The Mathematics Of Urban Morphology

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

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.

This book explores various ways of identifying and understanding the character of historic townscapes from a systematic and comparative perspective. It outlines several genetic approaches to the study of urban form, grounded in the traditions of geographical analysis but wholly interdisciplinary in their content and implications. It develops a philosophical and methodological basis for the field of urban morphology, stressing the reciprocal relations between town plan, building fabric and land and building utilisation. It views these elements as spatially variable accumulations and selective survivals of forms regulated by shifting patterns of corporate and individual decisions made from one historical period to another - in perpetual tension between resistance and change. Several of the essays in this collection establish and exemplify conceptual principles and axioms of urban morphological development in historic towns, and introduce numerous specific processes by which built forms are created and juxtaposed in urban space. Other essays apply these precepts by interpreting a number of case studies of historic towns in Britain, Germany, Japan, New Zealand and elsewhere. The closing essay offers a unique interpretation of the regional varieties to be found in medieval European urbanism, based on differing traditions of social formation and morphological outcomes.

'This is a textbook about cities or, more precisely, about the physical form of cities. It provides an overview of the main elements of urban form—streets, street blocks, plots and buildings—structuring our cities and the fundamental agents and processes of transformation shaping these elements. It applies this analytical framework to describe the evolution of cities over history as well as to explain the functioning of contemporary cities. After the initial focus on the 'object' (cities), the book introduces how different schools of thought have been dealing with this object since the emergence of Urban Morphology, as the science of urban form, in the turning to the twentieth century. Finally, the book identifies the main contributions of urban morphology to cities, societies and economies. This second edition of the book offers updated and more accurate knowledge on several morphological issues, presents expanded contents, and it has a more explicit didactic nature, including a set of exercises in the end of each chapter, that will help teachers and students (in architecture, geography, planning, history, sociology and urban studies) in acquiring and consolidating their urban morphological knowledge.

Conceived as a practical manual of morphological analysis, The Handbook of Urban Morphology focuses on the form, structure and evolution of human settlements – from villages to metropolitan regions. It is the first book in any language focused on specific, up-to-date ‘how-to’ guidance , with clear summaries of the central concepts, step-by-step instructions for carrying out the analysis, case studies illustrating specific applications and discussion of theoretical underpinnings tied to evidence from the field. Ideal for students as well as professionals and academics dealing with the built environment.

Mathematical Morphology in Geomorphology and GISci presents a multitude of mathematical morphological approaches for processing and analyzing digital images in quantitative geomorphology and geographic information science (GISci). Covering many interdisciplinary applications, the book explains how to use mathematical morphology not only to perform

This is a book about cities or, more precisely, about the physical form of cities. It starts presenting the main elements of urban form – streets, urban blocks, plots and buildings – structuring our cities and the fundamental actors and processes of transformation shaping these elements. It then applies this analytical framework to describe the evolution of cities over history as well as to explain the functioning of contemporary cities. After the initial focus on the ‘object’ (cities) the book describes how different researchers and different schools of thought have been dealing with this object since the emergence of Urban Morphology, as the science of urban form, in the turning to the twentieth century. Finally, the book tries to identify what are the most important (and specific) contributions that Urban Morphology has to offer to contemporary cities, societies and economies.

Urban planning and design studio report from the Harvard Graduate School of Design. Spring 2019.