Mathematics and Morphogenesis of the City: A Geometrical Approach
Thomas Courtat, Catherine Gloaguen, Stephane Douady

TL;DR
This paper introduces a comprehensive mathematical model for city morphogenesis that integrates geometrical, topological, and dynamical aspects to explain and generate diverse city layouts.
Contribution
It presents a novel geometrical and dynamical framework for modeling city development, unifying static analysis with a generative process.
Findings
Cities follow a division/extension logic in their development
The model reproduces diverse city shapes using simple rules
Static analysis of French towns supports the model's assumptions
Abstract
Cities are living organisms. They are out of equilibrium, open systems that never stop developing and sometimes die. The local geography can be compared to a shell constraining its development. In brief, a city's current layout is a step in a running morphogenesis process. Thus cities display a huge diversity of shapes and none of traditional models from random graphs, complex networks theory or stochastic geometry takes into account geometrical, functional and dynamical aspects of a city in the same framework. We present here a global mathematical model dedicated to cities that permits describing, manipulating and explaining cities' overall shape and layout of their street systems. This street-based framework conciliates the topological and geometrical sides of the problem. From the static analysis of several French towns (topology of first and second order, anisotropy, streets…
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