Fluid Grey: A Co-Living Design for Young and Old Based on the Fluidity of Grey Space Hierarchies to Retain Regional Spatial Characteristics

Abstract

Architectural design and urban renewal that adapt to an ageing society and are localized are urgent needs around the world. On the other hand, the concept of grey space, which refers to transitional space and is an in-between concept, has been proposed since the 1980s, but few studies have further explored its hierarchy, fluidity, and relationship with regional characteristics. Therefore, this study hopes to use the fluidity of the grey space hierarchy to solve the problem of design that adapts to an ageing society and preserves regional characteristics. This study mainly focuses on the spatial characteristics of Beitou Heart Village, summarizes five grey space hierarchies and fluidity modes, and finally designs social housing for young and old cohabitation in a bottom-up manner based on them, restoring local unique neighborhood care and multi-ethnic communication methods. There are three innovations in this study: (1) defining the division method of the grey space hierarchy; (2) exploring the richness and scalability of the grey space hierarchy in terms of fluidity; (3) using the grey space hierarchy to achieve neighborhood care and multi-ethnic communication, making social housing for urban renewal more people-oriented and retaining spatial regional characteristics. This paper may provide a theoretical foundation and practical help for grey-space-based design and urban renewal in the future.

1. Introduction

1.1. Background Analysis of Ageing Society and Social Housing

Ageing society is one of the urgent problems that the whole world must face in the 21st century. Internationally, proportions of people over 65 years old accounting for 7%, 14% and 20% of the total population are called an ageing society, an aged society, and a super-aged society, respectively [1]. The Taiwan Province of China became an ageing society in 1993, turned into an aged society in 2018, and is expected to become a super-aged society in 2025 [2]. However, starting from 2022, more than one-quarter of the counties and cities in Taiwan Province have gradually entered the super-aged group [3], which makes it more urgent that Taiwan consider communities and housing that adapt to an ageing society. On the one hand, the shrinking proportion of young people in an ageing society are also facing increasing pressure, such as low wages, long working hours, and accompanying difficulties in housing, family, and life [4]. On the other hand, the role of the elderly in society is not only one of a vulnerable group that needs to be cared for; their physical and spiritual needs should also be taken into account. The proportion of elderly couples and single people in Taiwan has increased, and they general hope to live with relatives and friends and continue to work or participate in social activities to make use of their remaining energy. However, more than 22% of them have difficulty renting a house [5,6]; therefore, there should be a variety of care methods and spaces for adaptation. However, in the past, social housing in Taiwan was planned and developed based on a single ethnic group living model. Moreover, its external form is generally single and has no regional characteristics. The interface between internal public and private spaces is rigid, and there are few public spaces. All of this has resulted in the need for diverse caring and mutual aid spaces that have been ignored for a long time. Therefore, against this social background, Taiwanese society has begun to pay attention to the research, planning, design and urban renewal of social housing in recent years, emphasizing diverse social housing forms and hoping to meet the living needs of different ethnic groups through mixed living spaces for both the young and old [7,8].

In addition to addressing the social development issues of ageing, social housing in urban renewal should also focus on retaining the local culture and features of the city itself. Except for a few aborigines, most of the current population in Taiwan, China, comes from immigrants from different periods and ethnic groups in history [9]. Each immigrant group first took root in Taiwan in the form of settlements, and after a few generations, these settlements were gradually neglected and abandoned as their descendants left. Therefore, how we might preserve and take over the historical relics, buildings and culture of aborigines and immigrants in the current circumstances that have neglected them is also a major issue that Taiwan’s urban renewal needs to face today [10]. Taiwan’s last large-scale immigration occurred from 1949 to the 1960s. Due to defeat in the second civil war between the Kuomintang and the Communist Party, the Kuomintang and their dependents fled to Taiwan to establish and deploy new settlement areas called military villages, which is also one of the most important historical and cultural relics in Taiwan’s modern history. The site of this research is located in Beitou Heart Village, Beitou District, Taipei, one of the 13 military village preservation areas in Taiwan. It is also one of the few remaining intact military villages in Taipei City, and the only hot spring medical military village in Taiwan [11]. Similarly, with the ageing of the population and the relocation of villagers, Beitou Heart Village has gradually fallen into desolation. Through surveys and interviews with old villagers, we found that the most significant spatial characteristic of Beitou Heart Village is its unique rich spatial hierarchy. The villagers achieved the fluidity of grey space by changing interfaces, thus forming abundant and diverse forms of neighborhood care; the whole village is as warm and helpful as a big family. Therefore, social housing for the revitalization and urban renewal of Beitou Heart Village should retain the rich spatial hierarchy and fluidity of the village, so that the spatial patterns and the culture of neighborhood care can remain in place in the future.

1.2. Grey Space Theory

1.2.1. Grey Space Hierarchy

The concept of grey space was first proposed by Japanese architect Kisho Kurokawa in the 1980s; it refers to transitional space and is a kind of in-between concept [12]. The in-between concept originates from the classification of public and private spaces in urban planning. In the West, it originated from figure–ground theory, one of the three major theories of Western urban design [13], while in the East, grey space theory can be traced back to the Spring and Autumn Period and the Warring States Period in China (770–221 BC) [14]. Figure–ground theory originated in the 14th century and studies the proportional relationship between the coverage of the building as a solid mass (figure) and the open space as a void (ground) [13]. From an initial single dichotomy, it gradually explored the diversity of in-betweens over the course of historical evolution and moved towards the blurring and enrichment of grey. As early as 1551, Leonardo Bufalini drew a figure–ground plan of ancient Rome in the form of black interiors and white exteriors. In the mid-18th century, when Giambattista Nolli drew the “Pianta Grande di Roma”, he not only enriched the map but also opened up the closed nature of the figure–ground, that is, leaving public indoor areas blank and making the inner and outer spaces of the city interpenetrate and blur with each other [15]. In 1889, Camillo Sitte used void and solid methods of depicting public spaces in his study of urban morphology in “The Art of Building Cities” [16]. These studies became popular again in the 1960s with the figure–ground mapping technique. In 1972, the book “Learning from Las Vegas” [17] reversed the figure–ground from black and white and added grey to indicate parking lots. In the same year, Oscar Newman also emphasized that semi-public spaces, such as foyers, play an important role in preventing crime [18]. Subsequently, in 1984, Colin Rowe and Fred Koetter introduced Gestalt psychology to perfect the modern figure–ground theory in their book “Collage City” [19], thus achieving the historical transformation of figure–ground from practice to theory.

In modern times, Westerners have refocused on the urban context, which has extended the objects of the in-between. In 1960, Kevin Lynch proposed environmental perception, which emphasized the importance of legibility, coherence, and meaning in urban environments [20] Influenced by Kevin Lynch, James J. Gibson first created affordance theory in 1966 [21] and emphasized that it is the mutual support and feedback between the environment and people that lead to the occurrence of behaviors [22]. In 1970, Richard Sennett proposed the importance of disorder to urban space in “The Uses of Disorder” [23]. The fold theory pioneered by Deleuze in 1988 can be used as an explanation for the ambiguity of space: architecture is a carrier of interaction between people and the environment, so space should also present their mutual wrapping and folding relationship, like folds [24,25]. Later, Greg Lynn responded to folding in architecture with blobs [26,27]. In 2020, Pablo Sendra further proposed three forms of infrastructure featuring design disorder based on Richard Sennett: (1) passage territories; (2) incomplete objects; and (3) nonlinear narratives [28]. The first is similar to Deleuze’s fold theory, and the latter two coincide with the work of Herman Hertzberger [29]. In 1996, Stan Allen proposed field conditions [30], which focus on exploring a space with no form field, similar to a wasp colony, whose scope and shape change over time. In the 21st century, Kim Dovey and Elek Pafka developed the urban DMA [31] inspired by assemblage theory and Jane Jacobs [32], arguing that cities rely on the complex synergy of density, mix, and access. The mix element of this explores the distribution of the three functions of visiting, life, and work in cities, proving that land use is multiple in any good city [31]. However, it only focuses on these three functions and lacks an in-depth understanding of functions and topology as well as a horizontal comparison of regional characteristics.

1.2.2. Fluidity of Grey Space

East Asian grid-shaped urban planning uses voids, solid entities, and clusters to express sequence and pays more attention to the uncertainty and fluidity of the edge in its evolution over thousands of years. East Asian urban planning originated from the “Rites of Zhou·Kao Gong Ji·Craftsman (《周礼·考工记》)” during the Spring and Autumn Period and the Warring States Period (770–221 BC) in China. The zoning plan was carried out in a chessboard pattern, with the royal palace as the center [14]; this is also the prototype of modern land use zoning. After that, the Tang Dynasty capital of Chang’an, which was founded in 581, further refined land use zoning and created the “Lifang system (里坊制)” (also known as the “Fangshi system (坊市制)”); at this time, the imperial palace was moved northward from the center; residential and commercial areas were separated, and the market was divided into east and west parts; all blocks were surrounded by walls; and gates were opened and closed on time [33]. In addition, there were multiple households and courtyards in each block, and the closed state of each interface could be changed, thus forming a variety of multi-level spaces and usage methods. However, overly clear functional zoning will cause inconvenience in life, reduce the number of residents on the edge of the city, and it can also breed crime and insecurity. Therefore, the capital of the Song Dynasty (in the late 10th century), Kaifeng, further developed the “Xiangfang system (厢坊制)”—a mix of commercial and residential areas and no restricted closing hours [33]—which is also the origin of today’s mixed residential and commercial model in Asia.

Influenced by the Tang Dynasty in China coupled with Japan’s small area and disaster-prone environment as well as the influence of religion [34], Japan has produced two main cultural concepts that have affected the characteristics of Japanese space. On the one hand, Japanese culture emphasizes “Impermanence (無常)”—everything in the world will eventually change, nothing will last forever, there is no law, and it is unpredictable. For example, Japan’s Ise Grand Shrine is rebuilt every 20 years according to a prototype, and the old palace is demolished; this ritual is used to express impermanence. “Kami (神)” is the Japanese belief that everything in the world is a god. “Himorogi (神籬)” that was born from this also became a concept in Japanese space—just by wrapping a circle of hemp rope around evergreen plants as pillars and adding paper hangings, a space is enclosed [34]. Therefore, unlike primitive huts in the West that were tightly wrapped on all sides, the space of “Himorogi (神籬)” does not have very clear boundaries and functional implications. On the other hand, the fundamental spirit of the Japanese is “Oku (奥)”—a mystery composed of psychological depth and sensory layers [35]. It is manifested in Japanese space as creases of multi-layered space and time, with emphasis on the process being felt through multiple senses [36,37]. “Oku (奥)” involves the ambiguity of the center, while “Ma (間)” involves the ambiguity of the boundary [38], emphasizing the gap between entities, which is an uncertain in-between grey with ambiguous relationships. The most typical example is “Engawa (縁側)”—the connective relationship between rooms being diversified through the opening and closing of doors, resulting in a varied uses, the function of space not being limited to a single one. Therefore, Japanese space tends to feature de-barrierization, while pursuing the multi-layered depth and fluidity of space.

After Japan’s defeat in World War II, the most important architectural school in Japan was Metabolism, which was developed by Kenzō Tange and others in the 1960s. They introduced the factor of time and believed that cities and buildings were not static but should be a dynamic process like biological metabolism. Since then, Metabolism architects have branched out into different areas. In 1978, Fumihiko Maki first developed Oku theory, arguing that an innermost area should exist at the core of this high-density space, which is organized into multiple layers like an onion [36,37], thus formally opening up the concepts of spatial hierarchy and fluidity in architectural history. In the 1980s, Kisho Kurokawa defined the concept of “grey space” (also known as “fan space”). On the one hand, it refers to the “Rikyu gray” expounded upon by Sen no Rikyū; unlike the grey of black and white in the West, it is a mixture of four opposing primary colours (red, blue, yellow, green) and white, implying the compatibility of grey space with functional diversity. On the other hand, it generally refers to transitional space, which is a generalization of space characterized by vagueness of boundaries, ambiguity of functions, and duality of perception [12]. In addition, the various color tendencies of Rikyu grey also correspond to the ambiguous parts of cities, buildings, or the lifestyle of life itself, which Kisho Kurokawa believes are the essential parts that have been lost in modern cities [12].

1.2.3. Grey Space and Regional Characteristics

Preserving spatial regional characteristics requires balancing the ‘extrinsic’ and ‘intrinsic’ properties of space—the former consists of invisible structural relationships, mainly the arrangement and topology of elements; the latter is visible and mainly presented through geometric properties, such as shape, size, volume, pattern and texture [39]. However, most modern theories only focus on one of them and find it difficult to balance the two [39]. On the one hand, critical regionalism, which historically emphasizes regional characteristics, places too much emphasis on the intrinsic properties of space. In 1981, the term critical regionalism was first proposed by Alexander Tzonis and Liane Lefaivre; it is a design and planning method that can promote the ecological, social and intellectual singularity and diversity of regions [40]. Subsequently, in 1983, Kenneth Frampton further proposed that its basic strategy is to mediate the influence of universal civilization with elements that are indirectly derived from specific local characteristics, such as culture, place–form, natural environment, vision, etc. [41]. However, it is difficult to make general statements about future impacts when only considering the ‘intrinsic’ properties of space [39]. On the other hand, urban planning, from ancient practice to modern urban network theory, has always been overly biased towards the extrinsic properties of space. The earliest practice of urbanism can be traced back to Pope Sixtus V’s reform of the ancient Roman city in the 16th century, which strengthened the symbol of religious power by strengthening the urban axis with obelisks and reorganizing streets [42]. From 1852 to 1870, Georges-Eugène Haussmann carried out an urban transformation plan for Paris based on this, thus forming the radial Paris road network of the Champs-Élysées [42]. It was not until the 20th century that urban network theory gradually developed a theoretical explanation of the urban linear topological hierarchy as industrialization in modernism, represented by the mass production of Ford cars, which caused a general change in transportation methods. In 1927, Ludwig Hilberseimer first proposed the street hierarchy, which embeds the importance of each road type into the network topology [43]. Jane Jacobs criticized that, although it helped promote the formation of a clear road network in cities, it also pushed cities towards being car-oriented and caused the demotion of pedestrians [32]. In the 1970s, Bill Hillier and Julienne Hanson et al. developed space syntax [44,45,46] based on network theories, which is a mathematical street network model for calculating topological spatial relationships [39]. Space syntax and urban DMA are the few theories that use systematic methods to quantify and compare the similarities and differences in different urban characteristics. They horizontally analyze and separately compare how cities in different regions achieve common points in accessibility and mixed uses in quantitative data under different modes from two perspectives: the richness of the road network system and mixed land use zoning.

In summary, how we might design buildings and urban renewal that adapt to an ageing society is a major issue that needs to be faced in this century. Furthermore, urban renewal, especially social housing, should also pay attention to retaining local characteristics and culture. In particular, the regional characteristics of Beitou Heart Village, the site of this study, should be maintained to achieve neighborhood care through the fluidity of multi-level grey space. In addition, in terms of theory, grey space theory also lacks quantitative practice, as few studies have combined grey space and fluidity, and few people have explored regional differences in grey spaces. Therefore, this study hopes to use the fluidity of grey space hierarchy to solve the problem of Beitou Heart Village’s design, that it might adapt to ageing society and retain regional characteristics.

This study mainly focuses on the spatial characteristics of Beitou Heart Village, summarizes five grey space hierarchies and fluidity modes, and finally designs social housing for young and old cohabitation in a bottom-up manner based on these modes, restoring the local unique neighborhood care and multi-ethnic communication methods. There are three innovations in this study: (1) defining the division method of the grey space hierarchy; (2) exploring the richness and scalability of the grey space hierarchy in terms of fluidity; and (3) using the grey space hierarchy to achieve neighborhood care and multi-ethnic communication, making social housing for urban renewal more people-oriented and retaining spatial regional characteristics. This paper may provide a theoretical foundation and practical help for grey-space-based design and urban renewal in the future.

2. Materials and Methods

This paper determines the division method and fluid mode of grey space hierarchy through qualitative research and then applies it to the spatial analysis of Beitou Heart Village, finally designing social housing for young and old people to live together in accordance with local characteristics. The reason for designing around grey space is that urban renewal and design should retain local characteristics and culture, and one regional characteristic of Beitou Heart Village (where the site is located) is neighborhood care through flowing multi-level grey space. This design process is mainly divided into the following two steps (Figure 1):

(1)

Grey Space Hierarchy, Fluidity, and Connection with Regional Characteristics: Based on the theories and practices of grey space, fluidity, and localization in the history of architecture, we qualitatively analyze and define the concept and division method of grey space hierarchy;

(2)

Design Application: Summarizing the grey space hierarchy and fluidity of Beitou Heart Village, we analyze the population composition of Beitou District and design residential units and social housing in a bottom-up process, so that the fluidity of grey space has scalability.

2.1. Grey Space Hierarchy, Fluidity and Connection with Regional Characteristics

Grey space is a transitional space that accommodates functional diversity and also corresponds to the ambiguous parts of the city, architecture, or life itself [12]. However, diverse human behavior and ambiguous ways of life are abundant, so the space level as its carrier should also be rich in diversity. Additionally, in turn, functions and people’s usage conditions will also determine the level of grey space. The theory of hierarchically dividing space within the history of architecture can be traced back to the figure–ground theory originating in the 14th century. Since then, people have divided space types into public and private poles, represented by white and black, respectively. Since then, in modern times, from network theory to space syntax, architects have applied graph theory to spatial analysis, starting from the most open main road or entrance space and adding pure mathematical depth to express the degree of privacy of the space. Although it adds richness to the spatial hierarchy, it becomes a purely mathematical problem and has nothing to do with function and how people use it. Therefore, the author hopes to make up for this shortcoming by integrating graph theory and grey space theory.

According to the definition of grey space mentioned above, the grey space hierarchy should be affected by both the depth of the space and the way it is used. The latter includes human-made factors such as functions, actual usage conditions, environment, and human relationships. In short, in contrast, the integration of space syntax is a simple spatial topological relationship without environmental influence. However, the grey space hierarchy is different in that it needs to consider the changes in the closeness of spatial connections caused by residents in actual use (Figure 2). Generally speaking, the more private the room, the higher the greyscale of the grey space. However, when changes in line of sight, accessibility, height difference, privacy, etc. occur between the two spaces, and thus the functions change, the greyscale will change accordingly. Among them, the most common influencing factor causing greyscale changes is the interface. Taking a home in Beitou Heart Village as an example, Rooms A and B are both bedrooms, and their depths in the integration division of space syntax are both 4. However, since Room A has a window to the outside and the fence of this home is a low wall, residents can even greet passers-by on the street through the window and low wall in Room A. Furthermore, there is a desk inside the window sill in Room A. When the window sill is opened, this interface becomes a long conversation area and reading corner between neighbors. Therefore, Room A is one level lower than Room B on the grey space level. However, on the other hand, if the resident closes the window in Room A and draws the curtains so that this visual communication is completely isolated, at this time, the grey space level of Room A will rise to the same level as Room B (Figure 2 and Figure 3). Therefore, since there are many similar interfaces in the village that can be enriched and practical, through the residents’ control of the interface switches and transparency in their daily lives, the greyscale of the space is also changing and flowing in real-time; this is the fluidity of grey space.

Therefore, in practical application, the grey space hierarchy division method is divided into two steps: (1) dividing the pure space depth; (2) adjusting and classifying the grey space level based on the actual use of the residents based on the former. Furthermore, by classifying the residents’ space use from private to public, combined with the grey space hierarchy, the grey space fluid mode and process of the building or area can be analyzed. After that, the application of grey space fluidity adopts a bottom-up approach to achieve scalability—we first design the smallest unit, and then achieve diversity and richness in scale through different arrangements and combinations.

2.2. Design Application

The site of this study is located in Beitou Heart Village, Beitou District, Taipei. First, the grey space hierarchy and fluidity of Beitou Heart Village are summarized. Then, the house type and distribution ratio are designed according to the population composition of Beitou District, and the public and private space functions are set according to the work and rest habits of the young and old groups. Then, combining the grey space hierarchy and resident analysis, residential units are designed, which are then combined to complete the design of the social housing as a whole. This bottom-up design approach ultimately allows the grey space to flow at different scales (inside units, between units, within each floor, between floors, and between the entire house and the entire old village community).

3. Results

3.1. Grey Space Hierarchy, Fluidity and Connection with Regional Characteristics

According to the definition of grey space hierarchy in the previous parts, the whole Beitou Heart Village was investigated, and it was concluded that there are five different spatial levels in the village. The first layer of grey space is mainly roads and public spaces, which are the place for large gatherings and daily communication activities of all village residents. The second layer of grey space is mainly public and personal courtyards, where villagers stay, chat, garden, barbecue and cook meals, and children play. The third layer of grey space is the space for indoor hospitality and main housework activities, including the living room, toilet, etc. The fourth floor is a space used daily by family members, neighbors and friends when they visit for neighborhood care, including study rooms, kitchens, warehouses, etc. The last grey space is the most private bedroom (Figure 4, lower left). The picture in the upper left corner of Figure 4 specifically analyzes and shows the process of grey space flowing and changing through interface switches in a home. In addition, since Beitou Heart Village is located on a hillside, the terrain height decreases from northeast to southwest. Therefore, according to the comfortable perspective of the human eye, the higher the height difference in the vertical direction, the higher the privacy and grey space level. Furthermore, the grey space level also changes with the line-of-sight penetration of the interface. The higher the transparency or visibility of the interface, the lower the privacy. Finally, based on the grey space levels summarized above, the overall figure–ground of this village (Figure 4, right) is obtained.

3.2. Design Application

Through a population survey of the entire Beitou District and an analysis of the daily routines of the young and old groups, the layout allocation of the social housing and the functional arrangement of the public space was obtained. From 2018 to 2023, the ratio of young and old in Beitou District was around 6:4, but the proportion of the elderly has increased by 5% in 5 years (Figure 5 and Figure 6), so it is set at a ratio of 1:1. This is the proportion of young and elderly apartment types in this social housing complex. Among them, because Beitou District is located on the edge of Taipei City, it serves as a satellite area in the center of Taipei. In particular, 650 m southwest of Beitou Heart Village is the New Beitou Metro Station. Therefore, the young people living in this area are mainly people who work in Taipei but cannot afford the housing prices in the city center, while the elderly are mainly local residents. Next, according to the work and rest time and life needs of the young and old groups, at the same time, it must be able to adapt to certain changes in family members, so this social housing unit has three types of unit. Units A and B are suitable for young people. The former can accommodate the changes in family members from being single to having a family, and the latter will be suitable for young people from starting a family to having children. Unit C mainly caters to the needs of the elderly and can accommodate the living needs of the elderly living alone or with their partners (Figure 7, left). On the other hand, the work and rest schedules of young and old people are analyzed to obtain the activities and time they can share. This will be the decisive factor in designing the mutual aid model and public space functions of this social residence. Since young people have to go to work on weekdays, the only time these two groups interact is on weekday evenings and weekends. The overlapping activities are mainly dinner and a small number of leisure activities on weekday evenings, while on weekends and holidays, there is an overlap between meals and activities throughout the day (Figure 7, right). Therefore, the model of mutual aid between young and old will be that the elderly will mainly help the young with cooking and other housework during the working day, while the young will reciprocate the support of the elderly on weekends. Under such a mutual aid model, the kind of self-worth that the elderly group actually values most will be reflected, while at the same time, the life difficulties of young people can be attenuated, and neighborhood care can be provided to elderly people in poor health.

Next, in a bottom-up manner, we first designed the residential units and then combined and improved the design of the entire social housing complex. First, according to the characteristics and needs of the residents, three different residential units, A, B, and C, were designed, and the grey space fluidity conditions within each unit were analyzed. Since Units A and B are for young people, they are designed as double-layer structures. Unit A is suitable for 1 to 2 young people, so it requires less private space than Unit B, which is a two-generation family unit. In addition, younger groups generally want to participate in more social activities; therefore, the first floor of Unit A is designed as a place for public gatherings and activities for neighbors. Unit B is for young families with children, so there are more private spaces in the double-layer design. Unit C is designed as a single floor instead of a duplex to meet the accessible living needs of elderly people living alone and in couples (Figure 8, left). Then, all the units were arranged and combined to analyze the grey space fluid and neighborhood communication conditions that could be formed under all neighborhood combinations (Figure 9). Then, to maximize contact between different ethnic groups and promote equal mutual assistance between the young and old groups, the three types of residential units were evenly distributed to obtain a spatial volume model of the entire social housing (Figure 8, right). Finally, we analyzed the spatial hierarchy fluidity of each floor (Figure 10, right). Therefore, in this social housing complex, the flow of grey space can be formed in response to human activities within the units, between units, within each floor, between floors, between the entire house and within the entire old village community, finally achieving the scalability of fluidity.

In the public sphere, this social housing complex wherein young and old people live together is set up in the southwest corner of Beitou Heart Village. The social issues that need to be faced are not only the cohabitation of young and old in an ageing society and the preservation of regional spatial characteristics mentioned above, but also the important tasks of revitalizing the surrounding communities and undertaking the development of this old village as a cultural reserve in the future. There is a height difference of about one floor from northeast to southwest within the site. Therefore, it is hoped that the first floor of this social housing can be used as an open area for interaction with the surrounding community and people, so the designer placed some public functional spaces on the first floor (including convenience stores, shared restaurants, shared kitchens, gyms, a Kindergarten, laundry room, and square). At the same time, part of the northern area on the second floor is connected to the cultural park workstation of Beitou Heart Village through a high-rise gap. Since there are roads to the west and south, other residential areas to the north, and middle schools to the west and south, external public functional areas are all located on the west and south of the site. Additionally, the public area within the social housing is located on the east side of the first floor. Finally, the location and relationship of various public spaces on the first floor, as well as the flow of grey space on the first floor, will be adapted to the overall figure–ground of the village (Figure 10, left).

In the outdoor renderings (Figure 11, top), it can be seen that the relationship between this social housing and the old Beitou Heart Village community is very harmonious, and people can carry out different activities and interactive communication through grey spaces at different levels. New people coming to the area can integrate here and help each other as equals with people from the old community. In the indoor renderings (Figure 11, bottom), it can also be seen that this social housing complex can continue the extremely harmonious and friendly neighborly relations between the old Beitou Heart Village communities. In this kind of friendly interaction, the elderly can also feel needed by society, and everyone can feel the warmth of society in this big family atmosphere.

4. Discussion

The first innovation of this study is to quantify the grey space hierarchy. Although many theories and practices have begun to extend the diversity of in-between in modern times, most of them have stopped at general theories and few quantitative studies. The latest breakthroughs in quantification are mainly focused on studying the changing relationship and interaction between the building’s physical environment and people. For example, the Mood State Correction Factor proposed by Turhan, C. et al. in 2023 shows the impact of the emotional state of residents on thermal sensation [49]. Another example is the use of graph neural networks to predict and optimize the control of central air-conditioning systems [50]. In comparison, the breakthrough of this study is its analysis and quantification from the urban context, especially the grey space theory, to fill the gap between theory and quantification.

The second breakthrough of this paper is the extension of the possibility of grey space in its fluidity and scalability. The fluidity of space is rarely mentioned in the history of architecture, and the only similar theories are Oku theory [36,37] and field conditions [30]. These few practices are only at the architectural scale, one example being field-based blur building. Therefore, this paper further combines and quantifies grey space and fluidity and achieves the scalability of fluidity to any scale through a bottom-up approach.

The third breakthrough of this paper is that it proposes solutions to urban renewal in the face of ageing and localization, and in particular, it proposes the correlation between grey space and regional characteristics. For one thing, in the past, design solutions for coping with ageing were mostly based on forms of infrastructure such as accessible design [51,52]. For another, past theories and practices found it difficult to balance the ‘extrinsic’ and ‘intrinsic’ properties of space with regional characteristics. So, this paper starts from the perspective of cultural heritage, and by continuing the local traditional neighborhood care mode, the needs of different ethnic groups are not only met by infrastructure. At the same time, this model can also continue to revitalize local communities.

5. Conclusions

This study applies the fluidity of grey space hierarchies to solve the problem of designing for an ageing society and preserving regional characteristics. Focusing on the spatial characteristics of Beitou Heart Village, five grey space levels and forms of fluidity are summarized. Finally, based on them, neighborhood care and multi-ethnic communication are achieved, and a social housing complex for young and old cohabitation that retains the spatial characteristics of the region and adapts to urban renewal in an ageing society is designed.

Therefore, there are three innovations in this study. First, this paper defines the specific division method of grey space hierarchy. Most of the previous concepts similar to the in-between remain at the stage of proposing general philosophical theories, and this study further develops it into specific quantitative and practical methods to make up for this shortcoming. The division method of grey space hierarchy is divided into two steps: (1) dividing the pure spatial depth; and (2) adjusting and classifying the grey space level based on the actual use of residents on the basis of spatial depth. The higher the privacy of the room, the higher the greyness of the grey space. When there are changes in sight, accessibility, height difference, privacy, etc. between two spaces, and then the function changes, the greyness will change accordingly. The most common influencing factor is the interface.

Second, this paper explores the richness and scalability of the grey space hierarchy in terms of fluidity. Previously, few theories have mentioned the fluidity of space; even field conditions and fluidity have remained at the theoretical stage, as in the previous point. This study not only quantified grey space, but also proposed methods to analyze and apply fluidity while achieving its scalability. Specifically, by classifying the spatial usage of residents according to a level from private to public and combining it with the grey space hierarchy, the grey space fluid mode and process of the building or region can be analyzed.

Third, in terms of practice, this study uses the grey space hierarchy to achieve neighborhood care and multi-ethnic communication, making social housing for urban renewal in response to ageing more people-oriented and retaining spatial regional characteristics. On the one hand, how we might deal with global ageing is one of the major issues of this century. In particular, as a vehicle for human activities, urban renewal that can cope with ageing and adapt to local conditions is imminent. On the other hand, previous theories and practices have mostly been unable to balance the ‘extrinsic’ and ‘intrinsic’ properties of space while retaining regional characteristics. This paper uses Beitou Heart Village as an application case to show how to quantify, localize, and apply the theory. Specifically, the most notable spatial feature of Beitou Heart Village is its unique rich spatial hierarchy. Since it was found that the residents’ lifestyles from public to private can be classified into five levels of communication depth, the grey space of the place was divided into five levels. After that, in the design stage, a bottom-up method was used to design the units first and then combine and improve them; finally, the updated social housing complex has a rich grey space hierarchy and can flow between different scales, restoring the original local living atmosphere.

In the future, at a practical level, as in the design case shown in this paper, the grey space hierarchy and fluidity theories extended by the author can be applied to the preservation of regional characteristics in architectural design and urban renewal. In addition, in terms of theory and research, the author is also combining it with other techniques of architectural design in an attempt to achieve quantification of preservation of regional characteristics. This combination will serve as a theoretical basis for horizontally comparing the spatial characteristics of different regions.