	0.318	0.956	0.333	2.252
SPX	0.384	0.199	0.614	0.957	0.333	2.601
JJ	0.275	0.316	0.417	0.959	0.333	2.901
TF	0.142	0.086	0.186	0.907	0.333	1.905

). This indicates that spatial convenience has the highest value.

The integration core of SPX is located in the parking lot, health center, and Manikang area (Figure 11). This area has the warmest axis color and the highest integration degree of 0.614 (Table 6), indicating its high accessibility. The local integration degree core map also shows the highest value near the white tower, with a value of 2.601 (Table 6), indicating high accessibility in this area.

The core of JJ village’s global integration degree is located at the intersection of the main street (Figure 11). This area has the warmest axis color and the highest integration degree of 0.417 (Table 6) due to the presence of important public buildings, such as the White Pagoda and temple. This suggests that the integration degree core of the village is also the center of public activity exchange and people flow. According to the R3 local integration map of JJ, the location of the local integration core coincides with the global location. This suggests that the structural layout of JJ has remained relatively stable during its development.

The main street area (Figure 11) is the global integration core of TF, with the warmest axial color and the highest integration degree of 0.186 (Table 6). Despite the absence of significant public buildings in this area, it serves as the core road connecting the lower half of the village clusters, indicating its high accessibility. According to the local integration degree core map, the highest value was found in the area of the temple and the village committee, with a value of 1.905 (Table 6). This suggests a connection between the integration degree core and the distribution of important public spaces.

4. Discussion

4.1. The Comparative Value of the External Spatial Form of the TVs

The spatial form of TVs always showed different temporal and spatial characteristics [8]. In this research, the results show that the majority of TVs in the HNP have a fractal dimension value greater than 1.5046 and belong to the fortified cluster grouping morphology type, by comparing the fractal dimension and shape index cross-sectionally. Previous studies have shown that different TVs have different clustering patterns [15,23,51]. As depicted in Figure 2, Figure 3 and Figure 4, the spatial form and layout of the TVs exhibit a self-similarity characteristic, consistent with the previous studies conducted by Chu et al. (2022) [19] and Zhu et al. (2023) [18]. Moreover, this discovery is consistent with the fractal characteristics of architectural complexes, which present similar conclusions for ethnic minority architectural complexes in other regions of China, except for the northwest [23,33,52]. Our results also reveal that a finger-like tendency is the most common subdivision trend of village boundary morphologies. Therefore, when planning and designing villages in the future, it is important to follow the topographic features, remodel the original spatial structure and texture, learn from the existing cultural lineage, and apply the inclusive elements of various cultures and historical periods to create unique and diverse village spaces.

4.2. The Comparative Value of the Internal Spatial Form of TVs

The results reveal that the TVs in the HNP have low overall spatial permeability. However, the center area has a strong aggregation force, which allows it to influence the surrounding area without isolating it. Like TVs in other regions, the central area of a village often has a strong gathering power [8,10,20]. The horizontal comparison of road space shows that the accessibility of road spaces in some villages in the HNP needs to be improved, and the integration of road spaces in villages is essential. The integration of road space not only improves the integration of roads in the village core area, but also provides material conversion space for the whole road network [10,18,21]. The accessibility of the village core area is improved by the horizontal and vertical intersection of the main streets, and the complementary relationship between the core area and the discrete area of the street space is established, which provides a clearer direction for the reorganization and integration of the street space [12,21]. It improves the connection between the main street and the traditional buildings and spatial elements within the village, opens up the paths between the houses that are blocked or separated by jungles or buildings, and maintains the accessibility to the internal transport in the village [13,14,25]. In addition, the village system is strengthened to achieve a better effect of dispersing the flow of people.

4.3. The Comparative Value of Public Spaces in TVs

Through comparative analyses of public spaces of TVs in the HNP, we found that the majority of public space in the village is concentrated along the main roads or at the center of the village. An analysis of the overall and local integration cores of TVs in the HNP reveals that they are primarily located in the center of the village. Villages with varying spatial forms share similarities in the layout and organization of their public spaces. The results show that the behavior of people in the space is closely related to the spatial form [11,20,24], and the area with a higher degree of integration has a stronger ability to gather people [53], and it is also easier to gather people to make it a public activity space [14,15]. Moreover, the space with a higher degree of integration can attract the building of important public buildings, such as ancestral halls and temples, in the village [41,54]. In addition to the role of gathering people, the core space also has the function of housing commercial buildings and public buildings because of its unique form of significance and transportation advantages. The core space is not only an important public activity space in the village, but also the heart of the village [8,18,25]. When planning and designing TVs in the future, the first thing to consider is the planning and design of the core space, the relationship between the core space and its surroundings, and the control of the core space of TVs over the surrounding space.

4.4. Limitations of This Study

It should be noted that the TVs are composed of physical buildings and people. As a part of the overall project, this study is based on a quantitative analysis, interpreting the spatial form of TVs in Huangnan from the perspective of spatial form, aiming to analyze the spatial form characteristics of Ando Tibetan villages. Nevertheless, this study did not analyze the formation of and historical and cultural associations of the villages, which are the contents of the subsequent research. In addition, the subsequent research will use satellite data with a high spatial resolution. As a result, further research on TVs needs to focus on genetic genealogy, intra-village space, and architectural structure characteristics.

5. Conclusions

Through the use of the fractal theory and spatial syntax model, this study quantitatively analyzes the spatial morphology of MHS, SPX, JJ, and TF villages in the HNP. The spatial morphology characteristics of TVs in the HNP were the most evident from the external (boundary, morphology, and fractal dimensions) and internal (overall space, linear space, and point space) perspectives.

Firstly, three out of the four sample villages display relatively high-fractal-dimension values, greater than 1.5046, and are classified as strongly structured settlements from the perspective of the overall morphological characteristics of the TVs. Patches of public space in the TVs have a complex morphology with typical fractal characteristics.

Secondly, the boundary morphology of the four sample villages mainly exhibits belt and mass types with no clear pointing. After further subdivisions, all of them can be classified as finger-like, including a belt tendency in MHS, a mass tendency in JJ, mass tendency pointing in SPX, and no clear tendency in TF.

Thirdly, regarding the village’s internal spatial form, poor spatial permeability makes it difficult to perceive the overall space within the local area. Generally, the degree of selection, average depth, and degree of integration are concentrated along the secondary roads and in the center of the village, with the degree of integration concentrated in its geometric center.

However, this study mainly focuses on the spatial morphology of four TVs in the HNP from a quantitative perspective. It should be noted that the data collected from a limited number of villages may not be fully representative of all types of TVs. This study is limited to analyzing the spatial morphology, including the internal and external spatial forms, without considering the influencing factors. Subsequent research will explore the socio-economic aspects and clan culture of TVs in the HNP. This study aims to understand how villages are formed historically and culturally.