Mathematics of Urban Morphology

“D’Acci has with this book provided a useful overview of the mathematical models used in relation to urban morphology. … the book also fills an apparent gap in the literature, coupling urban morphology and mathematics. It is to be hoped that this can be the start of a long series of books and papers where this ‘new’ direction in urban morphology can flourish and provide knowledge about how cities can be developed in more sustainable trajectories.” (Meta Berghauser Pont, Urban Morphology, Vol. 23 (2), 2019)“This monograph gives a comprehensive and contemporary overview of many recent advances on random walks over comb-like structures. … This monograph is written in an explanatory and concise manner with plenty of concrete examples rather than a formal definition-theorem-proof textbook form. Nevertheless, necessary elements and preliminaries are presented to the reader and the results covered here reflect the state-of-the-art of the research on comb structures.” (Yilun Shang, zbMATH 1410.91008, 2019)

• On Urban Morphology and Mathematics.- Part I: Fractals.- Fractal Dimension Analysis of Urban Morphology Based on Spatial Correlation Functions.- Central Place Theory and Power Laws for Cities.- Distribution of Cities Size: Zipf, Gibrat, Pareto Law.- Signature of Organic Urban Growth: Degree Distribution of the City's Street Network Structure.- A Fractal Approach to Explore Australian Urban Form and Its Impacting Factors at Neighborhood Scale.- Part II: Cellular Automata.- Geographic Cellular Automata for Urban Form.- Mathematical Foundations of Cellular Automata and Complexity Theory.- Part III: Spatial Networks and Space Syntax.- Mathematics of Urban Spatial Networks.- Space Syntax: A Network Based Configurational Approach to Studying Urban Morphology.- Applied Mathematics on Urban Space.- The Morphology and Circuity of Street Networks.- Part IV: Complexity.- Emergence of Complexity in Urban Morphology.- Complexity, Darwinian Mutations, and Selection in Urban Morphology Evolution: HowMathematics Looks at Escher Metamorphosis.- A Topological Representation for Taking Cities as a Coherent Whole.- Part V: Other Forms of Quantification.- A Multiscale Classification of the Urban Morphology for Use in Quantitative Models.- An Urban Morphogenesis Model Capturing Interactions Between Networks and Territories.- Continuum Percolation and Spatial Point Pattern in Application to Urban Morphology.- Urban Compactness: New Geometric Interpretations and Indicators.- Using Google Street View for Street Level Urban Form Analysis.- Examining Spatial Structure Using Gravity Models.- Part VI: Humanistic and Multidisciplinary Commentaries.- From Morphology to Morphogenesis: Putting Mathematics in Its Place.- Not Only ... But Also: Urban Mathematical Models and Urban Social Theory.- Urban Morphology or Townscape? Wholes Made of Many Parts.- Extending Urban Morphology: Drawing Together Quantitative and Qualitative Approaches.- Mathematics and Cities: A Long-Standing Relationship Fit forthe Future.- Mathematics and/as Humanities. Linking Humanistic Historical to Quantitative Approaches.- Urban Form, Agents and Processes of Change.- The Future of Streets.- Understanding and Quantifying Urban Density Towards a More Sustainable City Form.- To Not Talk Past Each Other: An Immodest Proposal for Cross-Conceptual Research in Urban Morphology.