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His research interests center on geospatial analysis of urban structure and dynamics, e.g., topological analysis, and scaling hierarchy applied to buildings, streets, and cities, or geospatial big data in general. Inspired by Christopher Alexander’s work, he developed a mathematical model of beauty - beautimeter, which helps address not only why a structure is beautiful, but also how much beauty the structure is. Homepage: giscience.hig.se/binjiang/; Twitter: https://twitter.com/binjiangxp
This paper examines the spatial and temporal distribution of all COVID-19 cases from January to June 2020 against the underlying distribution of population in the United States. It is found that, as time passes, COVID-19 cases become a power law with cut-off, resembling the underlying spatial distribution of populations. The power law implies that many states and counties have a low number of cases, while only a few highly populated states and counties have a high number of cases. To further differentiate patterns between the underlying populations and COVID-19 cases, we derived their inherent hierarchy or spatial heterogeneity characterized by the ht-index. We found that the ht-index of COVID-19 cases persistently approaches that of the populations; that is, 5 and 7 at the state and county levels, respectively. Mapping the ht-index of COVID-19 cases against that of populations shows that the pandemic is largely shaped by the underlying population with the R-square value between infection and population up to 0.82.
Bin Jiang; Chris de Rijke. A Power-Law-Based Approach to Mapping COVID-19 Cases in the United States. Mapping COVID-19 in Space and Time 2021, 13 -23.
AMA StyleBin Jiang, Chris de Rijke. A Power-Law-Based Approach to Mapping COVID-19 Cases in the United States. Mapping COVID-19 in Space and Time. 2021; ():13-23.
Chicago/Turabian StyleBin Jiang; Chris de Rijke. 2021. "A Power-Law-Based Approach to Mapping COVID-19 Cases in the United States." Mapping COVID-19 in Space and Time , no. : 13-23.
Sustainable urban design or planning is not a LEGO-like assembly of prefabricated elements, but an embryo-like growth with persistent differentiation and adaptation towards a coherent whole. The coherent whole has a striking character – called living structure – that consists of far more small substructures than large ones. To detect the living structure, this paper develops a new approach for uncovering the underlying living structure of urban environments. The approach takes an urban environment as a whole and recursively decomposes it into meaningful subwholes at different levels of hierarchy (or scale) ranging from the largest to the smallest. This approach helps us not only better understand an urban environment as a living structure, but also better plan or transform the urban environment to be living or more living, or equivalently to be beautiful or more beautiful.
Bin Jiang; Ju-Tzu Huang. A new approach to detecting and designing living structure of urban environments. Computational Urban Science 2021, 1, 1 .
AMA StyleBin Jiang, Ju-Tzu Huang. A new approach to detecting and designing living structure of urban environments. Computational Urban Science. 2021; 1 (1):1.
Chicago/Turabian StyleBin Jiang; Ju-Tzu Huang. 2021. "A new approach to detecting and designing living structure of urban environments." Computational Urban Science 1, no. 1: 1.
To say that beauty is in the eye of the beholder means that beauty is largely subjective so varies from person to person. While the subjectivity view is commonly held, there is also an objectivity view that seeks to measure beauty or aesthetics in some quantitative manners. Christopher Alexander has long discovered that beauty or coherence highly correlates to the number of subsymmetries or substructures and demonstrated that there is a shared notion of beauty—structural beauty—among people and even different peoples, regardless of their faiths, cultures, and ethnicities. This notion of structural beauty arises directly out of living structure or wholeness, a physical and mathematical structure that underlies all space and matter. Based on the concept of living structure, this paper develops an approach for computing the structural beauty or life of an image (L) based on the number of automatically derived substructures (S) and their inherent hierarchy (H). To verify this approach, we conducted a series of case studies applied to eight pairs of images including Leonardo da Vinci’s Mona Lisa and Jackson Pollock’s Blue Poles. We discovered among others that Blue Poles is more structurally beautiful than the Mona Lisa, and traditional buildings are in general more structurally beautiful than their modernist counterparts. This finding implies that goodness of things or images is largely a matter of fact rather than an opinion or personal preference as conventionally conceived. The research on structural beauty has deep implications on many disciplines, where beauty or aesthetics is a major concern such as image understanding and computer vision, architecture and urban design, humanities and arts, neurophysiology, and psychology.
Bin Jiang; Chris de Rijke. Structural Beauty: A Structure-Based Computational Approach to Quantifying the Beauty of an Image. Journal of Imaging 2021, 7, 78 .
AMA StyleBin Jiang, Chris de Rijke. Structural Beauty: A Structure-Based Computational Approach to Quantifying the Beauty of an Image. Journal of Imaging. 2021; 7 (5):78.
Chicago/Turabian StyleBin Jiang; Chris de Rijke. 2021. "Structural Beauty: A Structure-Based Computational Approach to Quantifying the Beauty of an Image." Journal of Imaging 7, no. 5: 78.
Sustainable urban design or planning is not a LEGO-like assembly of prefabricated elements, but an embryo-like growth with persistent differentiation and adaptation towards a coherent whole. The coherent whole has a striking character – called living structure – that consists of far more small substructures than large ones. To detect the living structure, natural streets or axial lines have been previously adopted to be topologically represent an urban environment as a coherent whole. This paper develops a new approach to detecting the underlying living structure of urban environments. The approach takes an urban environment as a whole and recursively decomposes it into meaningful subwholes at different levels of hierarchy (or scale) ranging from the largest to the smallest. We compared the new approach to natural street and axial line approaches and demonstrated, through four case studies, that the new approach is better and more powerful. Based on the study, we further discuss how the new approach can be used not only for understanding but also – probably more importanly – for effectively designing or planning an urban environment to be living or more living.
Bin Jiang; Ju-Tzu Huang. A new approach to detecting and designing living structure of urban environments. Computers, Environment and Urban Systems 2021, 88, 101646 .
AMA StyleBin Jiang, Ju-Tzu Huang. A new approach to detecting and designing living structure of urban environments. Computers, Environment and Urban Systems. 2021; 88 ():101646.
Chicago/Turabian StyleBin Jiang; Ju-Tzu Huang. 2021. "A new approach to detecting and designing living structure of urban environments." Computers, Environment and Urban Systems 88, no. : 101646.
This paper examines the spatial and temporal distribution of all COVID-19 cases from January to June 2020 against the underlying distribution of population in the United States. It is found that, as time passes, COVID-19 cases become a power law with cutoff, resembling the underlying spatial distribution of populations. The power law implies that many states and counties have a low number of cases, while only a few highly populated states and counties have a high number of cases. To further differentiate patterns between the underlying populations and COVID-19 cases, we derived their inherent hierarchy or spatial heterogeneity characterized by the ht-index. We found that the ht-index of COVID-19 cases persistently approaches that of the populations; that is, 5 and 7 at the state and county levels, respectively. Mapping the ht-index of COVID-19 cases against that of populations shows that the pandemic is largely shaped by the underlying population with the R-square value between infection and population up to 0.82.
Bin Jiang; Chris de Rijke. A power-law-based approach to mapping COVID-19 cases in the United States. Geo-spatial Information Science 2021, 1 -7.
AMA StyleBin Jiang, Chris de Rijke. A power-law-based approach to mapping COVID-19 cases in the United States. Geo-spatial Information Science. 2021; ():1-7.
Chicago/Turabian StyleBin Jiang; Chris de Rijke. 2021. "A power-law-based approach to mapping COVID-19 cases in the United States." Geo-spatial Information Science , no. : 1-7.
The wholeness, conceived and developed by Christopher Alexander, is what exists to some degree or other in space and matter, and can be described by precise mathematical language. However, it remains somehow mysterious and elusive, and therefore hard to grasp. This paper develops a complex network perspective on the wholeness to better understand the nature of order or beauty for sustainable design. I bring together a set of complexity-science subjects such as complex networks, fractal geometry, and in particular underlying scaling hierarchy derived by head/tail breaks—a classification scheme and a visualization tool for data with a heavy-tailed distribution, in order to make Alexander’s profound thoughts more accessible to design practitioners and complexity-science researchers. Through several case studies (some of which Alexander studied), I demonstrate that the complex-network perspective helps reduce the mystery of wholeness and brings new insights to Alexander’s thoughts on the concept of wholeness or objective beauty that exists in fine and deep structure. The complex-network perspective enables us to see things in their wholeness, and to better understand how the kind of structural beauty emerges from local actions guided by the 15 fundamental properties, and by differentiation and adaptation processes. The wholeness goes beyond current complex network theory towards design or creation of living structures.
Bin Jiang. A Complex-Network Perspective on Alexander’s Wholeness. Spatial Synthesis 2020, 339 -354.
AMA StyleBin Jiang. A Complex-Network Perspective on Alexander’s Wholeness. Spatial Synthesis. 2020; ():339-354.
Chicago/Turabian StyleBin Jiang. 2020. "A Complex-Network Perspective on Alexander’s Wholeness." Spatial Synthesis , no. : 339-354.
Human actions and interactions are shaped in part by our direct environment. The studies of Christopher Alexander show that objects and structures can inhibit natural properties and characteristics; this is measured in living structure. He also found that we have better connection and feeling with more natural structures, as they more closely resemble ourselves. These theories are applied in this study to analyze and compare the urban morphology within different cities. The main aim of the study is to measure the living structure in cities. By identifying the living structure within cities, comparisons can be made between different types of cities, artificial and historical, and an estimation of what kind of effect this has on our wellbeing can be made. To do this, natural cities and natural streets are identified following a bottom-up data-driven methodology based on the underlying structures present in OpenStreetMap (OSM) road data. The naturally defined city edges (natural cities) based on intersection density and naturally occurring connected roads (natural streets) based on good continuity between road segments in the road data are extracted and then analyzed together. Thereafter, historical cities are compared with artificial cities to investigate the differences in living structure; it is found that historical cities generally consist of far more living structure than artificial cities. This research finds that the current usage of concrete, steel, and glass combined with very fast development speeds is detrimental to the living structure within cities. Newer city developments should be performed in symbiosis with older city structures as a whole, and the structure of the development should inhibit scaling as well as the buildings themselves.
Chris A. De Rijke; Gloria Macassa; Mats Sandberg; Bin Jiang. Living Structure as an Empirical Measurement of City Morphology. ISPRS International Journal of Geo-Information 2020, 9, 677 .
AMA StyleChris A. De Rijke, Gloria Macassa, Mats Sandberg, Bin Jiang. Living Structure as an Empirical Measurement of City Morphology. ISPRS International Journal of Geo-Information. 2020; 9 (11):677.
Chicago/Turabian StyleChris A. De Rijke; Gloria Macassa; Mats Sandberg; Bin Jiang. 2020. "Living Structure as an Empirical Measurement of City Morphology." ISPRS International Journal of Geo-Information 9, no. 11: 677.
A new method for selecting optimal scales when mapping topographic or hydrographic features is introduced. The method employs rank-size partition of heavy-tailed distributions to detect nodes of rescaling invariance in the underlying hierarchy of the dataset. These nodes, known as head/tail breaks, can be used to indicate optimal scales. Then, the Fractal Net Evolution Assessment (FNEA) segmentation algorithm is applied with the topographic or hydrographic surfaces to produce optimally scaled objects. A topological transformation allows linking the two processes (partition and segmentation), while fractal dimension of the rescaling process is employed as an optimality metric. The new method is experimented with the two biggest river basins in Greece, namely Pinios and Acheloos river basins, using a digital elevation model as the only input dataset. The method proved successful in identifying a set of optimal scales for mapping elevation, slope, and flow accumulation. Deviation from the ideal conditions for implementing head/tail breaks are discussed. Implementation of the method requires an object-based analysis program and few common geospatial functions embedded in most GIS programs. The new method will assist in revealing underlying environmental processes in a variety of earth science fields and, thus, assist in land management decision-making and mapping generalization.
Christos Karydas; Bin Jiang. Scale Optimization in Topographic and Hydrographic Feature Mapping Using Fractal Analysis. ISPRS International Journal of Geo-Information 2020, 9, 631 .
AMA StyleChristos Karydas, Bin Jiang. Scale Optimization in Topographic and Hydrographic Feature Mapping Using Fractal Analysis. ISPRS International Journal of Geo-Information. 2020; 9 (11):631.
Chicago/Turabian StyleChristos Karydas; Bin Jiang. 2020. "Scale Optimization in Topographic and Hydrographic Feature Mapping Using Fractal Analysis." ISPRS International Journal of Geo-Information 9, no. 11: 631.
The Earth’s surface or any territory is a coherent whole or subwhole, in which the notion of “far more small things than large ones” recurs at different levels of scale ranging from the smallest of a couple of meters to the largest of the Earth’s surface or that of the territory. The coherent whole has the underlying character called wholeness or living structure, which is a physical phenomenon pervasively existing in our environment and can be defined mathematically under the new third view of space conceived and advocated by Christopher Alexander: space is neither lifeless nor neutral, but a living structure capable of being more alive or less alive. This paper argues that both the map and the territory are a living structure, and that it is the inherent hierarchy of “far more smalls than larges” that constitutes the foundation of maps and mapping. It is the underlying living structure of geographic space or geographic features that makes maps or mapping possible, i.e., larges to be retained, while smalls to be omitted in a recursive manner (Note: larges and smalls should be understood broadly and wisely, in terms of not only sizes, but also topological connectivity and semantic meaning). Thus, map making is largely an objective undertaking governed by the underlying living structure, and maps portray the truth of the living structure. Based on the notion of living structure, a map can be considered to be an iterative system, which means that the map is the map of the map of the map, and so on endlessly. The word endlessly means continuous map scales between two discrete ones, just as there are endless real numbers between 1 and 2. The iterated map system implies that each of the subsequent small-scale maps is a subset of the single large-scale map, not a simple subset but with various constraints to make all geographic features topologically correct.
Bin Jiang; Terry Slocum. A Map Is a Living Structure with the Recurring Notion of Far More Smalls than Larges. ISPRS International Journal of Geo-Information 2020, 9, 388 .
AMA StyleBin Jiang, Terry Slocum. A Map Is a Living Structure with the Recurring Notion of Far More Smalls than Larges. ISPRS International Journal of Geo-Information. 2020; 9 (6):388.
Chicago/Turabian StyleBin Jiang; Terry Slocum. 2020. "A Map Is a Living Structure with the Recurring Notion of Far More Smalls than Larges." ISPRS International Journal of Geo-Information 9, no. 6: 388.
As noted in the epigraph, a map was long ago seen as the map of the map, the map of the map, of the map, and so on endlessly. This recursive perspective on maps, however, has received little attention in cartography. Cartography, as a scientific discipline, is essentially founded on Euclidean geometry and Gaussian statistics, which deal respectively with regular shapes and more or less similar things. It is commonly accepted that geographic features are not regular and that the Earth’s surface is full of fractal or scaling or living phenomena: far more small things than large ones are found at different scales. This article argues for a new paradigm in mapping, based on fractal or living geometry and Paretian statistics, and – more critically – on the new conception of space, conceived and developed by Christopher Alexander, as neither lifeless nor neutral, but a living structure capable of being more living or less living. The fractal geometry is not limited to Benoit Mandelbrot’s framework, but tends towards Christopher Alexander’s living geometry and is based upon the third definition of fractal: A set or pattern is fractal if the scaling of far more small things than large ones recurs multiple times. Paretian statistics deals with far more small things than large ones, so it differs fundamentally from Gaussian statistics, which deals with more or less similar things. Under the new paradigm, I make several claims about maps and mapping: (1) the topology of geometrically coherent things – in addition to that of geometric primitives – enables us to see a scaling or fractal or living structure; (2) under the third definition, all geographic features are fractal or living, given the right perspective and scope; (3) exactitude is not truth – to paraphrase Henri Matisse – but the living structure is; and (4) Töpfer’s law is not universal, but the scaling law is. All these assertions are supported by evidence, drawn from a series of previous studies. This article demands a monumental shift in perspective and thinking from what we are used to in the legacy of cartography and GIS.
Bin Jiang. New Paradigm in Mapping: A Critique on Cartography and GIS. Cartographica: The International Journal for Geographic Information and Geovisualization 2019, 54, 193 -205.
AMA StyleBin Jiang. New Paradigm in Mapping: A Critique on Cartography and GIS. Cartographica: The International Journal for Geographic Information and Geovisualization. 2019; 54 (3):193-205.
Chicago/Turabian StyleBin Jiang. 2019. "New Paradigm in Mapping: A Critique on Cartography and GIS." Cartographica: The International Journal for Geographic Information and Geovisualization 54, no. 3: 193-205.
Discovered by Christopher Alexander, living structure is a physical phenomenon, through which the quality of the built environment or artifacts can be judged objectively. It has two distinguishing properties just like a tree: “Far more small things than large ones” across all scales from the smallest to the largest, and “more or less similar things” on each scale. As a physical phenomenon, and mathematical concept, living structure is essentially empirical, discovered and developed from miniscule observation in nature- and human-made things, and it affects our daily lives in some practical ways, such as where to put a table or a flower vase in a room, helping us to make beautiful things and environments. Living structure is not only empirical, but also philosophical and visionary, enabling us to see the world and space in more meaningful ways. This paper is intended to defend living structure as a physical phenomenon, and a mathematical concept, clarifying some common questions and misgivings surrounding Alexander’s design thoughts, such as the objective or structural nature of beauty, building styles advocated by Alexander, and mysterious nature of his concepts. For this purpose, we first illustrate living structure—essentially organized complexity, as advocated by the late Jane Jacobs (1916–2006)—that is governed by two fundamental laws (scaling law and Tobler’s law), and generated in some step by step fashion by two design principles (differentiation and adaptation) through the 15 structural properties. We then verify why living structure is primarily empirical, drawing evidence from Alexander’s own work, as well as our case studies applied to the Earth’s surface including cities, streets, and buildings, and two logos. Before reaching conclusions, we concentrate on the most mysterious part of Alexander’s work—the luminous ground or the hypothesized “I”—as a substance that pervasively exists everywhere, in space and matter including our bodies, in order to make better sense of living structure in our minds.
Bin Jiang. Living Structure Down to Earth and Up to Heaven: Christopher Alexander. Urban Science 2019, 3, 96 .
AMA StyleBin Jiang. Living Structure Down to Earth and Up to Heaven: Christopher Alexander. Urban Science. 2019; 3 (3):96.
Chicago/Turabian StyleBin Jiang. 2019. "Living Structure Down to Earth and Up to Heaven: Christopher Alexander." Urban Science 3, no. 3: 96.
Conceived and developed by Christopher Alexander through his life’s work, The Nature of Order, wholeness is defined as a mathematical structure of physical space in our surroundings. Yet, there was no mathematics, as Alexander admitted then, that was powerful enough to capture his notion of wholeness. Recently, a mathematical model of wholeness, together with its topological representation, has been developed that is capable of addressing not only why a space is good, but also how much goodness the space has. This paper develops a structural perspective on goodness of space (both large- and small-scale) in order to bridge two basic concepts of space and place through the very concept of wholeness. The wholeness provides a de facto recursive definition of goodness of space from a holistic and organic point of view. A space is good, genuinely and objectively, if its adjacent spaces are good, the larger space to which it belongs is good, and what is contained in the space is also good. Eventually, goodness of space, or sustainability of space, is considered a matter of fact rather than of opinion under the new view of space: space is neither lifeless nor neutral, but a living structure capable of being more living or less living, or more sustainable or less sustainable. Under the new view of space, geography or architecture will become part of complexity science, not only for understanding complexity, but also for making and remaking complex or living structures.
Bin Jiang. A Recursive Definition of Goodness of Space for Bridging the Concepts of Space and Place for Sustainability. Sustainability 2019, 11, 4091 .
AMA StyleBin Jiang. A Recursive Definition of Goodness of Space for Bridging the Concepts of Space and Place for Sustainability. Sustainability. 2019; 11 (15):4091.
Chicago/Turabian StyleBin Jiang. 2019. "A Recursive Definition of Goodness of Space for Bridging the Concepts of Space and Place for Sustainability." Sustainability 11, no. 15: 4091.
Capturing and characterizing collective human activities in a geographic space have become much easier than ever before in the big era. In the past few decades it has been difficult to acquire the spatiotemporal information of human beings. Thanks to the boom in the use of mobile devices integrated with positioning systems and location-based social media data, we can easily acquire the spatial and temporal information of social media users. Previous studies have successfully used street nodes and geo-tagged social media such as Twitter to predict users’ activities. However, whether human activities can be well represented by social media data remains uncertain. On the other hand, buildings or architectures are permanent and reliable representations of human activities collectively through historical footprints. This study aims to use the big data of US building footprints to investigate the reliability of social media users for human activity prediction. We created spatial clusters from 125 million buildings and 1.48 million Twitter points in the US. We further examined and compared the spatial and statistical distribution of clusters at both country and city levels. The result of this study shows that both building and Twitter data spatial clusters show the scaling pattern measured by the scale of spatial clusters, respectively, characterized by the number points inside clusters and the area of clusters. More specifically, at the country level, the statistical distribution of the building spatial clusters fits power law distribution. Inside the four largest cities, the hotspots are power-law-distributed with the power law exponent around 2.0, meaning that they also follow the Zipf’s law. The correlations between the number of buildings and the number of tweets are very plausible, with the r square ranging from 0.53 to 0.74. The high correlation and the similarity of two datasets in terms of spatial and statistical distribution suggest that, although social media users are only a proportion of the entire population, the spatial clusters from geographical big data is a good and accurate representation of overall human activities. This study also indicates that using an improved method for spatial clustering is more suitable for big data analysis than the conventional clustering methods based on Euclidean geometry.
Zheng Ren; Bin Jiang; Stefan Seipel; Ren. Capturing and Characterizing Human Activities Using Building Locations in America. ISPRS International Journal of Geo-Information 2019, 8, 200 .
AMA StyleZheng Ren, Bin Jiang, Stefan Seipel, Ren. Capturing and Characterizing Human Activities Using Building Locations in America. ISPRS International Journal of Geo-Information. 2019; 8 (5):200.
Chicago/Turabian StyleZheng Ren; Bin Jiang; Stefan Seipel; Ren. 2019. "Capturing and Characterizing Human Activities Using Building Locations in America." ISPRS International Journal of Geo-Information 8, no. 5: 200.
Authorities define cities—or human settlements in general—through imposing top-down rules in terms of whether buildings belong to cities. Emerging geospatial big data makes it possible to define cities from the bottom up, i.e., buildings determine themselves whether they belong to a city using the notion of natural cities and based on head/tail breaks, which is a classification and visualization tool for data with a heavy-tailed distribution. In this paper, we used 125 million building locations—all building footprints of America (mainland) or their centroids more precisely—to generate 2.1 million natural cities in the country (see the URL as shown in the note of Figure 1). In contrast to government defined city boundaries, these natural cities constitute a valuable data source for city-related research.
Bin Jiang. Natural Cities Generated from All Building Locations in America. Data 2019, 4, 59 .
AMA StyleBin Jiang. Natural Cities Generated from All Building Locations in America. Data. 2019; 4 (2):59.
Chicago/Turabian StyleBin Jiang. 2019. "Natural Cities Generated from All Building Locations in America." Data 4, no. 2: 59.
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.
Bin Jiang. A Topological Representation for Taking Cities as a Coherent Whole. Mathematical and Numerical Foundations of Turbulence Models and Applications 2019, 335 -352.
AMA StyleBin Jiang. A Topological Representation for Taking Cities as a Coherent Whole. Mathematical and Numerical Foundations of Turbulence Models and Applications. 2019; ():335-352.
Chicago/Turabian StyleBin Jiang. 2019. "A Topological Representation for Taking Cities as a Coherent Whole." Mathematical and Numerical Foundations of Turbulence Models and Applications , no. : 335-352.
This editorial briefly introduces Christopher Alexander, as a theorist, as a design practitioner, as an architect, and importantly as a scientist, as well as his life’s work—The Nature of Order—focusing not only on the trinity of wholeness, life, beauty, but also on his new organic cosmology.
Bin Jiang. Christopher Alexander and His Life’s Work: The Nature of Order. Urban Science 2019, 3, 30 .
AMA StyleBin Jiang. Christopher Alexander and His Life’s Work: The Nature of Order. Urban Science. 2019; 3 (1):30.
Chicago/Turabian StyleBin Jiang. 2019. "Christopher Alexander and His Life’s Work: The Nature of Order." Urban Science 3, no. 1: 30.
As noted in the introductory quotation, an ideal map was long ago seen as the map of the map, the map of the map, of the map, and so on endlessly. This recursive perspective on maps, however, has received little attention in cartography. Cartography, as a scientific discipline, is essentially founded on Euclidean geometry and Gaussian statistics, which deal with respectively regular shapes, and more or less similar things. It is commonly accepted that geographic features – such as rivers, cities, streets and building – are not regular and that the Earth’s surface is full of fractal or scaling or living phenomena with far more small things than large ones at different levels of scale. This paper argues for a new paradigm in mapping, based on fractal or living geometry and Paretian statistics, and – more critically – on the new conception of space, conceived and developed by Christopher Alexander, that space is neither lifeless nor neutral, but a living structure capable of being more living or less living. The fractal geometry is not limited to Benoit Mandelbrot’s framework, but is extended towards Christopher Alexander’s living geometry and based upon the third definition of fractal: A set or pattern is fractal if the scaling of far more small things than large ones recurs multiple times. Paretian statistics deals with far more small things than large ones, so it differs fundamentally from Gaussian statistics, which deals with more or less similar things. Under the new paradigm, I make several claims about maps and mapping: (1) Topology of geometrically coherent things – in addition to that of geometric primitives – enables us to see a scaling or fractal or living structure; (2) Under the third definition, all geographic features are fractal or living, given the right perspective and scope; (3) Exactitude is not truth – to paraphrase Henri Matisse – but the living structure is; and (4) Töpfer’s law is not universal, but scaling law is. All these assertions are supported by evidence, drawn from a series of previous studies. This paper demands a monumental shift in perspective and thinking from what we are used to on the legacy of cartography and GIS.
Bin Jiang. New Paradigm in Mapping: A Critique on Cartography and GIS. 2019, 1 .
AMA StyleBin Jiang. New Paradigm in Mapping: A Critique on Cartography and GIS. . 2019; ():1.
Chicago/Turabian StyleBin Jiang. 2019. "New Paradigm in Mapping: A Critique on Cartography and GIS." , no. : 1.
I have advocated and argued for a paradigm shift from Tobler’s law to scaling law, from Euclidean geometry to fractal geometry, from Gaussian statistics to Paretian statistics, and – more importantly – from Descartes’ mechanistic thinking to Alexander’s organic thinking. Fractal geometry falls under the third definition of fractal given by Bin Jiang – that is, a set or pattern is fractal if the scaling of far more small things than large ones recurs multiple times – rather than under the second definition of fractal by Benoit Mandelbrot, which requires a power law between scales and details. The new fractal geometry is more towards Christopher Alexander’s living geometry, not only for understanding complexity, but also for creating complex or living structure. This short paper attempts to clarify why the paradigm shift is essential and to elaborate on several concepts, including spatial heterogeneity (scaling law), scale (or the fourth meaning of scale), data character (in contrast to data quality), and sustainable transport in the big data era.
Bin Jiang. Spatial Heterogeneity, Scale, Data Character, and Sustainable Transport in the Big Data Era. Advances in Intelligent Systems and Computing 2018, 730 -736.
AMA StyleBin Jiang. Spatial Heterogeneity, Scale, Data Character, and Sustainable Transport in the Big Data Era. Advances in Intelligent Systems and Computing. 2018; ():730-736.
Chicago/Turabian StyleBin Jiang. 2018. "Spatial Heterogeneity, Scale, Data Character, and Sustainable Transport in the Big Data Era." Advances in Intelligent Systems and Computing , no. : 730-736.
Geographic space is better understood through the topological relationship of the underlying streets (note: entire streets rather than street segments), which enables us to see scaling or fractal or living structure of far more less-connected streets than well-connected ones. It is this underlying scaling structure that makes human activities predictable, albeit in the sense of collective rather than individual human moving behavior. This topological analysis has not yet received its deserved attention in the literature, as many researchers continue to rely on segment analysis for predicting human activities. The segment analysis-based methods are essentially geometric, with a focus on geometric details of locations, lengths, and directions, and are unable to reveal the scaling property, which means they cannot be used for the prediction of human activities. We conducted a series of case studies using London streets and tweet location data, based on related concepts such as natural streets, and natural street segments (or street segments for short), axial lines, and axial line segments (or line segments for short). We found that natural streets are the best representation in terms of human activities or traffic prediction, followed by axial lines, and that neither street segments nor line segments bear a good correlation between network parameters and tweet locations. These findings point to the fact that the reason why space syntax based on axial lines, or the kind of topological analysis in general, works has little to do with individual human travel behavior or ways that humans conceptualize distances or spaces. Instead, it is the underlying scaling hierarchy of streets – numerous least-connected, a very few most-connected, and some in between the least- and most-connected – that makes human activities predictable.
Ding Ma; Itzhak Omer; Toshihiro Osaragi; Mats Sandberg; Bin Jiang. Why topology matters in predicting human activities. Environment and Planning B: Urban Analytics and City Science 2018, 46, 1297 -1313.
AMA StyleDing Ma, Itzhak Omer, Toshihiro Osaragi, Mats Sandberg, Bin Jiang. Why topology matters in predicting human activities. Environment and Planning B: Urban Analytics and City Science. 2018; 46 (7):1297-1313.
Chicago/Turabian StyleDing Ma; Itzhak Omer; Toshihiro Osaragi; Mats Sandberg; Bin Jiang. 2018. "Why topology matters in predicting human activities." Environment and Planning B: Urban Analytics and City Science 46, no. 7: 1297-1313.
Hierarchies can be modeled by a set of exponential functions, from which we can derive a set of power laws indicative of scaling. The solution to a scaling relation equation is always a power law. The scaling laws are followed by many natural and social phenomena such as cities, earthquakes, and rivers. This paper reveals the power law behaviors in systems of natural cities by reconstructing the urban hierarchy with cascade structure. Cities of the U.S.A., Britain, France, and Germany are taken as examples to perform empirical analyses. The hierarchical scaling relations can be well fitted to the data points within the scaling ranges of the number, size and area of the natural cities. The size-number and area-number scaling exponents are close to 1, and the size-area allometric scaling exponent is slightly less than 1. The results show that natural cities follow hierarchical scaling laws very well. The principle of entropy maximization of urban evolution is then employed to explain the hierarchical scaling laws, and differences entropy maximizing processes are used to interpret the scaling exponents. This study is helpful for scientists to understand the power law behavior in the development of cities and systems of cities.
Yanguang Chen; Bin Jiang. Hierarchical Scaling in Systems of Natural Cities. Entropy 2018, 20, 432 .
AMA StyleYanguang Chen, Bin Jiang. Hierarchical Scaling in Systems of Natural Cities. Entropy. 2018; 20 (6):432.
Chicago/Turabian StyleYanguang Chen; Bin Jiang. 2018. "Hierarchical Scaling in Systems of Natural Cities." Entropy 20, no. 6: 432.