Research on the co-occurrence feature mining of the Qing Dynasty embroidery patterns based on temporal multilayer networks

Abstract

Embroidery is an important cultural heritage that traces the origins of Chinese civilization over five thousand years. Embroidery patterns function as cultural genes characterized by relative stability, inheritance, and variability. Excavating their intrinsic co-occurrence relationships and features can reveal underlying cultural transmission and evolution. By constructing a temporal multilayer network of embroidery pattern co-occurrence, we analyze intra-layer and inter-layer topological properties, identify key pattern nodes, and employ a link clustering algorithm for community detection. The key findings are as follows: (1) The pattern co-occurrence network exhibits scale-free and small-world properties. (2) The pattern co-occurrence network possesses a community structure with divisible and re-combinable functions. (3) The ‘Fu-Shou’ (fortune-longevity) patterns are the most representative cultural memory symbols of the Qing Dynasty. (4) The fluctuations in network topological properties and pattern node strength centrality are inherently linked to the transitions in social culture and political power.

Introduction

Chinese traditional culture is broad and profound. Patterns, as an important part of Chinese traditional culture, have always run through the entire process of China’s historical development, rich in content, and have changed with the continuous development of social, economic, political, and cultural aspects. Chinese traditional patterns reflect the customs, habits, and values of people in specific periods, possessing a strong sense of life and a unique artistic style, and are the crystallization of thousands of years of wisdom of the Chinese nation. Pattern generation consists of three parts: composition, pattern elements, and color, among which pattern elements are the foundation and key to pattern generation¹. Designers select the required pattern elements based on the composition, but the selection of patterns is entirely dependent on the designer. If designers do not understand the deep meaning of pattern elements and mechanically combine them, the resulting design will not inherit a certain style and lack the revelation of cultural connotation. Excavating the intrinsic associations and co-occurrence features between patterns can, on the one hand, provide cultural and creative designers with rich cultural knowledge to assist in cultural and creative design, ultimately promoting cultural prosperity and development; on the other hand, it reflects the changes in social culture and political power, providing valuable information for understanding social history and cultural development.

Currently, the interpretation of traditional patterns is mostly carried out by domain experts who organize data and present it through traditional media, which is a labor-intensive task with limited visualization and expressiveness². The use of computers and related technologies to study patterns can reveal their intrinsic associations, explore their development rules, and provide visual analysis, offering decision-making suggestions for designers. To date, there are few studies on knowledge discovery in patterns using computers and related technologies. In existing research, Lu et al.² have constructed a traditional pattern semantic network consisting of 1500 pattern nodes and 13,600 relationships, unearthing the spatiotemporal evolution rules of traditional patterns and predicting the evolutionary process of traditional patterns. Liang et al.³ have used the Song Dynasty stone carvings in Luxian County as a carrier to excavate the knowledge system of Song Dynasty stone carving patterns and constructed a knowledge graph of Song Dynasty stone carving patterns. These studies provide us with certain insights.

Complex networks are network structures composed of a large number of nodes and complex interconnections between these nodes. They are widely applied in many real-world systems, such as the Internet⁴, power and transportation networks⁵, biological networks⁶, economic and financial networks⁷, social networks⁸, scientific research and educational networks⁹, and more. Complex networks possess numerous features, such as the small-world effect¹⁰, scale-free property¹¹, community structure¹², etc. These characteristics make complex networks play an important role in knowledge discovery, such as revealing the internal structure of network systems, understanding the potential characteristics of complex networks, and discovering hidden laws of networks. However, traditional static networks cannot fully and accurately describe the diverse systems of the real world. In the case of patterns in cultural relics, the relationships between patterns are non-static and evolve continuously over time, which can be effectively represented by temporal networks¹³.

In embroidery artifacts, different patterns co-occur according to certain cultural connotations and esthetic rules, forming specific pattern combination motifs, such as the “Seawater and River Cliff Pattern(海水江崖纹)”, “Sanduo Pattern(三多纹)”, “Five Bats Circling a Chinese Character Stylized Longevity Pattern(五福捧寿纹)” and other stylized, explicitly named pattern combinations, as well as the “Hundreds of children and lake stones(百子和湖石头)” and other unnamed, implicit pattern combinations¹⁴. To more accurately express the associative relationships between patterns, a temporal multilayer network of embroidery pattern co-occurrences has been constructed. By employing the method of Temporal Multilayer Network Analysis, the cultural connotations and co-occurrence features of the patterns are explored and analyzed, providing inspiration and decision-making suggestions for designers. Integrating traditional culture into modern design, this approach ensures that design works are both contemporary and rich in cultural depth. At the same time, it offers a new perspective and method for cultural knowledge mining, serving as a reference for research in related fields.

As a unique symbol of cultural memory, patterns carry profound historical heritage, national emotions, hierarchical concepts, religious beliefs, and esthetic tastes. The study of patterns is of inestimable value for understanding the evolution of human civilization. Throughout the long history of pattern research, early scholars mostly relied on traditional methods such as literature review, field investigation, comparative research, and image analysis. Their research directions mainly focused on pattern identification and classification, analysis of pattern manufacturing techniques, exploration of the relationship between pattern styles and the esthetic concepts of the times, interpretation of the cultural connotations of patterns, and analysis of the origin and evolution of patterns. Among them, Dongliang Xu et al. collected clothing patterns for the Raojia ethnic group in Southeast Guizhou through field investigation. They classified the patterns in Raojia ethnic group’s clothing into six categories and 25 sub-categories according to the themes of the patterns, used the interview method to interpret the cultural connotations of the patterns, and finally named them¹⁵. Miao Su et al. conducted an in-depth analysis of the weaving techniques of the Li ethnic group in the Qi dialect area of Hainan Province from the perspective of weaving technology. Based on the principle of pattern formation, they discovered the compositional characteristics of the patterns¹⁶. Jun Liu analyzed the differences in the styles of clothing patterns in the Tang and Song dynasties, thus reflecting the differences in the esthetic concepts of the two dynasties behind them¹⁷. Based on the analysis of the meaning content and scope of silk patterns, Hui Zhou found that the meanings of ancient Chinese silk patterns were mainly expressed in three forms: symbolism, homophony, and metaphor¹⁸. Shuxia Li et al., based on physical sample pictures and relevant historical materials, took the Sihe Ruyi cloud pattern on fabrics and portraits of the Ming Dynasty as the research object, sorted out and summarized its development context, and analyzed and revealed the evolution process from four aspects: unit shape, basic organizational form, color expression, and fabric technology¹⁹. These studies have laid the foundation for further in-depth exploration of patterns and provided important clues and perspectives.

With the development of modern information technology, digital technology has greatly facilitated the research, display, and cultural dissemination of patterns. Through a review of relevant literature, current digital research on patterns mainly involves aspects such as pattern classification, pattern extraction, vectorization, generation, and restoration. Classifying patterns is a fundamental task in cultural heritage protection. Identifying the characteristics and values of different patterns can provide a basis for protecting, restoring, and inheriting cultural heritage, ensuring the proper preservation and continuation of these precious cultural legacies. Yanyu Li et al. developed a machine-learning model based on the YOLOv4 architecture to identify the inlaid patterns of traditional Chinese porcelain in the Lingnan region²⁰. Xiuzhi Qi et al. optimized the initial parameters of a convolutional neural network through the differential evolution algorithm and then classified the decorative patterns on Shang and Zhou bronzeware²¹. Pattern extraction, which involves extracting pattern elements from existing object images, is the foundation of digital pattern research. Qi Zheng et al. proposed a method for extracting Yuan blue and white porcelain patterns based on multi-scale Retinex and histogram multi-peak threshold segmentation. This method addresses the issues of image texture reflection and loss caused by the “crystallization” on the surface of Yuan blue and white ceramics²². Jingzhe Zhang achieved the intelligent extraction of decorative patterns of ethnic minorities in Northeast China based on the GABRS algorithm²³. Vector-format images have advantages such as being independent of device resolution, maintaining integrity when scaled, being editable by users, and having a small file storage size. Research on the vectorization of decorative patterns can provide strong support for the digitization and reuse of cultural resources. Based on an analysis of the types and characteristics of traditional Chinese paper-cutting patterns, Muzi Sun proposed a new pattern extraction and vectorization algorithm²⁴. Based on an analysis of the pattern characteristics of the three major branches and two regions of the Dai ethnic group in Yunnan, Tingyu Fang designed software suitable for the automatic vectorization of Dai brocade using Matlab²⁵. Currently, research related to computer-aided pattern design can be mainly categorized into research on traditional methods and research on generative AI methods. Traditional methods include image generation methods based on mathematical models such as fractal geometry principles²⁶, shape grammar theory²⁷, and geometric similarity features²⁸. Generative AI pattern design methods include GAN²⁹, Stable Diffusion³⁰, etc. Due to long-term burial underground or exposure to the natural environment, cultural relics are affected by natural factors such as temperature and humidity changes, microbial influence, and sunlight exposure. Their materials decay and the surface patterns fade, age, and become soiled^31,32,33. With the development of artificial intelligence technology, digital restoration of patterns has become a promising approach, greatly reducing the risk of secondary damage to cultural relics that may be caused by traditional restoration methods³⁴. Although digital technology can present the external forms of patterns, relying solely on digital methods makes it difficult to deeply explore the profound meanings and cultural connotations behind the patterns, and it is also hard to reveal the complex relationships among patterns.

Over the past two decades, driven by the growing demand for big data analysis, significant progress has been made in data mining and knowledge discovery using complex networks, which can describe various types of systems in nature and society. Complex network methods have also been applied to the research of interdisciplinary topics such as culture and art. Xiaojian Liu et al. constructed a color network of traditional patterns, developed a color extraction and recommendation system based on the CorelDRAW platform, and achieved the automatic generation of product color-matching schemes³⁵. Mei Yang proposed a method for constructing a color network model of Dunhuang murals and its application in product design, assisting designers in color-culture decoding design activities³⁶. Hongrun Wu conducted a comprehensive analysis of traditional and modern Minnan nursery rhymes through complex networks, revealing the heterogeneity of terms in the traditional and modern Minnan nursery rhyme networks and identifying five main image characteristics presented in Minnan nursery rhymes³⁷. In natural and social systems, various elements continuously evolve over time. Therefore, characterizing dynamical processes in a time-dependent complex system from observed time series of just one or more variables is a fundamental problem of significant importance in many fields ranging from physics and chemistry to economy and social science³⁸. That is, characterizing the dynamic processes in a transient complex system from the observed time series of only one or more variables is a very important basic problem in many fields, from physics and chemistry to economics and social sciences. Li et al. have demonstrated that temporal networks can, compared to their static counterparts, reach controllability faster, demand orders of magnitude less control energy, and have control trajectories, that are considerably more compact than those characterizing static networks³⁹. Complex network analysis of time series has been widely used to solve challenging problems in different research fields, including social networks⁴⁰, economic networks⁴¹, biological networks⁴², power and transportation networks⁴³, etc.

Regarding the patterns on cultural relics, the relationships among patterns are non-static and constantly develop and change over time. This characteristic makes it difficult for traditional static analysis methods to comprehensively and accurately reveal the hidden cultural connotations and historical evolution behind them. However, the temporal network analysis method in complex networks provides a new opportunity to solve this problem. By constructing a multi-layer temporal network of pattern co-occurrences, we can dynamically trace the inheritance and variation relationships among patterns in different historical periods, as well as how these changes are influenced by social and cultural factors of the time. This has reference significance for relevant cultural heritage research.

Methods

Research data

During the Qing Dynasty, the development of patterns reached its peak. It not only continued the classic patterns of the previous dynasties but also fully reflected the cultural characteristics of this period. The embroidery patterns of the Qing Dynasty comprehensively utilized various factors such as politics, economy, literature, history, customs, religion, and folklore as the basis for composition, reflecting the contemporary religious beliefs, imperial clan system, folk culture, and artistic esthetics. Moreover, a relatively rich collection of Qing Dynasty embroidery has been preserved to this day. Therefore, the patterns of Qing Dynasty embroidery are chosen as the research subject. The data content includes the image, name, and age of each artifact, totaling 11,054 pieces (refer Fig. 1).

Fig. 1: Stone blue satin embroidered seawater river cliffs flower butterfly pattern women’s jacket with double-breasted front and rolled sleeves.

This embroidery image comes from the Museum of Ethnic Costumes of Beijing Institute of Fashion Technology.

Technical process

This study includes three key steps: the identification of embroidery pattern nodes, the construction of pattern co-occurrence networks, and the analysis of the topological properties of pattern co-occurrence networks. Firstly, by integrating expert knowledge, academic literature, professional books, and domain terminology, Chinese Cultural Gene Tag Semantic Model (PatternNet) is constructed. New word detection algorithms are used to automatically identify new domain terms and update PatternNet. The identification of pattern nodes is carried out using a combination of dictionary-based automatic recognition and image-assisted manual verification. Secondly, based on the co-occurrence relationships of patterns in each piece of embroidery, the Qing Dynasty embroidery pattern co-occurrence network and the Qing Dynasty embroidery pattern temporal multilayer co-occurrence network are constructed. Thirdly, statistics on the topological properties within and between layers of the temporal multilayer network are conducted, key pattern nodes are identified, and pattern communities are discovered using the link communities algorithm. Finally, based on the conclusions drawn from the above steps, an analysis and summary are conducted to obtain the associative relationships and features of embroidery patterns. The specific technical process is shown in Fig. 2.

Fig. 2

Technical process for mining the co-occurrence relationships and features of embroidery patterns based on multilayer temporal networks.

The topological properties of temporal multilayer networks can quantitatively describe the fundamental features of complex systems. The study and analysis of the pattern co-occurrence temporal network are approached from four aspects: the definition of the temporal multilayer network, the statistical analysis of basic features, the identification of key pattern nodes, and the exploration of pattern community structures.

Definition and representation of temporal multilayer networks with embroidery pattern co-occurrence

Currently, the main temporal network models can be roughly divided into three categories: time aggregated graphs, snapshots-based temporal network models, and temporal network models with directed flows⁴⁴. Based on whether the relationships between snapshots are depicted, snapshot-based temporal network models can be categorized into two types: time-window graph models and multilayer graph temporal network models. Among these, in the multilayer graph temporal network model, only the same nodes are connected between layers, and the connection coefficient can be a fixed constant or based on the similarity of nodes between snapshots. The temporal network of pattern co-occurrence is a data structure model that describes the interaction of pattern nodes and their co-occurrence relationships (edges) in a time-sequenced manner. The pattern nodes and their co-occurrence relationships (edges) change over time and are ordered chronologically. In the temporal co-occurrence multilayer network, there are only connections between the pattern entity nodes within each time layer, and there are no connections between different pattern entity nodes. Based on this characteristic, the temporal co-occurrence multilayer network is defined according to the multilayer graph temporal network model, with the connection coefficients between layers being a fixed constant. The pattern co-occurrence multilayer temporal network is $G=\left({G}_{0}^{T},{\mathcal{E}}\right)$, illustrated in Fig. 3, and its mathematical definition is as follows⁴⁵:

$$\left\{\begin{array}{l}G=({G}_{0}^{T},{\boldsymbol{\varepsilon }})\\ {G}_{0}^{T}=\left\{{G}_{0},{G}_{1},...,{G}_{T}\right\}\\ {G}_{t}=({V}_{t},{E}_{t})\\ {V}_{t}=\left\{{\nu }_{t1},{\nu }_{t2},{\nu }_{t3},...,{\nu }_{tN}\right\}\\ {E}_{t}=\left\{{e}_{t1},{e}_{t2},{e}_{t3},...,{e}_{tm}\right\}\\ \varepsilon =\left\{{\omega }_{\alpha \beta }\subseteq {V}_{\alpha }\times {V}_{\beta };\alpha ,\beta =1,2,...,T,(\alpha \ne \beta )\right\}\end{array}\right.$$

(1)

Fig. 3

Temporal network model based on multilayer graphs.

The pattern co-occurrence multilayer temporal network can be represented by the static pattern co-occurrence network G_t at each moment and the inter-layer edges ${\mathcal{E}}$. G_t represents the set of changes in the pattern co-occurrence network over any time interval $\left[\begin{array}{c}0,n\end{array}\right](0\le t\le n)$, and the time interval [0, n] can be divided into T time windows, which further divides the pattern co-occurrence network ${G}_{0}^{T}$ into T discrete and ordered time layers G₀, G₁,...,G_T. V_t is the set of pattern nodes in the co-occurrence network at time t, N is the total number of pattern nodes in ${G}_{0}^{T}$; E_t is the set of edges in the co-occurrence network at time t, m is the number of edges in G_t. If the same pattern exists in time layers α and β, it is represented by an edge, which connects the pattern nodes in the time layers α and β.

Embroidery pattern temporal multilayer network statistical features

This study first explores the basic features of the pattern co-occurrence temporal multilayer network from a statistical perspective. The differences in these features signify differences in the internal structures of the network, which in turn lead to differences in the system’s functionality. Analyses are conducted on the basic statistical features within and between layers of the temporal multilayer network of pattern co-occurrences.

The descriptive statistical indicators for each layer of the network include the number of nodes, the number of edges, the average degree, graph density, network diameter, average clustering coefficient, and average path length. Since the pattern co-occurrence temporal multilayer network is an undirected network, the following explanations are based on the characteristics of undirected networks.

Number of nodes: the number of non-isolated pattern nodes in each layer, reflecting the scale of the pattern co-occurrence network.

Number of edges: the number of edges in each layer.

Average degree: the average value of the degree of all pattern nodes in the network. The degree of a pattern node is defined as the number of edges directly connected to that node. By analyzing the degree distribution or cumulative degree distribution of the network, one can determine whether the pattern co-occurrence network follows a power-law distribution.

Graph density: the ratio of the actual number of edges to the maximum possible number of edges in the network, used to measure the closeness of connections between patterns.

Network diameter: the maximum distance between any two pattern nodes in the network. The distance between two pattern nodes is defined as the number of edges in the shortest path connecting the two nodes.

Average clustering coefficient: the average of the clustering coefficients for all pattern nodes in the network. The clustering coefficient C_i of a pattern node i with degree k_i in the network is defined as:

$$Ci=\frac{{E}_{i}}{({k}_{i}({k}_{i}-1))/2}=\frac{2{E}_{i}}{({k}_{i}({k}_{i}-1))}$$

(2)

E_i is the number of edges that actually exist between the k_i neighboring nodes of pattern node i, that is, the number of neighbor pairs that actually exist between the k_i neighboring nodes of pattern node i, which reflects the degree to which pattern nodes in the network tend to cluster together.

Average path length: the average value of the distance between any two pattern nodes in the network, which can be used to determine whether the pattern co-occurrence network has the small-world feature without considering the edge weight.

In multilayer temporal networks, there are interactions between different network layers. Therefore, the inter-layer statistical properties are very important for understanding the temporal multilayer structure. The average node overlap degree can measure the relationships between layers. Average node overlap degree: it calculates the proportion of pattern nodes that appear in both layers relative to the total number of pattern nodes in the entire network. The formula for this is as follows⁴⁶:

$${Q}_{\alpha ,\beta }=\frac{1}{N}\mathop{\sum }\limits_{i=1}^{N}{{\boldsymbol{\nu }}}_{i}^{[\alpha ]}{{\boldsymbol{\nu }}}_{i}^{[\beta ]}$$

(3)

Here, ${v}_{i}^{\left[\begin{array}{c}\alpha \end{array}\right]}$ is an integer that takes a value of 0 or 1, where 1 represents pattern node i is active in layer α, meaning that the degree of pattern node i in layer α is greater than 0, and 0 represents inactivity. Q_α,β takes a value of 0 or 1; Q_α,β equals 1 indicates that all pattern nodes are active in both layers, and Q_α,β equals 0 indicates that there are no pattern nodes that appear commonly between the two layers, meaning that no pattern node is active at the same time in both layers.

Key node identification algorithm

Centrality is used to evaluate the importance of an individual. Degree centrality is the simplest indicator to characterize the importance of a node. The degree of a node in an undirected network is defined as the number of edges directly connected to the node. However, the pattern co-occurrence temporal multilayer network is a weighted network. Combining weight information can more comprehensively describe the structure and function of the network. The strength centrality of a pattern node in a single-layer network is defined as:

$${C}_{S}(i)=\frac{{q}_{i}}{Q}=\frac{\sum _{j\in {N}_{i}}{q}_{ij}}{Q}$$

(4)

Where q_i is the sum of the edge weights connecting pattern node i, Q is the sum of the edge weights in a single-layer network, N_i is the set of all pattern nodes connected to pattern node i, and q_ij is the edge weight connecting pattern nodes i and j. The strength centrality of multilayer networks is usually defined based on the operation of the multilayer adjacency tensor. In the case of an interconnected multilayer undirected network, the strength centrality of a multilayer network is defined as the mean of the multilayer in-degree and multilayer out-degree. The calculation formulas for the multilayer out-degree and multilayer in-degree are as follows⁴⁷:

$$\begin{array}{rcl}{S}^{i}&=&{M}_{j}^{i\alpha }{{\boldsymbol{U}}}_{\beta }^{\alpha }{{\boldsymbol{u}}}^{j}\\ {S}_{j}&=&{{\boldsymbol{M}}}_{j\beta }^{i\alpha }{{\boldsymbol{U}}}_{\beta }^{\alpha }{{\boldsymbol{u}}}_{i}\end{array}$$

(5)

Among them, the multilayer in-degree S_i is represented by a contravariant vector, the multilayer out-degree S_j is represented by a covariant vector, ${U}_{\beta }^{\alpha }={u}_{\alpha }{u}^{\beta }$ represents a second-order tensor with all elements equal to 1, and u_i and u^j represent first-order tensors with all components equal to 1.

Pattern community mining algorithm based on overlapping community division

Most community detection algorithms, including the Louvain algorithm, consider nodes as the objects of analysis, which means that a node can only be assigned to one community⁴⁸. However, this approach overlooks the diversity of node attributes. In actual network communities, there is often an overlapping feature, meaning that there are nodes in the network that belong to multiple communities simultaneously, referred to as “overlapping nodes”. This is also the case in the pattern network. For example, the lotus pattern is one of the “Eight Treasures Pattern (八宝纹),” and when Buddhism was introduced to China, the lotus was adopted as a symbol of Buddhism, regarded as a sacred flower representing “pure land” and symbolizing purity and auspiciousness. As a result, the lotus became a major decorative theme in Buddhist art. Meanwhile, the lotus with many seeds, often paired with the “Sanduo Pattern(三多纹)”, symbolizes a house full of children and grandchildren, and the blessings of many offspring. When the lotus pattern is combined with different patterns, the meaning expressed by the patterns is also different, thus indicating that the same pattern may belong to multiple communities.

There are mainly two commonly used algorithms for detecting overlapping communities: clique percolation algorithm and link communities algorithm. Link communities algorithm addresses the shortcoming of the clique percolation method, which requires pre-determining the number of pattern nodes contained within a community. Ahn et al.⁴⁹ proposed an link communities algorithm and conducted a comparison of detection performance across 11 network examples using different algorithms. The results showed that the algorithm exhibited better partitioning effects for networks of different sizes and densities, with a more pronounced advantage for weighted networks. The basic operational steps of the link communities algorithm involve merging edges with a certain degree of similarity into a community. The similarity between edge pairs e_ik and e_jk is defined as in formula 7:

$$S({e}_{ik},{e}_{jk})=\frac{\left\vert {n}_{+}(i)\cap {n}_{+}(j)\right\vert }{\left\vert {n}_{+}(i)\cup {n}_{+}(j)\right\vert }$$

(6)

where n₊(i) is the set of all nodes including node i and its neighbors.

The approach of using hierarchical clustering on edges to detect community structures involves the following specific steps: (1) Calculate the similarity for all connected edge pairs in the network and sort these edge pairs in descending order according to their similarity values. (2) The communities of edge pairs are merged in order of similarity, and the merging process is recorded in the form of a tree diagram. If some edge pairs have the same similarity, they are merged in the same step. (3) The merging process of communities can be continued until a certain step, up to the point where all edges belong to a single community. To obtain the best community structure, it is necessary to determine the optimal position in the tree diagram. The partition density is the edge density within the community, and the partition density is set as the objective function. Assuming a network containing M edges is divided into C communities {P₁, P₂, …, P_c}, where community P_c contains m_c edges and n_c nodes, the corresponding normalized density is ${D}_{C}=\frac{{m}_{C}-({n}_{C}-1)}{\frac{{n}_{C}({n}_{C}-1)}{2}-({n}_{C}-1)}$. The partition density of the entire network is defined as the weighted sum of D_c:

$$D=\frac{1}{M}\sum _{c}{m}_{c}{D}_{c}=\frac{2}{M}\sum _{c}{m}_{c}\frac{{m}_{c}-({n}_{c}-1)}{({n}_{c}-2)({n}_{c}-1)}$$

(7)

The maximum value of the partition density D corresponds to the optimal community division.

Results

Embroidery pattern co-occurrence temporal multilayer network construction

Before constructing the co-occurrence network of patterns, it is necessary to identify the pattern nodes contained in each piece of embroidery artifact and to identify the pattern nodes using dictionary-based automatic text recognition and image-assisted manual proofreading. Based on the co-occurrence relationships of patterns, the pattern co-occurrence network of the Qing Dynasty is constructed. Then, according to the co-occurrence relationships of patterns in each time period, the temporal sub-network of pattern co-occurrence is built. Finally, the temporal multilayer patterns co-occurrence network of Qing Dynasty embroidery is generated.

The pattern nodes of the pattern co-occurrence temporal multilayer network are identified by dictionary-based automatic text recognition and image-assisted manual proofreading. The names of Chinese cultural relics are named according to the industry standard of “Specification for registration of cultural relics in the collection of cultural institutions”, which is the most enriched metadata field for basic information on cultural relics. Embroidery cultural relics generally have a naming format of “color + (craft) + pattern + weaving method + (gender) + (single or cotton or leather) + function⁵⁰”, such as Bright Yellow Nasha Embroidered Colorful Clouds and Golden Dragons Pattern Male Single Courtly Robe (明黄色纳纱绣彩云金龙纹男单朝袍) and Red Five Bats Holding “Longevity” Character and Sanduo Pattern Brocade (红色五蝠捧寿三多纹妆花缎). Firstly, “color” (色) and “pattern” (纹) are used as delimiters, and the content before “color” (色) and the content after “pattern” (纹) are discarded. After cutting, the result is shown in Table 1.

Table 1 Result after segmentation of cultural relics names

The text after segmentation not only contains pattern information but also some unrelated information such as material, craft, and weaving method. Further segmentation of the text is performed to compare four commonly used Chinese segmentation tools: Tsinghua University’s THULAC, Peking University’s PKUseg, Harbin Institute of Technology’s LTP, and HanLP. THULAC segmentation tool is finally chosen for text segmentation, and the segmentation results of the four tools are shown in Table 2.

Table 2 Comparison of word segmentation results of four word segmentation tools

However, cultural relic names contain a large number of professional terms and vocabulary with special cultural meanings, such as “Five Bats Circling a Chinese Character Stylized Longevity(五福捧寿)”, “Sanduo Pattern(三多纹)” and “Sprinkled Thread Embroidery(洒线绣)”. It is difficult to accurately extract pattern-related terms using current segmentation tools. Therefore, Chinese Cultural Gene Tag Semantic Model (PatternNet)⁵¹ is constructed using data sources such as expert knowledge, academic literature, professional books, domain terms and other materials. New word detection methods are used to automatically discover new in the field and update PatternNet, and to assist in building professional word lists such as patterns, meanings, materials, colors and needlework techniques in the field of embroidery. The professional domain vocabulary constructed using the new term detection algorithm⁵¹ is shown in Table 3.

Table 3 Some keywords in the vocabulary of embroidery field

The word lists are added to the user-defined word segmentation dictionary, and then the THULAC word segmentation tool is used to segment the text to obtain pattern nodes. However, the same pattern may have different names depending on the colors and shapes. The different names that refer to the same pattern are merged, such as “Golden Butterfly Pattern”, “Colorful Butterfly Pattern”, and “Flying Butterfly Pattern” being merged into “Butterfly Pattern”. Finally, manual verification is conducted using image information to obtain 313 types of pattern nodes.

The Qing Dynasty embroidery collection consists of 11,054 pieces. From the time of Qing Shunzhi Emperor Fulin’s entry into the capital in 1644 to the Xinhai Revolution, the Qing Dynasty lasted for 268 years. The dynasty is divided into 10 time periods according to the era names: Shunzhi, Kangxi, Yongzheng, Qianlong, Jiaqing, Daoguang, Xianfeng, Tongzhi, Guangxu, and Xuantong. First, the overall pattern co-occurrence network of the Qing Dynasty is constructed, where the edge between two nodes represents the co-occurrence of two patterns in the same artifact, and the edge weight indicates the frequency of pattern co-occurrence. Visualize this network, as shown in Fig. 4.

Fig. 4

Qing Dynasty embroidery pattern co-occurrence relationship network.

Then, based on the pattern co-occurrence relationships in each time period, the temporal sub-networks of pattern co-occurrence are constructed. Within each layer, the edge between two nodes represents the co-occurrence of two patterns in the same artifact, and the edge weight indicates the number of co-occurrences of the patterns. The connection relationship between two patterns in different layers indicates the existence of the same pattern in the embroidery of the corresponding two era names, and the connection weight is a fixed constant of 1. Finally, a multilayer temporal co-occurrence network of patterns is obtained, containing 313 nodes, 2577 intra-layer relationships, and 5529 inter-layer relationships. The constructed multilayer temporal co-occurrence network of Qing Dynasty embroidery patterns is visualized as shown in Fig. 5.

Fig. 5

Temporal multilayer network of pattern co-occurrence in Qing Dynasty embroidery.

Intra-layer descriptive statistics

The descriptive statistics of the pattern co-occurrence network time slices corresponding to the ten reign titles and the overall pattern co-occurrence network of the Qing Dynasty are respectively performed, and the indicator statistical results are shown in Table 4. The pattern co-occurrence networks for the eras of Guangxu, Tongzhi, and Qianlong had the largest number of nodes and edges among the sub-networks. Embroidery patterns are the products of the externalization of esthetic tastes and spirit created by people in different periods, closely related to the geographical environment, level of productivity development, social ideology, folk customs, and even the political system and economic level of the creators. Combined with practical analysis, the Qianlong period was a time of social and economic prosperity and strong national power, with embroidery craftsmanship and pattern design reaching an unprecedented high level. Various auspicious patterns began to appear on clothing, and new elements such as pine trees and flowers were widely used. In the late Qing Dynasty, with the corruption of the imperial court and a pursuit of ease and luxury in court life, this trend was particularly pronounced in clothing patterns. Xu Ke of the Qing Dynasty recorded, “After the middle of the Guangxu era, officials in the capital and at court were extravagant, with their clothes being luxurious”⁵². It reflects the fashion of pursuing gorgeous clothing after the mid-Qing Dynasty. This fashion increasingly deviated from the original intention of the rulers of the early Qing Dynasty to regard the clothing system as part of the political system, or even as one of the measures to consolidate the regime⁵³. Therefore, the scale of the pattern co-occurrence networks in these three periods was relatively large. This indicates that the topology of the pattern co-occurrence temporal multilayer network is intrinsically linked to regime changes.

Table 4 Intra-layer descriptive statistics of the Qing Dynasty pattern co-occurrence temporal multilayer network

For the statistical analysis of the pattern co-occurrence network in the Qing Dynasty, the analysis of the cumulative degree distribution of the network is conducted first. The scatter plot of the cumulative degree distribution was plotted in a double logarithmic coordinate system and fitted with a straight line, as shown in Fig. 6. Here, x represents the degree of the pattern node, and P(X ≥ x) is the probability of the node with a degree greater than or equal to x. Using the method proposed by Clauset et al.⁵⁴ is used to determine whether the degree distribution of the network obeys a power-law distribution. This approach includes maximum-likelihood fitting, a hypothesis test based on the Kolmogorov-Smirnov goodness-of-fit statistic and likelihood ratio tests for comparing against alternative explanations. The calculation yielded p = 0.1068 ≥ 0.1, which means that the hypothesis that the cumulative degree distribution function of the pattern co-occurrence network nodes approximately follows a power-law distribution cannot be rejected. This indicates that the degree distribution of the pattern co-occurrence network is a power-law distribution. This suggests that most nodes in the pattern co-occurrence network have a relatively small degree, but a small number of nodes have a very large degree, which are the key patterns that often appear with other patterns in embroidery. These key patterns are core elements in the embroidery and weaving art of the Qing Dynasty. Further identification and analysis of these key pattern nodes and their evolution can help to deeply explore the esthetic preferences, value pursuits, and social background of the Qing Dynasty.

Fig. 6

Power-law distribution of pattern nodes in a double logarithmic coordinate system.

The Qing Dynasty pattern co-occurrence network was iteratively processed, with each iteration removing nodes with a degree of 1 and recording the number of nodes in the network. The network’s average path length was then calculated. A scatter plot of the network node number and average path length was plotted, and a logarithmic function was used to fit the scatter plot, as shown in Fig. 7. The fitting goodness-of-fit was 0.964. This indicates that the average path length of the pattern co-occurrence network increases logarithmically with the expansion of the network’s scale, demonstrating the small-world property. This indicates that there are close-connected local areas within the pattern co-occurrence network. Patterns within these local areas frequently co-occur due to reasons such as symbolic themes and cultural backgrounds, forming small “pattern communities”. At the same time, the entire network maintains good connectivity. Certain patterns play a bridging role between different communities, enabling patterns in different local areas to be connected through relatively short paths.

Fig. 7

Logarithmic fitting curve of network node number and average path length.

Inter-layer statistical features

The layer-layer average overlapping fraction of nodes of the Qing Dynasty pattern co-occurrence temporal multilayer network is calculated to measure the layer-layer relationships of the network. The results are shown in Fig. 8. On the whole, the layer-layer correlation is higher between adjacent eras, while the correlation between eras that are far apart in time is low, especially between Guangxu and Tongzhi, where the correlation is the highest. During the reigns of Emperor Guangxu and Emperor Tongzhi, Empress Dowager Cixi was in power. The design of the patterns had strong political intentions, and the emperor’s preferences also played a vital role. The selection of embroidery patterns and decorative styles changed little during this period, resulting in a larger layer-layer overlapping fraction of nodes.

Fig. 8

The layer-layer average overlapping fraction of nodes of the Qing Dynasty pattern co-occurrence temporal multilayer network.

Identification of key nodes

The multilayer strength centrality and single-layer strength centrality of the pattern nodes in the Qing Dynasty pattern co-occurrence temporal multilayer network are calculated separately. The larger the strength centrality of a node, the more important it is. The top 15 nodes based on multilayer strength centrality are displayed, with their specific values shown in Table 5. The top three pattern nodes are the Chinese character for longevity pattern, bat pattern, and auspicious cloud pattern. Among them, the “longevity” character symbolizes long life, health, and lasting happiness. In China, the concept of longevity originates from the “Five Blessings” in ancient texts, as recorded in Book of Documents (尚书): “The Five Blessings: the first is longevity, the second is wealth, the third is health and peace, the fourth is a fondness for virtue, the fifth is a natural end of life”⁵⁵. Longevity is considered the most important of the blessings, being at the core of the concept of the “Five Blessings” culture, encompassing people’s aspirations for longevity and happiness. Yuxiao Tu et al. sorted out the materials and physical objects of longevity-themed decorative patterns on the cuffs of the Qing Dynasty and classified the patterns related to longevity culture into longevity-character patterns and longevity-meaning patterns⁵⁶. In the Qing Dynasty, the use of the longevity character pattern reached its peak, with rich and diverse compositions and over one thousand different ways of writing. In terms of shape, there are round longevity character patterns with a circular outline, square longevity patterns with clear geometric lines, and longevity patterns with raised corners resembling goat horns, as shown in Fig. 9, the Blue and White Plate-mouthed Bottle with Hundred Longevity Patterns (now in the collection of the Taipei Palace Museum). In terms of combinations, the longevity character pattern is often paired with bat patterns to form the “Five Bats Circling a Chinese Character Stylized Longevity (五福捧寿)” auspicious pattern; with the Swastika pattern to create the “Ten Thousand Longevity (万寿)” auspicious pattern; with the Knot of eternity pattern to form the “Longevity without End (万寿无疆)” auspicious pattern, as shown in Fig. 10. Under the dual influence of external form and internal meaning, the construction methods of longevity-implication patterns transform abstract concepts and good wishes into vivid and concrete visual forms. There are three techniques in longevity-implication patterns: borrowing objects for homophonic allusion, borrowing objects for symbolic meaning, and borrowing objects for metaphorical representation. For instance, in traditional embroidery and weaving patterns, it is common to combine a cat, a butterfly, and a peony. This combination implies longevity and prosperity, using the technique of borrowing objects for homophonic allusion, which is an expression method relying on homophony. In Discourses on Salt and Iron: Filial Piety and Support, it is stated that “At seventy, one is considered “耄” (máo, an advanced age). In Erya: Explanation of Words, it is recorded that “At eighty, one is regarded as “耋” (dié, ripe old age) ”. A cat can catch mice and rid people of pests, thus being regarded as an auspicious creature, and the Chinese character for “cat” (猫, māo) is homophonic with “耄” (máo). A butterfly is colorful and is seen as a messenger of beauty, and the Chinese character for “butterfly” (蝶, dié) has the same pronunciation as “耋” (dié). The peony, known as the king of flowers, symbolizes wealth and honor. The combination of a cat, a butterfly, and a peony is called “Wealth and Longevity in Old Age”(富贵耋耄, dié), implying a long life filled with prosperity. Borrowing objects for symbolic meaning means using a thing to convey its related significance, which is generally associated with the natural properties of the thing, mythological stories, or social concepts. In Qing dynasty embroidery and weaving, elements such as longevity peaches, cranes, pine trees, and Shoushan stones were often used to express the meaning of “longevity”. A metaphor is a form of substituting the metaphorical similarities or associations between two objects or concepts. In the Qing Dynasty, there was an endless stream of patterns that used this construction method to metaphorically imply auspicious meanings. The classic pattern of “The Eight Immortals Celebrating Longevity”(八仙贺寿) metaphorically implies the wishes for “longevity and well-being”. The Eight Immortals achieved immortality through cultivation, breaking through the lifespan limit of ordinary people, and becoming representatives of metaphorical longevity. The longevity culture has almost permeated the entire history of traditional Chinese patterns, carrying the Chinese people’s beautiful expectations for life.

Table 5 Top 15 pattern node strength centrality in the Qing dynasty temporal multilayer network of pattern co-occurrence

Fig. 9: Blue and white plate-mouthed bottle with hundred longevity patterns.

The image comes from the Taipei Palace Museum.

Fig. 10: Combinations of longevity-character patterns with other patterns.

a Five bats circling a Chinese character stylized longevity (五福捧寿), b Ten thousand longevity (万寿), c Longevity without end (万寿无疆). This embroidery image a and c comes from the Museum of Ethnic Costumes of Beijing Institute of Fashion Technology, b comes from the Taipei Palace Museum.

In Chinese, the character for “bat”(蝠, fú) and the character for “happiness”(福, fú) have the same pronunciation, both pronounced as “fú”. People incorporate the image of bats into various auspicious patterns and decorations to express their longing and pursuit of happiness and good fortune. By observing things and extracting symbolic meanings, the ancients chose to use five bats to symbolize the “Five Blessings”. Moreover, bats have the habit of hanging upside down, which coincides with the connotation of “ happiness arrives”(福到) in traditional culture. Times are changing, but what remains constant is people’s inheritance of the Fu (happiness) culture. The Chinese people’s love for the character “Fu” is the most typical manifestation of the folk Fu culture in folk customs. In the real lives of the Chinese people, the character “Fu” is widely used. It is a character that appears very frequently among Chinese characters and has even become a symbol of spiritual pursuit. The preference for the character “Fu” in folk culture is first demonstrated by pasting the “Fu” character during the Spring Festival. The custom of pasting the “Fu” character during the Spring Festival has a long history and embodies people’s longing and anticipation for a happy life in the future. To more vividly express their yearning and wishes for happiness, apart from pasting the “Fu” character upright, there is also a folk custom of pasting it upside down, which implies that fortune and happiness have arrived. During the Spring Festival, when walking on the streets and alleys, you can see various forms of the “Fu” character almost everywhere. Even the red envelopes given to children as lucky money are printed with different styles of the “Fu” character. All these “Fu” characters reflect people’s anticipation for “Fu” (happiness). The auspicious cloud pattern is representative of traditional Chinese auspicious patterns and one of the most vital artistic forms, symbolizing auspiciousness, joy, and happiness, and representing symbiotic harmony. It is often combined with other mythical creatures like dragons, phoenixes, and qilins. From this, it is evident that the longevity and happiness patterns are the most representative cultural memory symbols of the Qing Dynasty, reflecting the importance and admiration for the culture of longevity and happiness, from emperors and generals to common people. Today, this culture still deeply influences people’s lifestyles and values.

Further draw a stacked bar chart of the strength centrality percentages for the top 15 pattern nodes ranked by multilayer strength centrality, as shown in Fig. 11. The relative intensity centrality of the patterns fluctuates significantly. The dragon pattern, which symbolizes power and imperial authority, accounted for a high proportion in the early Qing Dynasty and gradually decreased over time. Whereas patterns like butterfly, peony, chrysanthemum, and floral patterns, which are more delicate and graceful, had a lower proportion in the early Qing Dynasty and their proportion increased in the late Qing Dynasty. During the reigns of the emperors Kangxi, Yongzheng, and Qianlong, the dragon pattern, as an important symbol of imperial power and authority, was widely used and valued. However, during the reigns of Emperor Guangxu and Emperor Tongzhi, Empress Dowager Cixi was in power, and she had a deep fondness for flowers such as orchids, plum blossoms, and peonies throughout her life, as well as many patterns with longevity meanings. Cixi was extremely particular about her attire, from patterns to fabrics to styles. Her garments had to be meticulously sketched by the artists of the Hall of Self-fulfillment, revised multiple times, and only after after her personal approval were they allowed to be sent to the Jiangning Weaving Bureau for exquisite crafting, which was thousands of miles away. Therefore, there are many soft patterns such as floral patterns and butterfly patterns in the weaving and embroidery left over from the late Qing Dynasty. As time progresses and rulers change, cultural esthetic preferences, political power, and social values evolve, leading to significant changes in the types and styles of embroidery patterns. It can be seen that the fluctuations in the strength centrality of the pattern nodes pattern co-occurrence temporal multilayer network of Qing Dynasty reflect, to some extent, the transformations in social culture and political power.

Fig. 11

Stacked bar chart of pattern nodes strength centrality percentages.

Analysis of pattern communities based on link communities algorithm

The link communities algorithm is used to divide the entire Qing Dynasty pattern co-occurrence network into communities. Edges with a certain similarity are merged into a community. The maximum partition density is 0.215. At this point, the total number of communities is 163, and the largest community contains 61 nodes. Among them, the Swastika pattern, Shou character pattern, and Ruyi pattern are the three patterns that belong to the largest number of communities, with the swastika pattern being a member of 42 communities. Table 6 shows some communities and the patterns they contain, and it can be observed that some communities have a very high degree of node overlap. Therefore, the relationship between communities is explored according to the number of shared nodes between communities, and the communities are further merged. The Jaccard coefficient evaluates the pairwise similarity between communities based on the number of shared nodes, and hierarchical clustering of the communities is performed based on the Jaccard coefficient.

Table 6 Results of pattern community division based on the link communities algorithm

By incorporating the Louvain algorithm to ascertain the optimal number of pattern communities, the initial 163 communities were clustered into 11 larger communities. The results of the community hierarchical clustering are shown in Fig. 12. Table 7 shows the pattern nodes and the number of pattern nodes in each of the 11 communities after clustering. The pattern network is visualized in Fig. 13, where nodes and edges belonging to the same community are assigned the same color identifier. The larger the node, the higher the degree value of the node. Overlapping nodes have multiple colors. It can be seen that there is a significant distinction between communities, and the theme is clear. Based on the patterns contained in the 11 communities, the themes of these 11 communities can be summarized as follows: rare bird patterns, zodiac animal patterns, insect patterns, Buddhist patterns, artifact patterns, Taoist patterns, auspicious patterns, treasure patterns, flower patterns, longevity and happiness patterns, and other patterns.

Fig. 12

Process of hierarchical community clustering.

Table 7 Communities after clustering and patterns contained within each community

Fig. 13

Results of hierarchical community clustering.

Rare bird patterns: Rare birds originally referred to precious and exotic flying birds, and later generally referred to birds that are loved and cherished by people. Among them, the phoenix is one of the most representative images in rare bird patterns. It is regarded as the king of birds and symbolizes auspiciousness, beauty, happiness, and prosperity. In Chinese culture, the phoenix often appears together with the dragon, representing the harmony of yin and yang and the auspiciousness of the combination of the dragon and the phoenix. The peacock is highly favored by people for its beautiful feathers and elegant posture. It symbolizes good luck, happiness, and a blissful life. In some cultures, the peacock is also regarded as a sacred bird, believed to have the function of dispelling evil spirits and safeguarding the house. The crane is regarded as a symbol of longevity. It is often combined with elements such as pine trees to form the auspicious pattern of “pine and crane representing a long life (松鹤延年)”. At the same time, the crane also implies elegance, purity, and transcendence from the mundane. The mandarin duck is a symbol of love. They always appear in pairs, signifying deep affection between husband and wife and a long life together. In traditional wedding costumes and home decorations, mandarin duck patterns are often used. Rare bird patterns are widely applied in traditional clothing. For example, the clothing of ancient emperors, generals, and ministers was often embroidered with patterns of phoenixes, cranes, etc., to show their noble status. Among the common people, auspicious rare bird patterns such as mandarin ducks and magpies were also used on the clothing of women and children, adding beauty and auspicious implications to the clothing.

Zodiac animal patterns: the zodiac elements consist of twelve animals: rat, ox, tiger, rabbit, dragon, snake, horse, goat, monkey, rooster, dog, and pig. The Heavenly Stems and Earthly Branches chronology is a time-keeping system with the 12 zodiac animals as symbols. Its characteristic is to match the 12 animals with the 12 Earthly Branches, and a person’s birth year determines their corresponding zodiac animal. The zodiac culture reflects the ancient working people’s psychological pursuit of exorcising evil and praying for blessings, as well as their animal worship. It is deeply rooted in the blood of every Chinese person. During the Zhou Dynasty, the 12 zodiac animals were classified into 12 signs, forming a calendar system specifically used for sacrifices and divinations. In modern times, during the Spring Festival, people paste Spring Festival couplets and window decorations. The year when a person’s zodiac sign repeats are called the “year of offending Tai Sui (太岁)”, also known as the “benmingnian (本命年, zodiac year) ”. Tai Sui is a kind of star god, mainly composed of water in the Five Elements. Water in the Five Elements has restrictive, draining, and consuming effects on people. People are likely to be affected by the “year of offending Tai Sui” in their zodiac year, with relatively poor luck. To avoid harm, people will wear red clothes and red underwear. In China, the twelve zodiac animals are often used in marriage-matching. “Liuhe (六合, six harmonious combinations)” is considered an excellent marriage match, while “Liuchong (六冲, six conflicting combinations)” is not suitable for marriage. It is also common to infer a person’s fate based on their zodiac sign. Besides “Liuhe” and “Liuchong”, there are also “generation (相生)” and “restriction (相克)” in the theory of the Five Elements. By combining the twelve zodiac animals with the Five Elements, people can infer and analyze good and bad luck, blessings, and misfortunes. Evidently, since ancient times, the Chinese people have had a high sense of identity and belonging towards the zodiac, which has influenced people’s thoughts, behaviors, esthetics, and other aspects.

Insect patterns: similar to patterns of other themes, apart from expressing idyllic charm and being purely for ornamental purposes, the insect patterns in traditional weaving and embroidery are also often rich in auspicious implications. Take the spider, for example. It is an ordinary small insect, but due to its alias “${\rm{X}}{\overline{{\rm{l}}}}$ zi (嬉子)”, which is homophonic with the Chinese character “xi (喜, meaning happiness)”, it has been associated with happy events. The appearance of a spider is regarded as an omen of good news. As a result, people cherish this small insect and widely embroider it on clothes, hats, quilts, curtains, and pendants, giving it the beautiful name “Happiness descends from heaven (喜从天降)”. What’s most interesting is that venomous insects such as scorpions, centipedes, and lizards are also used in weaving and embroidery patterns. The fifth day of the fifth lunar month is the Dragon Boat Festival. At this time, it is early summer, and viruses and plagues are prone to spreading. Folk people regard this day as an exorcism day. Both men and women wear sachets, drink realgar wine, hang calamus on the lintel, and draw five venomous insects, namely scorpions, centipedes, geckos, vipers, and mythical water-shooting insects, and paste them on the door to pray for disaster-elimination, disease-prevention, and longevity. These five venom-related symbols are often used as weaving and embroidery patterns and are collectively called “Five Venoms (五毒)”. In Yan Qing. Guyu Five Venoms written by Lü Zhongyu in the Qing Dynasty, it is recorded: “ In ancient times, in the Qingzhou and Qizhou, on Guyu day, people would draw the Five Venoms Talisman, depicting the shapes of scorpions, centipedes, vipers, wasps, and mythical water-shooting insects, each with a needle stabbed on it, and then distribute and paste them in every household to exorcize insect poisons”⁵⁷.

Buddhist patterns: the Eight Auspicious Symbols pattern is a common Buddhist decorative pattern, which is a combined pattern formed by eight Buddhist ritual implements, namely the Dharma Wheel, the Conch Shell, the Precious Parasol, the Canopy, the Lotus, the Vase, the Golden Fish, and the Knot of Eternity. The Dharma Wheel represents the circular wheel of the Dharma. It symbolizes that the Buddha’s harmonious and all-encompassing teachings are invincible, breaking through ignorance and afflictions, cutting off the cycle of reincarnation, and radiating the brilliance of righteous knowledge. Passed down from generation to generation, it is a symbol of the endlessness of life. The Conch Shell is one of the musical instruments used in Buddhist activities, also known as the Sanskrit Conch. In the combination of the Eight Auspicious Symbols, the shape of the Conch Shell symbolizes the sound of the Dharma preached by the Buddha. The wonderful and auspicious sound resounds throughout the world. The Precious Parasol implies that the operation and dissemination of the Dharma are flexible and unobstructed. The Parasol represents covering everything, being able to open and close freely, and is a symbol of protecting all sentient beings. The Canopy describes the Dharma as a sacred canopy, covering the boundless world. It widely spreads compassion and benefits all sentient beings. The Canopy represents covering the world, purifying the universe, and is a symbol of liberation from poverty and illness. The Lotus implies the purity of the Dharma. Just as the lotus is fresh and fragrant, it guides sentient beings to break away from defilement with its refreshing fragrance. The Lotus represents sacred purity and being free from contamination, and is a symbol of rejecting pollution. The Vase implies that the Dharma is profound and strong, gathering complete and abundant blessings and wisdom, just like a vase with no leakage. The Vase represents the perfection of blessings and wisdom without any flaws and is a symbol of achieving success. The Golden Fish implies that the Dharma has infinite vitality. Just as fish swim freely in water, it can break free from disasters and handle situations with ease. The Golden Fish represents being lively, healthy, and full of vitality and is a symbol of seeking good fortune and avoiding evil. The Knot of Eternity implies the strong vitality of the Dharma. Like an infinite knot, it continues to extend and circulate, being passed down forever without end. The Endless Knot represents pervading everything and being endless and is a symbol of a long life.

Artifact patterns: patterns composed of utensils and objects are referred to as artifact patterns. The ancients imbued some artifacts with typical characteristics with a lot of auspicious connotations. For example, the tripod (鼎, an important type of bronze ware in ancient China) became a symbol of the power and status of rulers as well as a symbol of the state. The yi (彝) was not only a wine vessel but also an important ritual object, carrying the ancient sacrificial culture and the reverence for ancestors. The Chinese character “瓶 (píng, vase)” has the same pronunciation as “平 (píng, peace)”, thus taking on the meaning of peace, and so on. In addition, the Bogu pattern is a highly representative type of artifact pattern. During the Daguan period of the Northern Song Dynasty, Emperor Huizong ordered Wang Fu and others to compile and paint the bronze wares collected in the Xuanhe Palace. The book was titled Xuanhe Bogutu, from which the term “Bogu (博古)” originated. The Bogu pattern is a decorative pattern featuring ancient artifacts. Common ones include: vases, tripods, zuns (a type of ancient wine vessel), jars, ruyi, qins (a plucked string instrument), fans, jade bi (a disc-shaped jade ornament), ox horns, ancient coins, etc., symbolizing noble and elegant qualities.

Taoist patterns: the Hidden Eight Immortals patterns initially originated from the magical instruments held by the Eight Immortals in Taoism, serving as the “Symbols” of the Eight Immortals. Later, through secularization, processing, and refinement by the folk, they were added with narrative implications and gradually evolved into an independent system separate from the Eight Immortals. The Hidden Eight Immortals specifically include the fishing drum, the magic sword, the jade flute, the gourd, the lotus flower, the precious fan, the jade tablet, and the flower basket. Each of these magic treasures has its unique functions and implications. The gourd of Tieguai Li is said to contain the elixir of immortality, symbolizing the relief of all living beings and eternal life. The round fan of Han Zhongli has the power to bring the dead back to life, representing longevity and the hope of turning things around in desperate situations. The fishing drum of Zhang Guolao is a celestial instrument for divination, capable of predicting the past and the future and divining one’s life, implicitly referring to understanding the will of heaven and conforming to the mandate of heaven. The magic sword of Lü Dongbin can slay demons and evil spirits, meaning suppressing and expelling evil demons. The lotus flower of He Xiangu symbolizes purity and elegance, enabling people to cultivate their moral character and stay away from distractions. The flower basket of Lan Caihe is said to be filled with celestial items, capable of communicating widely with the deities. The transverse flute of Han Xiangzi can bring vitality to all things, symbolizing a vibrant and lively atmosphere. The yin-yang tablet of Cao Guojiu can purify the environment and calm people’s minds, implying a peaceful state of mind and spiritual clarity. The Hidden Eight Immortals patterns for decoration emerged in the mid-Ming Dynasty. Since the Qing Dynasty, they have been even more widely used, expressing people’s wishes and blessings for a better life.

Auspicious patterns: auspicious patterns are decorative patterns composed of graphics or characters with auspicious meanings, reflecting people’s eagerness for life and pursuit of ideals. Such patterns have been most popular since the Ming and Qing dynasties, accounting for a large proportion. Especially in the Qing Dynasty, almost most of the decorations carried the principle that “every pattern must have a meaning, and the meaning must be auspicious”, forming the decorative characteristics of this period. Emphasis was placed not only on the formal beauty of the patterns but also on their semantic beauty. During the long-term development and evolution, auspicious patterns have formed a wide variety of artistic expression techniques, mainly including symbolism, implication, homophony, analogy, symbolization, and the use of characters⁵⁸. The basic symbolic themes of auspicious patterns include the pursuit of good fortune, longevity, scholarly honor, official rank, wealth, celebration, having many children, peace, harmony, and imperial virtue. The creation and application of these auspicious-meaning patterns reflect the different life ideals and esthetic tastes of people from all walks of life.

Treasure patterns: treasure patterns usually refer to patterns composed of a specific precious treasure as the theme or element. There is a wide variety of treasure images selected for these patterns. In the Song Dynasty, there were only more than 10 types, such as round coins, ivory, coral, and ruyi. Later, with the introduction and prosperity of religions, the treasures revered by religions were also incorporated, such as the Eight Auspicious Symbols of Buddhism and the objects held by the Eight Immortals in Taoism. In the Qing Dynasty, the Bogu pattern, which embodied the literati temperament and the social fashion of that time, was also incorporated into it. This included the Four Treasures of the Study, porcelain, books, tripods, scroll paintings, astronomical instruments, etc., bringing the number of types to more than 30. Various different treasures can be combined together. Since there are no fixed rules for choosing the treasure images and they can be selected as one wishes, the combined patterns are called the Miscellaneous Treasures pattern⁵⁹. Some folk artists arbitrarily select eight of the above-mentioned treasures to form a pattern, which is called the “Eight Treasures”. However, this pattern is quite different from the Eight Auspicious Symbols pattern mentioned earlier. During the Yuan Dynasty, the Miscellaneous Treasures pattern mostly appeared as an auxiliary decorative pattern within the deformed lotus petals on the shoulders or shanks of porcelain. During the Ming and Qing dynasties, the Miscellaneous Treasures pattern was mostly scattered in the blank spaces of the main pattern. In the Qing Dynasty, there were even works that used the Miscellaneous Treasures pattern as the main pattern.

Flower patterns: flower patterns are the mainstream in plant patterns. Among them, peony patterns, lotus patterns, plum blossom patterns, chrysanthemum patterns, and baoxiang flower patterns are the most common. Some flower patterns are often combined with various birds, insects, beasts, and figures. The peony is gorgeous, charming, and exudes an air of elegance and luxury. It is renowned as the “flower of wealth and honor (富贵花)”. Therefore, in traditional auspicious patterns, the peony often represents wealth and prosperity. For example, when combined with Chinese flowering crabapple, the pattern is named “Wealth and Honor Filling the Hall (富贵满堂)”. When the peony is combined with the swastika character pattern, the pattern is named “Wealth and Honor for Ten Thousand Years(富贵万年)”. When the peony is combined with ruyi, it forms an auspicious pattern named “Wealth, Honor, and Good Luck (富贵如意)”. The lotus grows out of the mud yet remains unstained. It has earned the reputation of being a “gentleman among flowers (花中君子)” and is the incarnation of holiness, elegance, and a symbol of virtue. After Buddhism was introduced into China, the lotus was adopted as its symbol. Buddhists regard the lotus as a sacred flower, symbolizing holiness and implying good fortune. Thus, the lotus has become a major decorative theme in Buddhist art. The baoxiang flower pattern is a Buddhist decorative pattern formed by artistically combining the shapes of flowers, flower buds, and leaves of peonies, lotuses, etc. Its design is magnificent and luxurious, hence the name “Baoxiang Flower(宝相花),” which implies auspicious meanings of “treasure” and “immortality,” and symbolizes wealth, good luck, and happiness.

Happiness and longevity patterns: in the long-standing Chinese culture, happiness and longevity patterns hold a unique and significant position. They carry people’s yearning for a happy life and their wishes for longevity, health, and well-being, embodying the core of auspicious culture. In Book of Documents (尚书), it is stated that there are five aspects of blessing: the first is longevity, the second is wealth, the third is health and peace, the fourth is a fondness for virtue, and the fifth is a natural end of life. As for why longevity is ranked first, the book also explains: “Only when people have longevity can they enjoy all other blessings.” To express their eagerness for happiness, people write the Chinese character “福 (fú)” on bright red paper and paste it together with couplets on the screen wall of the main gate or other prominent places during the Spring Festival. In addition to directly using the Chinese character “福 (fú)”, to express the meaning of “good fortune”, people often take advantage of the homophony of “蝠 (fú)” in “蝙蝠 (bat)” and “佛 (fú)” in “佛手 (Buddha’s hand fruit)” with “福 (fú)”, and apply these elements extensively in auspicious patterns. The hope for longevity is a common aspiration of humanity. In patterns expressing the meaning of “longevity”, symbols such as cranes, pine trees, longevity peaches, Shoushan stones, ribbon-tailed birds, or the Chinese character for longevity pattern are commonly used to represent longevity. These elements may appear alone or be combined with each other, forming various auspicious patterns like “ Pine and Crane for Everlasting Spring (松鹤长春)”, “Crane and Deer in Spring (鹤鹿同春)”, and “Offering the Peaches of Immortality for Longevity (蟠桃献寿)”, conveying people’s boundless longing for longevity.

Other patterns: this community includes geometric patterns such as square patterns, fret patterns, stripe patterns, and checkerboard patterns. It also encompasses figure patterns of farmers, fishermen, woodcutters, and hermits, as well as auspicious animal patterns like those of qilins, chi tigers (螭虎), lions, and mythical beasts. Geometric patterns are regular patterns composed of points, lines, and planes, forming squares, triangles, octagons, rhombuses, circles, polygons, etc. These basic patterns can be repeated, overlapped, and interlaced to create various shapes. Generally, they are mainly abstract, but some are also combined with natural images to form patterns. Geometric patterns are one of the most commonly used decorative patterns in traditional weaving and embroidery. Figures from historical stories, literary allusions, and folklore are important themes in traditional weaving and embroidery patterns. Those popular and beloved character stories that have been passed down among the people for thousands of years are widely woven and embroidered on various clothing and decorative items by unknown artists. These patterns reflect people’s spiritual realm, moral values, and esthetic preferences. In ancient times, animals with auspicious connotations were called “auspicious beasts”. Among them, some animals exist in the real world, such as tigers, lions, goats, and deer, as well as mythical beasts created according to folklore, like taoties (饕餮), qilins, heavenly horses, and chi tigers (螭虎). The artistic images of these auspicious beasts are widely used in weaving and embroidery.

Discussion

The temporal multilayer network of embroidery pattern co-occurrences has been constructed, and temporal multilayer network analysis method has been employed to mine and analyze the associations and cultural connotations of the patterns. The research results indicate:

• (1) The pattern co-occurrence network exhibits scale-free and small-world properties. The degree distribution of the Qing Dynasty pattern co-occurrence network was calculated, and the cumulative degree distribution plot for the pattern nodes was drawn in a double logarithmic coordinate system. It passed the K-S hypothesis test, confirming that the pattern co-occurrence network follows a power-law distribution, which means that the pattern co-occurrence network exhibits scale-free properties. The Qing Dynasty pattern co-occurrence network was iteratively processed, with each iteration removing nodes with a degree of 1 and recording the number of nodes in the network. The network’s average path length was then calculated. A scatter plot of the network node number and average path length was plotted. The plot revealed that the average path length of the network increases logarithmically with the number of nodes, indicating that the pattern co-occurrence network exhibits the small-world property.

• (2) The pattern co-occurrence network possesses a community structure with divisible and re-combinable functions. Taking into account the overlapping nature of the community structure in the pattern co-occurrence network, link communities algorithm was used to mine the pattern communities. It was found that some community have a very high degree of nodes overlap. Therefore, the relationship between communities is explored according to the number of shared nodes between communities, and the communities are further merged. By incorporating the Louvain algorithm to ascertain the optimal number of pattern communities, the initial communities were clustered into 11 larger communities. The results indicate that there is a significant distinction between the communities, and the theme is clear. Designers can use the outcomes of the community division to combine related patterns, thus creating design works with enhanced coherence and consistency.

• (3) The Happiness (福, Fú) and Longevity (寿, Shóu) patterns are the most representative cultural memory symbols of the Qing Dynasty. The multilayer strength centrality and single-layer strength centrality of the pattern nodes in the Qing Dynasty pattern co-occurrence temporal multilayer network are calculated separately to identify the relatively important nodes. The top three pattern nodes with the highest multilayer strength centrality are the Chinese character for longevity pattern, bat pattern, and auspicious cloud pattern. Additionally, the Chinese character for longevity pattern was a node with consistently high strength centrality across each time layer. By conducting overlapping community detection on the patterns, Swastika pattern, Shou character pattern, and Ruyi pattern are the three patterns that belong to the largest number of communities. From this, it is evident that the Happiness (福, Fú) and Longevity (寿, Shóu) patterns are the most representative cultural memory symbols of the Qing Dynasty, reflecting the importance and admiration for the culture of longevity and good fortune, from emperors and generals to common people. Today, this culture still deeply influences people’s lifestyles and values.

• (4) The topological properties of the temporal multilayer network of pattern co-occurrences and the fluctuations in the strength centrality of pattern nodes are inherently linked to the transitions in social culture and political power. In the pattern co-occurrence temporal multilayer network, the pattern co-occurrence networks for the eras of Guangxu, Tongzhi, and Qianlong had the largest number of nodes and edges among the sub-networks. Between layers, the layer-layer correlation is higher between adjacent eras, while the correlation between eras that are far apart in time is low, especially between Guangxu and Tongzhi, where the correlation is the highest. As time progresses and rulers change, cultural esthetic preferences, political power, and social values evolve, leading to some continuity and some changes in the types and styles of embroidery patterns. This has resulted in fluctuations in the strength centrality of the pattern nodes.

In summary, by constructing the Qing Dynasty embroidery pattern co-occurrence multilayer temporal network, mining the co-occurrence relationships and characteristics of embroidery patterns. The study revealed the cultural heritage and evolution underlying them, demonstrated their unique value in the process of Chinese civilization’s development, and provided a scientific basis for the exploration of the origins of Chinese culture.