Mathematics and morphogenesis of cities: A geometrical approach
Mathematics and morphogenesis of cities: A geometrical approach
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DOI：
10.1103/physreve.83.036106
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发表时间：
2011-03-11
影响因子：
2.4
通讯作者：
Douady, Stephane
中科院分区：
文献类型：
--
作者：
Courtat, Thomas;Gloaguen, Catherine;Douady, Stephane
城市是有生命的有机体。它们是不平衡的开放系统，永远不会停止发展，有时甚至会死亡。当地的地理环境就像是限制其发展的外壳。简而言之，城市当前的布局是运行形态发生过程中的一个步骤。因此，城市呈现出巨大的形状多样性，而随机图、复杂网络理论或随机几何的传统模型都没有在同一框架中考虑城市的几何、功能和动态方面。我们在这里提出一个专门针对城市的全球数学模型，它可以描述、操纵和解释城市的街道系统的整体形状和布局。这个基于街道的框架解决了问题的拓扑和几何方面的问题。通过对几个法国城镇的静态分析（一阶和二阶拓扑、各向异性、街道缩放），我们做出假设：城市的发展遵循空间划分或延伸的逻辑。我们提出了一个模仿这种逻辑的动态模型，通过简单的一般规则和一些参数，成功地生成了多种多样的城市并再现了静态分析所指出的一般特征。
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 the traditional models, from random graphs, complex networks theory, or stochastic geometry, takes into account the 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 scaling) we make the hypothesis that the development of a city follows a logic of division or extension of space. We propose a dynamical model that mimics this logic and that, from simple general rules and a few parameters, succeeds in generating a large diversity of cities and in reproducing the general features the static analysis has pointed out.