Project

ALEXANDER: Automated generation of living structure for biophilic urban design

Goal: Living structure, which is characterized by far more small things than large ones globally and more or less similar things locally, exists inherently in any part of space: towns, streets, buildings, gardens, and even artifacts. To measure the degrees of livingness or beauty, I have developed a mathematical model that helps address not only why a space is alive, but also how much alive it is. I have used geospatial big data to demonstrate the living structure at country and city levels. Based on these previous studies both theoretically and empirically, this present project - named in honor of Christopher Alexander - intends to develop a design tool for automatically generating living structure for biophilic urban design. We will develop a suite of differentiating algorithms to create living structures based on city plans of historical cities such as Venice, Rome, and Amsterdam. We will set up SimCity-like simulations to conduct what-if modeling in order to better understand why and how these living structures work. The developed tool will be testified and improved through experiments with spatial planning students and design practitioners. The design tools targeted at biophilic urban design – in terms of creating living structures rather than increasing buildings’ aesthetic appeal through inserting trees and shrubs – provide an alternative to existing industrial design tools such as AutoCAD, and thus help make or remake urban environments living, beautiful, and sustainable. As Alexander claimed, the goodness or quality of a built environment is not a matter of opinion as we currently conceive, but a matter of fact. This fact is founded on the scientific notion of living structure or wholeness or life or beauty. This project will send a clear message to the design world that there is a better alternative to the industrial design models for sustainable urban design.

Updates
0 new
30
Recommendations
0 new
9
Followers
0 new
98
Reads
8 new
3802

Project log

Bin Jiang
added a research item
A commentary reflects on Christopher Alexander's (1936-2022) pursuit of living structure in cities, published online in Buildings and Cities: https://www.buildingsandcities.org/insights/commentaries/christopher-alexander.html
Bin Jiang
added a research item
The third view of space states that space is neither lifeless nor neutral, but a living structure capable of being more living or less living, which was formulated by Christopher Alexander under the organismic world view that was first conceived by the British philosopher Alfred Whitehead (1861–1947). The living structure is defined as a physical and mathematical structure or simply characterized by the recurring notion (or inherent hierarchy) of far more small substructures than large ones. The more substructures the more living or more beautiful structurally, and the higher hierarchy of the substructures the more living or more beautiful structurally. This paper seeks to lay out a new kind of city science on the notion of living structure and on the third view of space. The new city science aims not only to better understand geographic forms and processes but also-maybe more importantly-to make geographic space or the Earth's surface living or more living. We introduce two fundamental laws of living structure: Tobler's law on spatial dependence or homogeneity and scaling law on spatial interdependence or heterogeneity. We further argue that these two laws favor statistics over exactitude, because the statistics tends to make a structure more living than the exactitude. We present the concept of living structure through some working examples and make it clear how a living structure differs from a non-living structure. In order to make a structure or space living or more living, we introduce two design principles-differentiation and adaptation-using two paintings and two city plans as working examples. The new city science is a science of living structure, dealing with a wide range of scales, from the smallest scale of ornaments on walls to the scale of the entire Earth's surface.
Bin Jiang
added a research item
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. 关键词 城市设计/规划;结构美;空间句法;自然街道;活力;整体
Bin Jiang
added a research item
The third (or organismic) view of space states that space is neither lifeless nor neutral, but a living structure capable of being more living or less living, thus different fundamentally from the first two mechanistic views of space: Newtonian absolute space and Leibnizian relational space. The living structure is defined as a physical and mathematical structure or simply characterized by the recurring notion (or inherent hierarchy) of far more small substructures than large ones. This paper seeks to lay out a new geography as a science of the Earth’s surface founded on the third view of space. The new geography aims not only to better understand geographic forms and processes but also – maybe more importantly – to make geographic space or the Earth’s surface to be living or more living. After introducing two fundamental laws of geography: Tobler’s law on spatial dependence (or homogeneity) and scaling law on spatial heterogeneity, we argue that these two laws are fundamental laws of living structure that favor statistics over exactitude, because the former (or statistics) tends to make a structure more living than the latter (or exactitude). We present the concept of living structure through some working examples and make it clear how a living structure differs from a non-living structure, under the organismic worldview that was first conceived by the British philosopher Alfred Whitehead (1861–1947). In order to make a structure or space living or more living, we introduce two design principles – differentiation and adaptation – using two paintings and two city plans. The new geography is a science of living structure, dealing with a wide range of scales, from the smallest scale of ornaments on walls to the scale of the entire Earth’s surface. Keywords: Scaling law, Tobler’s law, differentiation, adaptation, head/tail breaks, natural streets, the third view of space
Bin Jiang
added 2 research items
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 for effectively designing or planning the living structure of an urban environment to be more living or more livable. Keywords: Urban design or planning, structural beauty, space syntax, natural streets, life, wholeness
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 for effectively designing or planning the living structure of an urban environment to be more living or more livable. Keywords: Urban design or planning, structural beauty, space syntax, natural streets, life, wholeness
Bin Jiang
added a research item
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
added 2 research items
This lecture is divided into two parts: The first part is on Christopher Alexander, focusing on this person as a scientific maverick in architecture. He is not only a design theorist, but also a design practitioner. His influence goes beyond architecture towards computer science and many other fields. The second part is on his life’s work The Nature of Order, or the theory of living structure, and how it can be used to transform modern cities to be living or more living.
This lecture is divided into two parts: The first part is on Christopher Alexander, focusing on this person as a scientific maverick in architecture. He is not only a theorist, but also a design practitioner. His influence goes beyond architecture towards computer science and many other fields. The second part is on his life’s work The Nature of Order, or the theory of living structure, and how it can be used to transform modern cities to be living or more living.
Bin Jiang
added a research item
Objectives: • To advocate living structure as a scientific foundation of city science • To bridge space and place through the concept of living structure or wholeness • To practice on big data analytics using open-source data
Bin Jiang
added a research item
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
added a research item
This presentation is intended to bridge together two separate concepts – space and place – through the very concept of wholeness. Space is external to our body and mind, while place is how space is experienced in our heart and mind, so it is internal. Wholeness (or living structure) exists physically in our surrounding (just like air), can be defined mathematically, and well reflected in our heart and mind psychologically. The term "spatial healing" has two different meanings: the healing effect of good space on people on the one hand, and space to be healed to become living or more living on the other. A key message of this presentation is that there is a shared notion of the goodness of space or place among peoples regardless their cultures, faiths, and ethnicities. The goodness of space is largely determined by the underlying living structure that consists of numerous substructures. A general rule goes like this: the more substructures, the more beautiful; the higher hierarchy of the substructures, the more beautiful.
Bin Jiang
added a research item
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. In a good system, we would expect to find the following conditions: Any identifiable subsystems, we would hope, would be well-that is to say, in good condition. And we would hope that the larger world outside the complex system is also in good order, and well. Thus, the mark of a good system would be that it helps both the systems around it and those which it contains. And the goodness and helping towards goodness is, in our ideal complex system, also reciprocal. That is, our good system, will turn out to be not only helping other systems to become good, but also, in turn, helped by the goodness of the larger systems around it and by the goodness of the smaller ones which it contains.
Bin Jiang
added a research item
Living structure is a physical phenomenon and mathematical concept, through which the quality of buildings or artifacts can be judged objectively. Living structure is to beauty what temperature is to warmness. Just like a tree, a living structure has two distinguishing properties: "far more small things than large ones" (so called scaling law) across all scales from the smallest to the largest, and "more or less similar things" (so called Tobler's law) on each scale. Living structure can be only generated in some step by step fashion by two design principles (differentiation and adaptation) through the 15 structural properties. 关键词 生命结构;第三空间观;整体性;生命;美
Bin Jiang
added a research item
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.
Bin Jiang
added a research item
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.
Bin Jiang
added a research item
In this session, we are interested in papers that contribute to a better understanding of sustainable spatial planning for promoting human health and emotional wellbeing. Some related keywords include but not limited to living structure, space syntax, smart cities, biophilia, fractals, and design patterns.
Bin Jiang
added a research item
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
added a research item
It is a reprint by the magazine Coordinates from the previous journal article published by MDPI.
Bin Jiang
added a research item
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, 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
added a research item
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. This paper helps people understand why beautiful things are beautiful, and why ugly things are ugly, through the underlying living structure. Living structure is to beauty what temperature is to warmness. Readers may recall that we published the down to earth part of the paper in March issue. Here we present the up to heaven and concluding part of the paper
Bin Jiang
added a research item
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. This paper helps people understand why beautiful things are beautiful, and why ugly things are ugly, through the underlying living structure. Living structure is to beauty what temperature is to warmness. We present here the first part of the paper or the down to earth part. The second part or the up to heaven and concluding part will be published in April issue.
Bin Jiang
added a research item
Based on the theory of Christopher Alexander, this paper develops a complex network perspective on the wholeness to better understand the nature of order or beauty for sustainable design. The author brings together a set of complexity-science subjects in order to make Alexander's profound thoughts more accessible to design practitioners and complexity science researchers, make it better understand how the kind of structural beauty emerges. The wholeness goes beyond current complex network theory towards design or creation of living structures. 关键词 中心理论;分形几何;克里斯托弗·亚历山大;头尾分割;美
Bin Jiang
added a research item
Living structure is a physical phenomenon, just like a tree, that has two distinguishing properties: “more or less similar things” at each scale, and “far more small things than large ones” across all scales ranging from the smallest to the largest. These two notions underlie the two fundamental laws of living structure: Tobler’s Law and Scaling Law. The Earth’s surface is essentially a living structure. ... . In this workshop, we will attempt to challenge the current paradigm of our discipline, regardless how it is named, either geography or cartography or GIScience, by advocating a new mapping paradigm. We will use the two concepts – natural cities and natural streets – to demonstrate the ubiquity of living structure and Scaling Law, and further demonstrate the automatic generation of all small-scale databases from a single large-scale database. The generated databases are not only for discrete map scales, but also for any scale in between. Some hands-on work will be carried out with two tools: Axwoman and head/tail breaks.
Bin Jiang
added a research item
A good space has a healing effect. Mechanistic view of space (Newton, Leibnitz, and Descartes). Organic view of space (Alexander). Living structure as a mathematical structure of physical structure (external). Place is human-experienced space (internal). Two laws of living structure: scaling law and Tobler’s law. Goodness of space as a fact rather than opinion. Conclusion: Two concepts of space and place are not separated – as currently perceived, or under the current mode of thinking – but can be bridged through the very concept of wholeness. Goodness of space can be objectively judged as a matter of fact rather than of opinion. * The more the centers, the more beautiful; * The higher the hierarchy, the more beautiful. Goodness of space can be well reflected as our inner experience with a good sense of belonging, well-being, and healing.
Bin Jiang
added a research item
As Christopher Alexander conceived and defined through his life's work – The Nature of Order – wholeness is a recursive structure that recurs in space and matter and is reflected in human minds and cognition. Based on the definition of wholeness, a mathematical model of wholeness, together with its topological representation, has been developed, and it is able to address not only why a structure is beautiful, but also how much beauty the structure has. Given the circumstance, this paper is attempted to argue for the wholeness as the scientific foundation of sustainable urban design and planning, with the help of the mathematical model and topological representation. We start by introducing the wholeness as a mathematical structure of physical space that pervasively exists in our surroundings, along with two fundamental laws – scaling law and Tobler's law – that underlie the 15 properties for characterizing and making living structures. We argue that urban design and planning can be considered to be wholeness-extending processes, guided by two design principles of differentiation and adaptation, to transform a space – in a piecemeal fashion – into a living or more living structure. We further discuss several other urban design theories and how they can be justified by and placed within the theory of wholeness. With the wholeness as the scientific foundation, urban design can turn into a rigorous science with creation of living structures as the primary aim.
Bin Jiang
added a research item
There are three fundamental issues about a transport system or geographic space in general: How it looks, how it works, and what it ought to be. In terms of how it looks and works, there are two laws governing geographic forms and processes or urban structure and dynamics in particular: scaling law and Tobler’s law. Scaling law is available across all scales ranging from the smallest to largest, and it states that there are "far more smalls than larges" in geographic space. For example, there are "far more small mountains than big ones"; "far more low elevations than high ones"; "far more short rivers than long ones"; "far more small cities than big ones"; "far more less-connected streets than well-connected ones"; and "far more meaningless locations than meaningful ones". Tobler’s law is available at one scale, and it states that "more or less similar things" tend to be nearby or related. For example, your housing price is more similar to those of your neighbors than to those of your neighbors’ neighbors; two elevations one meter away are more similar than two that are 10 meters away; and today’s weather is more similar to that of yesterday than to that of the day before yesterday. These two laws, complementary each other and recurring at different levels of scale, well characterize a transport system or the Earth’s surface. Geographic forms or urban structure change nonlinearly, so geographic processes or urban dynamics are essentially unpredictable, but they can be effectively dealt with from the topological and scaling perspective. In terms of what it ought to be, there are two design principles that help make a better transport system: differentiation and adaptation, in line respectively with the scaling law and Tobler’s law. In this workshop, I will use two concepts of natural cities and natural streets to demonstrate the ubiquity of scaling law, and further argue how to make a transport system more living or more sustainable based on these two design principles. Some hands-on will be carried out with two tools: Axwoman and head/tail breaks.
Bin Jiang
added a research item
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 bears two distinguished 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 substantial 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. Keywords: Living structure, third view of space, wholeness, life, beauty, new cosmology
Bin Jiang
added a research item
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 – 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
added a research item
Summary of the teaching - 1 + 2 + 3: 1 whole: All works of Alexander is one; 1 order: order in nature is the same as one in what we make or build; 1 world: human and reality is not separated (Alexander's organic world picture); 1 piece: science and art in one, towards the third culture; 1 piece: science and religion in one, under the organic worldview; 1 making: design and building in one (against paper-based design); 2 fundamental laws: scaling law + Tobler's law; 2 design principles: differentiation + adaptation; 2 tools: AXWOMAN + head/tail breaks; 2 concepts: natural streets + natural cities; 2 geometries: fractal geometry + living geometry; 2 ways of thinking: topology + scaling; 2 papers: on spatial heterogeneity + scale; 2 masters: Alexander + Mandelbrot; 3 definitions of fractal (3rd definition in particular); 3 aspects of architecture or geography (looks, works, and creation/ought to be); 3 terms with a same meaning: scaling, fractal, living; 3 terms with a same meaning: wholeness, life, and beauty; 3 aspects of the wholeness, mathematically, physically, and psychologically.
Bin Jiang
added a research item
The Summer Camp at Danang University of Science and Technology (DUT) offers traditional and non-traditional students in architecture, urban planning and urban design from around the world, the opportunity to study with renowned scholars from the United States, Israel, Sweden, and Vietnam. Students will experience a truly international environment, get insights in urban design, planning and architecture, and build life-long friendship. DUT is located in Danang, the city where Asia-Pacific Economic Cooperation (APEC 2018) organized. Emerges as a famous destination for global travelers. Students can also enjoy sandy beaches and mountains with spectacular views around the city. Meet global peers and learn from world-class experts for the fantastic International Summer School experience!
Bin Jiang
added a research item
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
added a research item
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
Bin Jiang
added an update
The social values of this project can be seen from the design and simulation tools used to generate living structures of our built environments, and its impacts on the field of urban design and planning. In the last century, the urban design industry has been dominated by industrial design models that conceive cities as collections of mechanical parts rather than as generated coherent wholes. Infected by modernism, postmodernism, and deconstructionism, our built environments have been deteriorating. A devastating consequence of this is that more and more dead structures have been produced in our cities or our built environments. This situation is still particularly apparent in developing countries, where skyscrapers and glass buildings are considered to be a sign of modernization. This misperception has had a major effect on higher education in architecture and urban design over the past 100 years or so. Instead of AutoCAD, the design and simulation tools that we intend to develop will be used in classrooms of urban design and planning for real design of living structures. Urban design theory has long been criticized as being pseudoscientific due to the lack of a robust, consistent scientific underpinning (Jacobs 1961, Marshall 2012). On the other hand, Christopher Alexander (2003, 2009) has devoted his life to a new way of doing architecture – a rigorous scientific foundation for architecture and urban design, and a new way of computation – a science of harmony-seeking computation. Therefore, the present project will make a significant contribution to complexity science, not only for understanding complexity by many of prominent scientists (Thompson 1917, Webster and Goodwin 1996, Wolfram 2003), but also for making and creating living or complex structures (Alexander 2003, 2009). This is probably the project’s most significant social value or its most fundamental impact on society. As Alexander claimed, the goodness or quality of a built environment is not a matter of opinion as we currently perceive, but a matter of fact. This fact is founded on the scientific notion of living structure or wholeness or life or beauty, which is governed by the scaling law of far more small things than large ones. Together with the new Master’s program in Architecture, this project will send a clear message to the world that there is a better alternative to the industrial design models for sustainable urban design.
 
Bin Jiang
added a research item
According to Christopher Alexander, wholeness is defined as a mathematical and physical structure of space that pervasively exists in our surroundings: not only in built environment such as buildings, streets, and cities, but also in art such as artifacts and paintings. This tutorial provides a structural perspective on goodness of space – both large- and small-scale – in order to bridge together the two concepts of space and place through the very concept of wholeness. 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 is considered a matter of fact rather than of opinion under the new view of space of Alexander: space is neither lifeless nor neutral, but a living structure capable of being more living or less living. Under the new view of space or new cosmology, geography will become part of complexity science not only for understanding complexity, but also for making and remaking complex or living structures. To paraphrase Alexander (1983, as cited in Grabow 1983, p. xi) – geography would significantly re-shape our world picture of the 21st and 22nd centuries towards an organic one, just as physics did in the 19th and 20th centuries in framing our mechanistic world view.
Bin Jiang
added a research item
As noted in the introductory quotation, 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 with respectively 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 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 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 have used to on the legacy of cartography and GIS. KEYWORDS: Third definition of fractal, fractal or living geometry, wholeness, head/tail breaks (ht-index), scaling law
Bin Jiang
added a research item
Topics to cover: * Large- and small-scale spaces * Topological analysis using the example of space syntax * Principle of space syntax * Syntactical measures * Why topology is important?
Bin Jiang
added an update
Christopher Alexander is our hash tag, so one can cross check many related updates through BinsTweets: https://twitter.com/binjiangxp/
 
Bin Jiang
added an update
Two conferences directly inspired by Christopher Alexander will take place in Portland, OR, the home of The Oregon Experiment:
The PLoP is the 25th of the conference series, in where Christopher Alexander is widely recognized as the father of pattern design movement in computer science. In 1996, Alexander talked about pattern language and the nature of order at ACM Conference on Object-Oriented Programs, Systems, Languages and Applications (OOPSLA).
 
Bin Jiang
added an update
The topological representation of wholeness we developed has finally published and assigned with volume and issue with Geographical Analysis:
Jiang B. (2018), A topological representation for taking cities as a coherent whole, Geographical Analysis, 50(3), 298–313. Reprinted in D'Acci L. (editor, 2019), Mathematics of Urban Morphology, Springer: Berlin.
It will be reprinted with the upcoming book "Mathematics of Urban Morphology", to be published by Springer.
 
Bin Jiang
added an update
We invite papers on Alexander's work and its potential applications and development, with a focus on The Nature of Order but also addressing other aspects of his contributions related to urban science including both understand and making of better built environments. The purpose of this special issue is not only to debate Alexander's legacy, but also to try to assess previously-unrecognized potential applications of Alexander's most recent work. Submissions may include research papers, reviews, or case studies. The editors will curate the selection of submissions, and if appropriate, the selected submissions will follow the subsequent peer review processes.
 
Bin Jiang
added a research item
We invite papers on Alexander's work and its potential applications and development, with a focus on The Nature of Order but also addressing other aspects of his contributions related to urban science including both understand and making of better built environments. The purpose of this special issue is not only to debate Alexander's legacy, but also to try to assess previously-unrecognized potential applications of Alexander's most recent work. Submissions may include research papers, reviews, or case studies. The editors will curate the selection of submissions, and if appropriate, the selected submissions will follow the subsequent peer review processes.
Bin Jiang
added 2 research items
This work builds upon the research agenda for cartography and Big Data, specifically linking to data-based artworks in a geovisual analytics context. Art is a medium that potentially affords easily-assimilated, complex and flexible representations of data. The generation of such artworks using two fractal-based methods is initially described, supported by the example of New Zealand cities and city streets. On one hand, the use of head/tail breaks to extract "natural cities" and within them, "natural streets" captures emergent organic hierarchies based on size as well as producing shapes of aesthetic value. On the other hand, attribute and geometric parameters associated with spatial data can be used to build fractally-generated "objects of beauty" such as the Barnsley fern leaf (in effect becoming a multivariate symbol such as the Chernoff face). These are the building blocks of the artwork, which finally undergoes a style transfer process (using the convolutional neural network-based Google Deep Dream). Since the artwork is explicitly built on data, it would be possible to place this display in a linked and brushed geovisual analytics tool. This paper ends with a discussion of the possibilities of art-enabled geovisual analytics.
The street network's angular properties were found more suitable than metric properties for capturing the observed pedestrian and vehicle movement flows in space syntax modeling. Some studies relate this state to the underlying street network structure that create the potential for movement across the network. The aim of this paper is to clarify why the angular structure of the network has superiority over the metric structure. The investigation entailed analysis of street network'centralities and movement flows obtained through agent-based simulations conducted for two cities that differ in the pattern and size of street network. The findings indicate that the superiority of the angular structure can be explained by two structural properties: (i) a multi-scale correlation between to-movement and through-movement potentials (centrality measures) of the same distance type; and (ii) an overlap between movement potentials of different distance types across scales of the network. These structural properties create coherent and dominant angular foreground structures that fit movement flows in both study cities.
Bin Jiang
added an update
Not Gaussian, but Paretian thinking
Not Tobler’s law, but scaling law
Not Euclidean geometric, but fractal or living geometric thinking
Not data quality, but data character
Not topology of geometric primitives, but topology of meaningful geographic features
Not bigness about big data, but the three characteristics
Not mechanistic, but organic thinking
 
Bin Jiang
added an update
Keynote speech addressed to CSUM 2018: Conference on Sustainable Urban Mobility, May 24-25, 2018, Skiathos Island, Greece
 
Bin Jiang
added a research item
Scaling law should become the first law of geography, for it is universal and global. Topology should be defined among meaningful geographic features together with among geometric primitives such as pixels, points, lines and polygons. Data character, or the underlying wholeness – living structure, is more important than data quality. A paradigm shift is expected from Tobler’s law to scaling law, from Euclidean geometry to fractal geometry, from Gaussian statistics to Paretian statistics, and from Descartes’ mechanistic to Alexander’s organic thinking.
Bin Jiang
added a research item
* Two fundamental laws of geography or any living structure: Scaling law + Tobler’s law * Asymmetry (symmetry breaking + wholeness-enhanced transformaton) underlies geographic forms and processes * The 3rd definition of fractal (scaling law + head/tail breaks) helps reveal asymmetries * Living structure or wholeness as a new asymmetric structure and mechanism * Ubiquity of asymmetry or living structure
Bin Jiang
added a research item
To be presented at the upcoming AAG annual meeting: https://aag.secure-abstracts.com/AAG%20Annual%20Meeting%202018/abstracts-gallery/15272
Bin Jiang
added a research item
Inspired by Christopher Alexander’s conception of the world – space is not lifeless or neutral, but a living structure involving far more small things than large ones, a topological representation has been previously developed to characterize the living structure or the wholeness of geographic space. This paper further develops the topological representation and living structure for predicting human activities in geographic space. Based on millions of street nodes of the United Kingdom extracted from OpenStreetMap, we established living structures at different levels of scale in a nested manner. We found that tweet locations at different levels of scale, such as country and city, can be well predicted by the underlying living structure. The high predictability demonstrates that the living structure and the topological representation are efficient and effective for better understanding geographic forms. Based on this major finding, we argue that the topological representation is a truly multi-scale representation, and point out that existing geographic representations are essentially single scale, so they bear many scale problems such as modifiable areal unit problem, the conundrum of length,and the ecological fallacy. We further discuss on why the living structure is an efficient and effective instrument for structuring geospatial big data, and why Alexander’s organic worldview constitutes the third view of space. KEYWORDS: Organic worldview, topological representation, tweet locations, natural cities, scaling of geographic space
Bin Jiang
added a research item
The PhD student will be working in the ALEXANDER project that intends to develop a design tool for automatically generating living structure, which is characterized by far more small things than large ones globally (scaling law) and more or less similar things locally (Tobler's law), for biophilic urban design. It aims to develop a suite of differentiating algorithms to create living structures based on city plans of historical cities such as Venice and Rome. It will set up SimCity-like simulations to conduct what-if modeling in order to better understand why and how these living structures work. The developed tool will be tested and improved through experiments with spatial planning students and design practitioners. The design tools targeted at biophilic urban design – in terms of creating living structures rather than increasing buildings’ aesthetic appeal through inserting trees and shrubs – provide an alternative to existing industrial design tools such as AutoCAD, and thus help make or re-make urban environments living, beautiful, and sustainable.
Bin Jiang
added 2 research items
I am going to talk on … * Current mapping essentially for regular, or more or less similar things, BUT * geographic space is irregular, or with far more small things than large ones. * The Earth’s surface is a continuum, BUT it is chopped mechanically for mapping. * A series of new concepts and tools for bridging between fractal and living geometry, and * A new paradigm in mapping based on living geometry – wholeness.
AXWOMAN as a topological analysis tool for better understanding not only "how a city looks", but also "how a city works". AXWOMAN as a tool not only for understanding, but also for making – "what it ought to be", or urban design and planning. AXWOMAN as a scaling or fractal analysis tool for showing that a city is a living structure with far more small things than large ones. AXWOMAN as a tool not only for diagnosis but also for design.
Bin Jiang
added 2 research items
A mathematical model of beauty enables us to better understand why a design is beautiful, and how much beautiful the design is. It was presented at Future of Places III, 29 June - 1 July 2015, Stockholm, Sweden. This talk is based on the following paper: https://www.researchgate.net/publication/272159333_Wholeness_as_a_Hierarchical_Graph_to_Capture_the_Nature_of_Space
There are two fundamental laws of geography: scaling law and Tobler's law. Scaling law is available across all scales ranging from the smallest to the largest, and it states that there are far more small things than large ones in geographic space. Tobler's law is available in one scale, and it states that more or less similar things tend to be nearby or related. In this short article, I claim scaling as a design principle for cartography, but what I really wanted to convey is that scaling must become a dominant principle, if not the principle, of cartographic design. All other principles can, should, and must be subordinated to the major and dominant one.
Bin Jiang
added a research item
Topological and scaling perspective for better understanding and (re-)making sustainable cities, 12 June 2018, Lund, Sweden • To promote topological and scaling ways of thinking for geospatial big data analytics • To introduce two fundamental laws of geography for understanding cities: Scaling law and Tobler’s law • To discuss two fundamental principles for making sustainable cities: Differentiation and adaptation KEYWORDS: Head/tail breaks, ht-index, 3rd definition of fractal, wholeness, living structure, beauty
Bin Jiang
added an update
See the attached diagram for the vision
 
Bin Jiang
added an update
Once upon time, there was no thermometer, so people relied on their feelings to sense temperature. Not long ago, there was no beautimeter, so beauty is said to be in the eye of the beholder. Christopher Alexander, widely known for his classic “A city is not a tree”, and “A pattern language”, spent his life in pursuing beauty in buildings, cities, streets, gardens, ancient carpets, and even artifacts. The beauty is defined mathematically as a recursive structure, exists inherently in space and matter physically, and reflects in our minds and cognition psychologically. Based on the definition of beauty or life or wholeness or living structure, I developed a mathematical model of beauty, which helps address not only why a design is beautiful, but also how much beauty the design has. The beautiful or living structure is characterized by far more small things than large ones globally and more or less similar things locally. Unfortunately, existing computer design tools such as AutoCAD are unable to create the kind of beautiful or living structure, although they have sophisticated drawing functionality. On the other hand, infected by modernism, postmodernism, and deconstructionism, our built environments have been deteriorating and are not sustainable. The urban design industry of the past century has been very much dominated by industrial design models, which conceive a city as a collection of mechanical parts rather than a generated coherent whole. As a devastated consequence, more and more dead structures have been produced in our cities and built environment world widely. This situation still continues particularly in many of developing countries, where skyscrapers and glass buildings are considered to be a sign of modernization. This misperception has major effect in higher education in architecture and urban design over the past century.
We have started a new Master program of Architecture http://buildingbeauty.net/ built on the legacy of Alexander and his life's work pursuing beauty. The program aims for wholeness-oriented design, beginning with construction rather than paper based design as most architecture schools do. It intends to create buildings or cities with a high degree of wholeness or life or beauty, instead of slick buildings as most modernist architects do.
 
Bin Jiang
added 5 research items
According to Christopher Alexander’s theory of centers, a whole comprises numerous, recursively defined centers for things or spaces surrounding us. Wholeness is a type of global structure or life-giving order emerging from the whole as a field of the centers. The wholeness is an essential part of any complex system and exists, to some degree or other, in spaces. This paper defines wholeness as a hierarchical graph, in which individual centers are represented as the nodes and their relationships as the directed links. The hierarchical graph gets its name from the inherent scaling hierarchy revealed by the head/tail breaks, which is a classification scheme and visualization tool for data with a heavy-tailed distribution. We suggest that (1) the degrees of wholeness for individual centers should be measured by PageRank (PR) scores based on the notion that high-degree-of-life centers are those to which many high-degree-of-life centers point, and (2) that the hierarchical levels, or the ht-index of the PR scores induced by the head/tail breaks can characterize the degree of wholeness for the whole: the higher the ht-index, the more life or wholeness in the whole. Three case studies applied to the Alhambra building complex and the street networks of Manhattan and Sweden illustrate that the defined wholeness captures fairly well human intuitions on the degree of life for the geographic spaces. We further suggest that the mathematical model of wholeness be an important model of geographic representation, because it is topological oriented that enables us to see the underlying scaling structure. The model can guide geodesign, which should be considered as the wholeness-extending transformations that are essentially like the unfolding processes of seeds or embryos, for creating beautiful built and natural environments or with a high degree of wholeness. KEYWORDS: Centers, ht-index, head/tail breaks, big data, complexity, scaling
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. KEYWORDS: Theory of centers, living geometry, Christopher Alexander, head/tail breaks, and structural beauty
Two fundamental issues surrounding research on the image of the city respectively focus on the city's external and internal representations. The external representation in the context of this paper refers to the city itself, external to human minds, while the internal representation concerns how the city is represented in human minds internally. This paper deals with the first issue, i.e., what trait the city has that make it imageable? We develop an argument that the image of the city arises from the underlying scaling of city artifacts or locations. This scaling refers to the fact that, in an imageable city (a city that can easily be imaged in human minds), small city artifacts are far more common than large ones; or alternatively low dense locations are far more common than high dense locations. The sizes of city artifacts in a rank-size plot exhibit a heavy tailed distribution consisting of the head, which is composed of a minority of unique artifacts (vital and very important), and the tail, which is composed of redundant other artifacts (trivial and less important). Eventually, those extremely unique and vital artifacts in the top head, i.e., what Lynch called city elements, make up the image of the city. We argue that the ever-increasing amount of geographic information on cities, in particular obtained from social media such as Flickr and Twitter, can turn research on the image of the city, or cognitive mapping in general, into a quantitative manner. The scaling property might be formulated as a law of geography. Keywords: Scaling of geographic space, face of the city, cognitive maps, power law, and heavy tailed distributions.
Bin Jiang
added a project goal
Living structure, which is characterized by far more small things than large ones globally and more or less similar things locally, exists inherently in any part of space: towns, streets, buildings, gardens, and even artifacts. To measure the degrees of livingness or beauty, I have developed a mathematical model that helps address not only why a space is alive, but also how much alive it is. I have used geospatial big data to demonstrate the living structure at country and city levels. Based on these previous studies both theoretically and empirically, this present project - named in honor of Christopher Alexander - intends to develop a design tool for automatically generating living structure for biophilic urban design. We will develop a suite of differentiating algorithms to create living structures based on city plans of historical cities such as Venice, Rome, and Amsterdam. We will set up SimCity-like simulations to conduct what-if modeling in order to better understand why and how these living structures work. The developed tool will be testified and improved through experiments with spatial planning students and design practitioners. The design tools targeted at biophilic urban design – in terms of creating living structures rather than increasing buildings’ aesthetic appeal through inserting trees and shrubs – provide an alternative to existing industrial design tools such as AutoCAD, and thus help make or remake urban environments living, beautiful, and sustainable. As Alexander claimed, the goodness or quality of a built environment is not a matter of opinion as we currently conceive, but a matter of fact. This fact is founded on the scientific notion of living structure or wholeness or life or beauty. This project will send a clear message to the design world that there is a better alternative to the industrial design models for sustainable urban design.