D'Acci The Mathematics of Urban Morphology

1. Auflage 2019
ISBN: 978-3-030-12381-9
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 556 Seiten

Reihe: Modeling and Simulation in Science, Engineering and Technology

This edited volume provides an essential resource for urban morphology, the study of urban forms and structures, offering a much-needed mathematical perspective. Experts on a variety of mathematical modeling techniques provide new insights into specific aspects of the field, such as street networks, sustainability, and urban growth. The chapters collected here make a clear case for the importance of tools and methods to understand, model, and simulate the formation and evolution of cities.
The chapters cover a wide variety of topics in urban morphology, and are conveniently organized by their mathematical principles. The first part covers fractals and focuses on how self-similar structures sort themselves out through competition. This is followed by a section on cellular automata, and includes chapters exploring how they generate fractal forms. Networks are the focus of the third part, which includes street networks and other forms as well. Chapters that examine complexity and its relation to urban structures are in part four.The fifth part introduces a variety of other quantitative models that can be used to study urban morphology. In the book's final section, a series of multidisciplinary commentaries offers readers new ways of looking at the relationship between mathematics and urban forms.
Being the first book on this topic, Mathematics of Urban Morphology will be an invaluable resource for applied mathematicians and anyone studying urban morphology. Additionally, anyone who is interested in cities from the angle of economics, sociology, architecture, or geography will also find it useful.
'This book provides a useful perspective on the state of the art with respect to urban morphology in general and mathematics as tools and frames to disentangle the ideas that pervade arguments about form and function in particular. There is much to absorb in the pages that follow and there are many pointers to ways in which these ideas can be linked to related theories of cities, urban design and urban policy analysis as well as new movements such as the role of computation in cities and the idea of the smart city. Much food for thought. Read on, digest, enjoy.'  From the foreword by Michael Batty

Autoren/Hrsg.

D'Acci, Luca

Inhaltsverzeichnis

1;Foreword: The Morphology of Cities;6
2;Contents;11
3;On Urban Morphology and Mathematics;14
3.1;1 Morphology, Urban and Mathematics;14
3.2;2 Urban Morphology;16
3.3;3 Mathematical Treatment of Urban Forms;17
3.4;4 Cities Between Hard and Soft Sciences;20
3.5;5 In Search of Universal Laws: From Calvino to Santa Fe;21
3.6;6 Complex Self-organizing Systems Urban Approaches;24
3.7;7 Laplace’s Demon in Cities;25
3.8;8 A Science but not a Science?;26
3.9;9 The Language of Mathematics;26
3.10;10 The Art and Science of Cities;27
3.11;Bibliography;29
4;Fractals;32
5;Fractal Dimension Analysis of Urban Morphology Based on Spatial Correlation Functions;33
5.1;1 Introduction;33
5.2;2 Theoretical Models;35
5.2.1;2.1 Basic Postulates;35
5.2.2;2.2 Spatial Correlation Functions;37
5.2.3;2.3 Fractal Parameter Equations;41
5.2.4;2.4 New Analytical Framework for Urban Morphology;45
5.3;3 Case Study;48
5.3.1;3.1 Methodology;48
5.3.2;3.2 Study Area, Datasets, and Results;50
5.4;4 Questions and Discussion;55
5.4.1;4.1 Methodological Outline;55
5.4.2;4.2 Model Generalization;58
5.5;5 Conclusions;62
5.6;References;63
6;Central Place Theory and the Power Law for Cities;66
6.1;1 Introduction;66
6.2;2 Central Place Theory;70
6.2.1;2.1 Model and One-Good Equilibrium;70
6.2.2;2.2 Hierarchy Equilibrium;72
6.3;3 Power Law for Cities;73
6.4;4 A Dynamic Programming Approach to Central Place Theory;76
6.4.1;4.1 The Sequence Problem;77
6.4.2;4.2 The Dynamic Programming Problem;77
6.4.3;4.3 The Central Place Property;82
6.5;5 Concluding Remarks;84
6.6;References;85
7;Distribution of City Size: Gibrat, Pareto, Zipf;87
7.1;1 Introduction;88
7.2;2 Methodology and Data;89
7.2.1;2.1 Testing for a Power-Law Tail;90
7.2.2;2.2 Data Description;92
7.3;3 Empirical Results;93
7.3.1;3.1 Test Results;93
7.3.2;3.2 Estimates of the Shape Parameter;94
7.3.3;3.3 Emergence of a Power-Law Upon Aggregation;95
7.4;4 Discussion and Conclusion;98
7.5;References;99
8;The Signature of Organic Urban Growth;102
8.1;1 Introduction;103
8.2;2 Of Street Networks and Degree Centrality Distributions;104
8.2.1;2.1 The Topology of Street Networks;105
8.2.2;2.2 Street Network Representation;105
8.2.3;2.3 Degree Distribution and Power Law Fitting;106
8.2.4;2.4 Related Work;107
8.3;3 Datasets and Methods;107
8.3.1;3.1 Objects of Study;108
8.3.2;3.2 Sources of Street Network Data;108
8.3.3;3.3 Street Network Model Considerations;110
8.3.4;3.4 Methodological Process;114
8.3.5;3.5 Software Used in the Process;115
8.4;4 Results;115
8.4.1;4.1 Derived Parameters of Degree Distribution;115
8.4.2;4.2 The Evolution of Paris;120
8.4.3;4.3 Comparison of Cities;122
8.5;5 Discussion;123
8.5.1;5.1 Organic and Planned Growth Processes;123
8.5.2;5.2 The Classification of Cities;124
8.6;6 Conclusions;127
8.7;References;128
9;A Fractal Approach to Explore Australian Urban Form and Its Impacting Factors at Neighbourhood Scale;131
9.1;1 Introduction;131
9.2;2 Methodology, Study Context and Data;134
9.2.1;2.1 The Fractal Methods;134
9.2.2;2.2 Spatial Correlation Analysis;139
9.2.3;2.3 Study Context: Brisbane, Australia;139
9.2.4;2.4 Data;140
9.3;3 Results;142
9.3.1;3.1 D and ? Values of Brisbane Neighbourhoods;142
9.3.2;3.2 Correlation Between Fractal Measures and Classical Spatial Form Metrics;144
9.4;4 Discussion;146
9.5;5 Conclusion;149
9.6;References;150
10;Cellular Automata;153
11;Geographic Cellular Automata for Realistic Urban form Simulations: How Far Should the Constraint be Contained?;154
11.1;1 Introduction;155
11.2;2 CA-Based Discrete Modeling;156
11.2.1;2.1 CA Formal Definition;156
11.2.2;2.2 CA Limits;157
11.3;3 Suitable Constraints for Urban Modeling;160
11.3.1;3.1 Temporal Constraint;161
11.3.2;3.2 Spatial Constraint;163
11.4;4 Constraint Geographical CA;164
11.5;5 Discussion;166
11.6;6 Conclusion;167
11.7;References;168
12;Mathematical Foundations of Cellular Automata and Complexity Theory;170
12.1;References;175
13;Spatial Networks and Space Syntax;178
14;Assessing Complexity of Urban Spatial Networks;179
14.1;1 ``We Shape Our Buildings; Thereafter They Shape Us'';179
14.2;2 Spatial Graphs of Urban Environments;180
14.2.1;2.1 Locally Anisotropic Random Walks on Graphs;181
14.2.2;2.2 Stationary Distributions of Locally Anisotropic Random Walks;183
14.2.3;2.3 Entropy of Anisotropic Random Walks;184
14.2.4;2.4 The Relative Entropy Rate for Locally Anisotropic Random Walks;185
14.3;3 Information Decomposition for Markov Chains;186
14.3.1;3.1 Conditional Information Measure for the Downward Causation Process;187
14.3.2;3.2 Conditional Information Measure for the Upward Causation Process;188
14.3.3;3.3 Ephemeral Information in Markov Chains;188
14.4;4 Exploring Graph Structures by Random Walks;189
14.4.1;4.1 Affine Probabilistic Geometry of Graphs;190
14.4.2;4.2 Probabilistic Interpretation of Euclidean Geometry;190
14.5;5 How a City Should Look?;192
14.5.1;5.1 Labyrinths;192
14.5.2;5.2 Manhattan's Grid;195
14.5.3;5.3 German Organic Cities;198
14.5.4;5.4 The Diamond Canal Network of Amsterdam;200
14.5.5;5.5 The Canal Network of Venice;201
14.6;6 Conclusion;202
14.7;References;202
15;Space Syntax: A Network-Based Configurational Approach to Studying Urban Morphology;204
15.1;1 Introduction;205
15.2;2 Space Syntax: Standard Concepts, Methods, and Measures;206
15.2.1;2.1 Configurations;207
15.2.2;2.2 Axial and Segment Maps;208
15.2.3;2.3 Measures;210
15.3;3 Mathematical Developments in Space Syntax;215
15.3.1;3.1 Normalization of Integration and Choice;215
15.3.2;3.2 Geometric and Topological Measures Versus Metric Measures in Space Syntax;219
15.3.3;3.3 Scaling and Universality in the Axial and Segment Maps;221
15.3.4;3.4 Boundary Effects on Space Syntax Measures;222
15.3.5;3.5 Shape and Space in Space Syntax;224
15.3.6;3.6 3D Descriptions in Space Syntax;226
15.3.7;3.7 Space Syntax and GIS;228
15.4;4 Research Applications of Space Syntax;231
15.4.1;4.1 The Syntactic Cores and Types of Spatial Configurations;231
15.4.2;4.2 The Whole and the Parts Relationships of Spatial Configurations;233
15.4.3;4.3 The Re/Production of Society and Culture Using Spatial Configurations;235
15.4.4;4.4 The Generative Functions of Spatial Configurations;238
15.4.5;4.5 Spatial Configurations and Social Capital;240
15.4.6;4.6 Spatial Configurations and Urban Historical Studies;241
15.5;5 Summary and Conclusions;243
15.6;References;244
16;Applied Mathematics on Urban Space;257
16.1;1 Introduction;257
16.2;2 Definition of Urban Space;258
16.3;3 The Method of Calculations;259
16.4;4 Space Syntax’ Contribution to Theory Building and Understanding on How to Build Environments Works;270
16.5;References;272
17;The Morphology and Circuity of Walkable and Drivable Street Networks;275
17.1;1 Introduction;275
17.2;2 Analytical Background;277
17.3;3 Methods;279
17.4;4 Results;282
17.5;5 Discussion;282
17.6;6 Conclusion;287
17.7;References;288
18;Complexity;292
19;Emergence of Complexity in Urban Morphology;293
19.1;1 Introduction;293
19.2;2 Fractal Nature of Urbanized Regions in Seoul;295
19.3;3 State Vector Description of Urban Areas;298
19.4;4 Modeling Urban Morphology;302
19.4.1;4.1 Model Description;302
19.4.2;4.2 Monte Carlo Simulations and Mean-Field Approximation;305
19.4.3;4.3 Criticality in the Urban Morphology of Seoul;308
19.5;5 Discussion;313
19.6;References;315
20;On the Complex Interaction Between Mathematics and Urban Morphology;317
20.1;1 Motivations and Plan of the Chapter;317
20.2;2 Reasonings on the Metamorphosis by Cornelis Escher;319
20.3;3 Mathematical Models for Complex Systems;323
20.4;4 Towards a Mathematics for Urban Morphology;326
20.4.1;4.1 Agent-Based Modeling Tools;327
20.4.2;4.2 Active Particles Kinetic Modeling Tools;328
20.4.3;4.3 Towards Research Perspectives;330
20.5;References;333
21;A Topological Representation for Taking Cities as a Coherent Whole;336
21.1;1 Introduction;337
21.2;2 Wholeness or Living Structure, and Its 15 Fundamental Properties;338
21.3;3 The Topological Representation for Taking Things as a Whole;341
21.4;4 Living Structures of China and UK Natural Cities;343
21.4.1;4.1 Data and Data Processing;343
21.4.2;4.2 Visualization of Differentiation and Adaptation;344
21.5;5 Discussions on the Topological Representation and Analysis;348
21.6;6 Conclusion;350
21.7;References;351
22;Other Forms of Quantification;354
23;A Multiscale Clustering of the Urban Morphology for Use in Quantitative Models;355
23.1;1 Introduction and State of the Art;355
23.2;2 Data Model;356
23.2.1;2.1 Local and Global Data;356
23.2.2;2.2 An Object Driven Data Model;357
23.2.3;2.3 Methods of Geoprocessing;357
23.3;3 Scales and Attributes;358
23.3.1;3.1 Building;358
23.3.2;3.2 Composition;359
23.3.3;3.3 Neighborhood and District;360
23.3.4;3.4 Municipality and Region;362
23.4;4 Examples of Location Types;364
23.4.1;4.1 Building;364
23.4.2;4.2 Composition;365
23.4.3;4.3 Neighborhood;365
23.4.4;4.4 Municipality;366
23.5;5 Clustering;366
23.5.1;5.1 Classification Versus Clustering;366
23.5.2;5.2 Methodology;367
23.5.3;5.3 Principal Component Analysis;368
23.5.4;5.4 Number of Clusters and Runtime;369
23.6;6 Clusters Results;371
23.7;7 Summary and Discussion;378
23.8;References;380
24;An Urban Morphogenesis Model Capturing Interactions Between Networks and Territories;383
24.1;1 Introduction;384
24.1.1;1.1 Urban Morphology;384
24.1.2;1.2 Urban Morphology and Interactions Between Networks and Territories;385
24.2;2 Measuring Morphology: Method;386
24.2.1;2.1 Urban Morphology;386
24.2.2;2.2 Network Measures;386
24.2.3;2.3 Correlations;388
24.3;3 Empirical Application;388
24.3.1;3.1 Urban Morphology;389
24.3.2;3.2 Network Topology;389
24.3.3;3.3 Effective Static Correlations and Non-stationarity;392
24.4;4 Urban Morphogenesis Model;398
24.4.1;4.1 Model Rationale;398
24.4.2;4.2 Model Description;399
24.4.3;4.3 Simulation Results;400
24.5;5 Discussion;404
24.5.1;5.1 Quantifying Urban Form;404
24.5.2;5.2 Modeling Urban Morphogenesis;405
24.5.3;5.3 Implications for Policies;406
24.6;References;407
25;Continuum Percolation and Spatial Point Pattern in Application to Urban Morphology;410
25.1;1 Introduction;410
25.2;2 Percolation in Mathematical Physics;413
25.2.1;2.1 Description;413
25.2.2;2.2 Phase Transition;413
25.3;3 Continuum Percolation and Spatial Arrangement of Points;415
25.3.1;3.1 General Ideas;415
25.3.2;3.2 Characterisation of Spatial Distribution of Points;417
25.3.3;3.3 Comparison with Other Methods;421
25.4;4 Interpretation of the Patterns in Urban Morphology;422
25.4.1;4.1 Single-scale Regular Pattern;423
25.4.2;4.2 Multi-scale Regular Pattern;424
25.4.3;4.3 Clustered Pattern;424
25.4.4;4.4 Dispersed Pattern;425
25.5;References;426
26;Urban Compactness: New Geometric Interpretations and Indicators;429
26.1;1 Introduction;429
26.2;2 Compact Cities;431
26.2.1;2.1 The Compact City Policy Debate;431
26.2.2;2.2 Urban Compactness;431
26.2.3;2.3 Learning from Density;432
26.3;3 Geometric Interpretations of Compactness;433
26.4;4 A New Interpretation and Indicator of Compactness;437
26.4.1;4.1 Interpreting Compactness;437
26.4.2;4.2 Quantification of Compactness;438
26.5;5 Application to Urban Areas;440
26.5.1;5.1 Initial Illustration;440
26.5.2;5.2 Compactness for a Range of Urban Areas;440
26.5.3;5.3 Compactness Distinct from Density;445
26.6;6 Compactness Revisited;445
26.6.1;6.1 Wholes and Parts;446
26.6.2;6.2 The Core Meaning of Compactness;448
26.6.3;6.3 Further Kinds of Compactness;449
26.7;7 Conclusions;451
26.8;References;452
27;Using Google Street View for Street-Level Urban Form Analysis, a Case Study in Cambridge, Massachusetts;455
27.1;1 Introduction;455
27.2;2 Data Preparation;456
27.2.1;2.1 Google Street View (GSV) Panorama Collection;456
27.2.2;2.2 Geometric Transform of Google Street View (GSV) Panoramas;458
27.2.3;2.3 Image Classification;458
27.3;3 Estimating and Mapping the Sky View Factor in Different Seasons;461
27.4;4 Estimating Direct Sunlight Duration in Street Canyons;463
27.5;5 Other Potential Applications;464
27.6;6 Discussion and Conclusion;465
27.7;Appendix A;467
27.8;References;467
28;Examining Spatial Structure Using Gravity Models;469
28.1;1 Introduction;469
28.2;2 Functional Spatial Structure;470
28.2.1;2.1 Functional Polycentricity;471
28.2.2;2.2 Spatial Interdependencies;473
28.3;3 Gravity Models and Spatial Structure;473
28.4;4 Estimation of the Gravity Model;474
28.5;5 Concluding Remarks;475
28.6;References;476
29;Humanistic and Multidisciplinary Commentaries;478
30;Urban Morphogenesis: Putting Mathematics in Its Place;479
30.1;1 Introduction;479
30.2;2 Morphogenesis: Conventional Approaches;480
30.3;3 Complexity: From Weak to Strong Emergence;481
30.4;References;484
31;Not Only … But Also: Urban Mathematical Models and Urban Social Theory;486
31.1;1 Introduction;486
31.2;2 Mathematics Modelling Versus Social Theory;488
31.3;3 From Either/or to not Only/but also;490
31.4;References;491
32;Urban Morphology or Townscape? Wholes Made of Many Parts;493
32.1;References;496
33;Extending Urban Morphology: Drawing Together Quantitative and Qualitative Approaches;497
33.1;1 The Nature of Urban Morphology;497
33.2;2 Contributions to a ‘New Urban Morphology’?;500
33.3;3 Conclusion: Unhelpful Dichotomies of Old and New, Quantitative and Qualitative—Moving Forward;504
33.4;References;506
34;Mathematics and Cities: A Long-Standing Relationship Fit for the Future?;510
34.1;References;514
35;Mathematics and/as Humanities–Linking Humanistic Historical to Quantitative Approaches;516
35.1;1 Mathematics as Humanities;516
35.2;2 Quantitative Approaches in Urban Morphology;517
35.3;3 Imminent Changes;520
36;Urban Forms, Agents, and Processes of Change;522
36.1;1 Urban Morphology;522
36.2;2 The Historico-Geographical Approach;523
36.3;3 The Process-Typological Approach;525
36.4;4 Combining Different Approaches in the Study of Urban Form;527
36.4.1;4.1 The Historico-Geographical Approach;527
36.4.2;4.2 The Process-Typological Approach;527
36.5;References;528
37;Future of Streets;529
37.1;References;537
38;Understanding and Quantifying Urban Density Toward more Sustainable City Form;539
38.1;1 Introduction;539
38.2;2 Defining Urban Density;540
38.3;3 Defining Density with Regard to the Compact City;542
38.4;4 The Ongoing Density Debate;544
38.5;5 A Proposed Framework for “Quality Density”;545
38.6;6 Learning to Live in More Compact and Denser Communities;546
38.7;References;547
39;To Not Talk Past Each Other: An Immodest Proposal for Cross-Conceptual Research in Urban Morphology;549
39.1;1 Desire for Integration;551
39.2;2 Cross-Conceptual Initiatives;552
39.3;3 Evidence and Theory;553
39.4;4 The Challenge;554
39.5;References;555