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Fractal versus Euclidean patterns (Note: The left pattern appears appears metaphorically in traditional buildings, in the sense of all scales involved rather than of precisely the same pattern, whereas the right pattern is pervasively seen in modern buildings metaphically and in terms of precisely the same pattern.)
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A city is not a tree but a semi-lattice. To use a perhaps more familiar term, a city is a complex network. The complex network constitutes a unique topological perspective on cities and enables us to better understand the kind of problem a city is. The topological perspective differentiates it from the perspectives of Euclidean geometry and Gaussia...
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Context 1
... example, to characterize a tree, we tend to only measure its height, rather than all its branches. To illustrate, let us examine two patterns shown in Figure 3. The left pattern appears appears metaphorically in traditional buildings, in the sense of all scales involved rather than of precisely the same pattern, whereas the right pattern is pervasively seen in modern buildings metaphically and in terms of precisely the same pattern.) ...
Context 2
... square of one unit is cut into nine congruent squares, and the middle one is taken away. The same procedure is recursively applied to the remaining eight squares again and again, until we end up with the pattern commonly known as Sierpinski carpet (Figure 3a). This particular carpet of three iterations comprises one square of scale 1/3, eight squares of scale 1/9, and 64 squares of scale 1/27. ...
Citations
... In Finding Lost Space (Trancik, 1986) trees can be used to help stitch back dysfunctional or dead urban space in cities-block by block-reflecting Dover and Massengale's seven key roles of urban street trees, by: 1. Redefining the space of the street; 2. Redefining pedestrian space; 3. Calming traffic and provides protection from cars; 4. Filtering the sunlight 5. Bringing order in geometric patterns 6. Visually softening the streetscape; 7. Providing a living natural environment. (Dover and Massengale, 2013:19) Note: The left pattern appears metaphorically in traditional buildings, in the sense of all scales involved rather than of precisely the same pattern, whereas the right pattern is pervasively seen in modern buildings (Jiang, 2015). ...
... In terms then of fractal and living structures "A city is indeed a tree… our thinking in architecture and urban design is very much dominated by Euclidean and Gaussian thinking as opposed to fractal ( Figure 138). For example, to characterize a tree, we tend to only measure its height, rather than all its branches" (Jiang, 2015). "Unfortunately, modern architecture has been deadly misguided by Euclidean geometry and Gaussian thinking towards so-called geometric fundamentalism (Mehaffy and Salingaros 2006, cited in Jiang, 2015. ...
Trees don’t shout, they don’t need to. This study explores two recurring strands of a central theme around how trees and the space formed by trees are relevant to urban design—the practical and the magical. Practical relevancy extends beyond environmental, health, social, and economic concerns to include sensitivity and careful consideration of type, size, mix, placement, and spacing of trees. Magical relevancy lies in the ‘sense of wonder’—a fine mist through which people invested in the evolution of our towns and cities are drawn, where light and shade filter both noise and quiet.
... Thus how to transform the scattered information to useable geographic information became an important methodological problem for historians. Therefore, a series of new attempts have been promoted and some methods have been demonstrated as useful (Jiang 2015). GIS technology makes it possible for historians to make full and simultaneous use of digital maps containing three components: space, attributes and time and then to analyze in combination with other historical elements. ...
... The scaling hierarchy is a distinguishing feature of complex networks or complex systems in general. For example, a city is a complex system, and a set of cities is a complex system (Jacobs 1961;Alexander 1965;Salingaros 1998;Jiang 2015c), both having scaling hierarchy seen in many other biological, social, informational, and technological systems. This paper demonstrates that the wholeness bears the same scaling hierarchy as complex networks or complex systems in general. ...
This paper explores the impacts of changes in industrial structure, energy total factor efficiency (energy efficiency) and energy structure on changes in carbon emission (CO2) in 31 provinces of China. From the perspective of spatial-temporal analysis, this paper first examines the dynamic spatial characteristics of these indicators from 2000 to 2015 based on the exploratory spatial data analysis (ESDA) theory. Afterward, a set of spatial panel econometric models (SDM, SAR and SEM) is used to estimate the spatial effect of each indicator to verify the scale effect hypothesis of industry structure and the Jevon’s Paradox of energy efficiency. The study also tests the source of spatial interaction effects and spillover effects. With the truth of fuel energy domains in China, the results figured out that industrial structure is in line with the scale effects which having positive influence on CO2, and energy total factor efficiency is in line with the Jevon’s paradox which having positive influence on CO2.
... Thus how to transform the scattered information to useable geographic information became an important methodological problem for historians. Therefore, a series of new attempts have been promoted and some methods have been demonstrated as useful (Jiang 2015). GIS technology makes it possible for historians to make full and simultaneous use of digital maps containing three components: space, attributes and time and then to analyze in combination with other historical elements. ...
... The scaling hierarchy is a distinguishing feature of complex networks or complex systems in general. For example, a city is a complex system, and a set of cities is a complex system (Jacobs 1961;Alexander 1965;Salingaros 1998;Jiang 2015c), both having scaling hierarchy seen in many other biological, social, informational, and technological systems. This paper demonstrates that the wholeness bears the same scaling hierarchy as complex networks or complex systems in general. ...
The official history, chorography and family trees constitute Chinese national history. Family trees contain a large amount of information regarding Chinese society, economy, culture, population, history and geography. To make full use of family trees and help resolve related problems in the humanities and social sciences, it is important to systematically collect, arrange, analyze, and integrate family tree information. This study proposes a strategy to construct the Family Tree Geographical Information System (FTGIS) by incorporating modern information technologies, such as databases, GIS, and web technologies, into the research on family trees. First, the concept and objectives of the FTGIS are discussed. Second, the key issues of the FTGIS are described in detail, including a unified spatial-temporal framework, FTGIS data model, family tree information specification and sharing as well as mass family tree information collection. Finally, a multilevel architecture is designed, and a prototype of the FTGIS platform is developed.
... A city can be regarded as a complex network (Jiang 2016). As the two backbones of the city, roads and buildings are the most important features on maps. ...
Buildings are among the most important features of cities. In the suburban or rural regions, buildings are normally constructed along the roads, which forms the smooth and consistent patterns so that the building arrangements also can be described with network models. In previous studies, network theory has achieved good performance in cartography and GIS. In this paper, a study of a building-network is proposed, including the concepts, generation methods and centrality analysis. Firstly, with the constraint Delaunay triangulation and the refinement strategy by facing ratio, the building-network is generated by considering the buildings and the proximal segments as the nodes and segments of the network, respectively. Then, centrality analysis is applied on the building-network, aiming to reveal the crucial relationships among buildings, which is useful for understanding the structural properties of the complex network. Four different centrality measures, i.e. degree, closeness, betweenness, and eigenvector centrality, are calculated based on the building-networks. The buildings show different distribution effects and patterns under the four centrality measures. From the results, the degree centrality reveals the local centre of the region; closeness and eigenvector centrality have the ability to cluster buildings into different groups; while betweenness centrality can detect the linear patterns. Therefore, using network theory to analyse buildings can reveal some inner relationships of buildings and has great potential in the application of building pattern detection, classification, clustering and further generalization.
... We ignored urban scientists such as Luis Bettencourt who saw Alexander's recursive, patterned, extendable, compositions as a template for open-ended urban design [34]. On the core themes of the essay, we did not investigate Bin Jiang's computational methods for Alexandrian Beauty using PageRank and other techniques [35,36]. We paid no mind to Sergio Porta, Yodan Rofè, and MariaPia Vidoli who pragmatically took up the point where we end this essay by suggesting that the Gate from here to there lies in the interstices of System A [37]. ...
Beauty. Christopher Alexander’s prolific journey in building, writing, and teaching was fueled by a relentless search for Beauty and its meaning. While all around him the world was intent on figuring out how to simplify, Alexander came to embrace complexity as the only path to his goal. The Beauty and life of that which he encountered and appreciated—an Indian village, a city, a subway network, an old Turkish carpet, or a campus—lay in its well-ordered complexity. As a designer and maker he found that simplicity came from choosing—at every step—the simplest way to add the necessary complexity. The failure of so much of our modern world, in Alexander’s eyes, was oversimplification, wantonly bulldozing context, misunderstanding the relationships of part and whole, ignoring the required role of time in the shaping of shapes, and ultimately dismissing, like Esau, our birthright of Value in favor of a lentil pottage of mere Fact. Ever elusive, Beauty demands of her suitors a constant return of attention to see what might be newly revealed, and Alexander duly returned again and again in pursuit of the mystery. In this essay—essentially biographical and descriptive of one man’s endeavors—we examine the full arc of his work from dissertation to most recent memoir. We don’t shy away from his failures, and we don’t simplify his journey. We leave work done by other scholars for another day. We reach no conclusion, rather, we invite readers to reflect on what Alexander’s lifelong effort suggests to them about their own path, their own sense of aesthetics and order, innate cognitive shortfalls, and professional blind alleys.
... It is a little as though the members of a family were not free to make friends outside the family, except when the family as a whole made a friendship. ( [5], p. 15) By contrast, what he termed a "semilattice"-what we would today call a complex network [23]-had overlap, redundancy, ambiguity, and interactive relationships (Figure 2). For a city, this was an essential feature of its dynamism, its complexity and richness: ...
... (a) (b) Figure 2. Subsequently in "A City Is Not a Tree" Alexander illustrated how a "semilattice", or what we would now refer to as a complex network [23], has interconnecting or overlapping sets. Again, this is shown as a set diagram in (a) and a network diagram in (b). ...
... However, for cities this can be immensely destructive: Figure 2. Subsequently in "A City Is Not a Tree" Alexander illustrated how a "semilattice", or what we would now refer to as a complex network [23], has interconnecting or overlapping sets. Again, this is shown as a set diagram in (a) and a network diagram in (b). ...
Christopher Alexander published his longest and arguably most philosophical work, The Nature of Order, beginning in 2003. Early criticism assessed that text to be a speculative failure; at best, unrelated to Alexander’s earlier, mathematically grounded work. On the contrary, this review presents evidence that the newer work was a logically consistent culmination of a lifelong and remarkably useful inquiry into part-whole relations—an ancient but still-relevant and even urgent topic of design, architecture, urbanism, and science. Further evidence demonstrates that Alexander’s practical contributions are remarkably prodigious beyond architecture, in fields as diverse as computer science, biology and organization theory, and that these contributions continue today. This review assesses the potential for more particular contributions to the urban professions from the later work, and specifically, to an emerging “science of cities.” It examines the practical, as well as philosophical contributions of Alexander’s proposed tools and methodologies for the design process, considering both their quantitative and qualitative aspects, and their potential compatibility with other tools and strategies now emerging from the science of cities. Finally, it highlights Alexander’s challenge to an architecture profession that seems increasingly isolated, mired in abstraction, and incapable of effectively responding to larger technological and philosophical challenges.
... Thus the service area generation can be represented by the classic Thiessen polygon method (or The generation of Thiessen polygons can be easily implemented by the Create-Thiessen-Polygons toolbox in ArcGIS. The service area polygons generated would be expected to show the fractal features as Jiang indicated [27], there will be a large number of small units in the urban area. Natural city boundaries can then be aggregated with polygons by an appropriate extraction method. ...
... The generation of Thiessen polygons can be easily implemented by the Create-Thiessen-Polygons toolbox in ArcGIS. The service area polygons generated would be expected to show the fractal features as Jiang indicated [27], there will be a large number of small units in the urban area. Natural city boundaries can then be aggregated with polygons by an appropriate extraction method. ...
The natural city, which is essential to understand urban physical scale and identify urban sprawling in urban studies, represents the urban functional boundaries of the city defined by human activities rather than the administrative boundaries. Most studies tend to utilize physical environment data such as street networks and remote sensing data to delimitate the natural city, however, such data may not match the real distribution of human activity density in the new cities or even ghost cities in China. This paper suggests aggregating the natural city boundary from the service area polygons of points of interest based on Reilly's Law of Retail Gravitation and the maximum entropy method, since most points of interests provide services for surrounding communities, reflecting the vitality in a bottom-up way. The results indicate that the natural city defined by points of interests shows a high resolution and accuracy, providing a method to define the natural city with POIs.
... 1 研究背景 区域与城市的空间结构对社会经济和环境有着多尺度的影响，如资源需求增加、城市拥 挤、生物多样性降低等 [1][2] 。测度城市与区域中的聚居空间规模和分布形态，对区域空间结 构和城镇体系的认知至关重要 [3] 。 城市规模等级及边界研究一直以来都是城镇体系等级结构研究的核心内容。 当前城市规 模等级划定的标准是 2014 年国务院颁布的《关于调整城市规模划分标准的通知》 ，据此人口 是规模认定和等级划分的标准，与之相呼应的"位序-规模"方法仍是当前城镇与等级模式 界定的主要方法 [4][5][6] 。大部分学者认同城市规模清晰呈现出幂律分布，即规模大的城市少， 规模小的城市多的齐普夫(Zipf)模式 [5,7] ，也被称为长尾效应 [8] 。当前位序-规模的研究只 能在排序中寻找规律，多为结合排名时间变化的分析测度 [9][10][11] ，而无法找出合适的分级方法。 城市规模研究需要更精细和准确的数据和新的分级支持。 当前的位序-规模的排序多以传统人口和经济数据作为依据， 不能反映城市实际经济活 动规模，而更开源和更新更快的数据有利于更实时、更便捷和更全面地了解城市规模，扩展 自然城市的研究方法。基于实际经济活动规模的边界划定，对城市边界划定和判断有重要的 现实意义，是增长边界划定的基础。基于边界划定而形成的等级分类则为当前城市群发展策 略下的区域城镇体系内中心的划定提供依据。 在当前的大数据时代背景下，涌现出越来越多的可用数据源，城市规模界定也呈现出更 加多元的研究方法，例如通过灯光遥感数据、交通路网交叉口数量、交通连接度、手机数据 以及社交网络位置数据等来重新测度自然城市的分布规模和等级 [12][13][14][15][16] 。 自然城市(natural cities)的理念来自于"城市并非树形" ，指空间上聚集的地理事件， 认为城市是动态的、开放的半网络结构，提供了基于复杂网络的城市研究视角 [17] ，其规模 测度方法强调使用自然、真实的人居和活动数据 [18] 。迈克尔·巴蒂(Michael Batty)以流、 引力和势能来解释自然城市的形成与发展，以联系度和相关性研究来构建城市新科学 [19] 。 相对于基于统计渠道的传统的人口和经济数据， 大数据刻画的自然城市更能全面和真实地反 映人类聚居和活动的强度。人居环境内在的多样性和非线性动力，使得自然城市继承了城市 分形的本质美学特征 [20][21][22][23] 但是自然断裂点法仍然没有解决 Zipf 模式下长尾数据分类的科学问题： (1)仍然无法 在类别数目上刻画出长尾数据的大头和长尾数据特性； (2)类值间隔需要人工指定，具有较 强的主观性。 针对分级数目和分级间距无法划定的缺陷， 瑞典耶夫勒大学 (University of Gävle) 的江斌(Bin Jiang)教授提出了 H/T 断裂点法(head/tail breaks) [14] 。 ...
Abstract: Scale hierarchy and boundary delimitation play an important role in urban research. Traditional statistic data such as population and economic scale cannot precisely define the real status, alternatively, new data such as light remote sensing, mobile phone signaling, road intersection and location-based social network (LBSN) have been introduced recently by more and more studies, intending to delimit the built-up area boundary, to measure the size and scale of the city with bottom-to-up approach. However, there are still two problems: lacking dividing standards and representing feature, therefore the H/T breaks point method is provided to classify scale and define boundary for cities. Based on point of interest (POI) data which representing various economic activities to make a triangular irregular network (TIN), the H/T breaks method is applied classifying the natural city scale in China mainland. The results show that the natural city boundary based on POI reflects the relative scale and density of human settlements, the H/T breaks point classification follows the Zipf’s law in rank-size method, offers a more scientific classifying method for naturally grouping of city scale according to the long tail rule and fractal structure of natural cites. The method has promotional value on urban scale measuring and classifying, with the advantage of precision and real data acquisition.
... This is because the degrees of wholeness under the influence of spatial configuration are more adapted to each other than to the cities' sizes. Second, with respect to Figs. 5 and 7, the foregrounds are hierarchal trees, while the foregrounds and backgrounds together constitute complex networks (Jiang 2015c). In other words, cities are near decomposable in terms of Simon (1962), or cities are not trees but semilattices (Alexander 1965). ...
... This is a deadly misperception (Alexander 1965). As demonstrated in the above case studies and elsewhere (Jiang 2015c), a city is not a tree, but a complex network. In other words, a complex network is no less orderly than a tree. ...
... A complex network is no less orderly than a tree. To put it in another way, a city is not a tree, but a complex network (Alexander 1965;Jiang 2015c). Living structures are governed by two laws: Tobler's law at a same scale and scaling law across all scales, or equivalently the two spatial properties of dependence and heterogeneity. ...
A city is a whole, as are all cities in a country. Within a whole, individual cities possess different degrees of wholeness, defined by Christopher Alexander as a life-giving order or simply a living structure. To characterize the wholeness and in particular to advocate for wholeness as an effective design principle, this paper developed a geographic representation that views cities as a whole. This geographic representation is topology-oriented, so fundamentally differs from existing geometry-based geographic representations. With the topological representation, all cities are abstracted as individual points and are put into different hierarchical levels, according to their sizes and based on head/tail breaks—a classification and visualization tool for data with a heavy-tailed distribution. These points of different hierarchical levels are respectively used to create Thiessen polygons. Based on polygon–polygon relationships, we set up a complex network. In this network, small polygons point to adjacent large polygons at the same hierarchical level and contained polygons point to containing polygons across two consecutive hierarchical levels. We computed the degrees of wholeness for individual cities, and subsequently found that the degrees of wholeness possess both properties of differentiation and adaptation. To demonstrate, we developed four case studies of all China and UK natural cities, as well as Beijing and London natural cities, using massive amounts of street nodes and Tweet locations. The topological representation and the kind of topological analysis in general can be applied to any design or pattern, such as carpets, Baroque architecture and artifacts, and fractals in order to assess their beauty, echoing the introductory quote from Christopher Alexander.
... This is because the degrees of wholeness under the influence of spatial configuration are more adapted to each other than to the cities' sizes. Second, with respect to Figs. 5 and 7, the foregrounds are hierarchal trees, while the foregrounds and backgrounds together constitute complex networks (Jiang 2015c). In other words, cities are near decomposable in terms of Simon (1962), or cities are not trees but semi-lattices (Alexander 1965). ...
... This is a deadly misperception (Alexander 1965). As demonstrated in the above case studies and elsewhere (Jiang 2015c), a city is not a tree, but a complex network. In other words, a complex network is no less orderly than a tree. ...
... A complex network is no less orderly than a tree. To put it in another way, a city is not a tree, but a complex network (Alexander 1965;Jiang 2015c). Living structures are governed by two laws: Tobler's law at the same scale and scaling law across all scales, or equivalently the two spatial properties of dependence and heterogeneity. ...
A city is a whole, as are all cities in a country. Within a whole, individual cities possess different degrees of wholeness, defined by Christopher Alexander as a life-giving order or simply a living structure. To characterize the wholeness and in particular to advocate for wholeness as an effective design principle, this paper develops a geographic representation that views cities as a whole. This geographic representation is topology-oriented, so fundamentally differs from existing geometry-based geographic representations. With the topological representation, all cities are abstracted as individual points and put into different hierarchical levels, according to their sizes and based on head/tail breaks - a classification and visualization tool for data with a heavy tailed distribution. These points of different hierarchical levels are respectively used to create Thiessen polygons. Based on polygon-polygon relationships, we set up a complex network. In this network, small polygons point to adjacent large polygons at the same hierarchical level and contained polygons point to containing polygons across two consecutive hierarchical levels. We computed the degrees of wholeness for individual cities, and subsequently found that the degrees of wholeness possess both properties of differentiation and adaptation. To demonstrate, we developed four case studies of all China and UK natural cities, as well as Beijing and London natural cities, using massive amounts of street nodes and Tweet locations. The topological representation and the kind of topological analysis in general can be applied to any design or pattern, such as carpets, Baroque architecture and artifacts, and fractals in order to assess their beauty, echoing the introductory quote from Christopher Alexander.
KEYWORDS: Wholeness, natural cities, head/tail breaks, complex networks, scaling hierarchy, urban design
