城市的标度效应：体量、规模与形状

Urban Scaling Revisited: Size, Scale, and Shape

迈克•巴蒂
英国伦敦大学学院高级空间分析中心 主席，教授，博士生导师 英国皇家科学院院士，中国科学院外籍院士 m.batty@ucl.ac.uk

沈 尧
同济大学建筑与城市规划学院 同济大学中英联合城市科学实验室 副教授，博士生导师

胡玶妍（译）
同济大学建筑与城市规划学院 硕士研究生

摘要: 归纳了4组城市标度效应，用以描述和解释城市及其空间区位随规模变化的理论与方法。“城市标度律”指的是城市各类规模要素随城市发展而变化的趋势，如人口增长等，其反映了城市系统间的时序演化关系。这些关系涵盖了城市位序与规模法则、基于区位的人口密度函数、基于空间距离的空间相互作用引力模型，以及与城市规模相关的社会经济要素（如收入等）随着城市规模扩张的异速增长规律。这些规则可以被4个定律所解释，分别是齐普夫定律（Zipf's Law）、克拉克定律（Clark's Law）、托布勒定律（Tobler's Law）和马歇尔定律（Marshall's Law）。以高精度、广覆盖的英国城市就业和人口分布为案例，讨论这些理论和定律在城市中的应用，反映出一种顺应规律发现的空间智能形式。

Abstract: In this research, we define four different sets of relationships that tie together theories and methods that describe and explain how cities and their spatial locations change as they scale. By scaling we mean changes in the size of urban phenomena such as population that take place as cities grow and more generically, how cities change over time. These relationships cover city size distributions and the rank size rule, urban density functions that relate to how dense populations are with respect to their location around the central area of cities, how gravitational interactions between locations scale with respect to distance, and finally how attributes relating to size in cities such as income scale allometrically as cities change in size. These four relationships can be associated with those who first popularised their form, which in the order we introduce them, are what we call Zipf’s Law, Clark’s Law, Tobler’s Law, and Marshall’s Law. Having described their form, we illustrate their application to the distribution of employment and populations for small areas and for whole cities in the UK, reflecting a form of spatial intelligence for planning informed by the principles of urban scaling.

关键词：标度律；异速增长；规模；人口；就业

Keyword: scaling; allometry; size; population; employment

中图分类号：TU981

文献标识码: A

KOFFKA K. The principles of gestalt psychology[M].
London: Routledge and Kegan Paul, 1935.
WEST G. Scale: the universal laws of life and death
in organisms, cities and companies[M]. London: Weidenfeld and Nicolson, 2017.
BATTY M. Cities and complexity: understanding cities with cellular automata, agent-based models, and
fractals[M]. Cambridge MA: The MIT Press, 2005.
BATTY M, LONGLEY P A. Fractal cities: a geometry of form and function[M]. London and San Diego:
Academic Press, 1994.
ZIPF G K. Human behavior and the principle of least
effort[M]. Cambridge MA: Addison-Wesley, 1949.
CLARK C. Urban population densities[J]. Journal of
the Royal Statistical Society, Series A (General), 1951,
114: 490-496.
TOBLER W. A computer movie simulating urban growth in the Detroit region[J]. Economic Geography,
1970, 46(s): 234-240.
MARSHALL A. Principles of economics[M]. London: MacMillan Company, 1890.
BETTENCOURT L M A, LOBO J, HELBING D, et
al. Growth, innovation, scaling, and the pace of life
in cities[J]. Proceedings of the National Academy of Sciences, 2007, 104(17): 7301-7306.
ARCAUTE E, MOLINERO C, HATNA E, et al. Cities and regions in Britain through hierarchical
percolation[J]. Royal Society Open Science, 2016, 3(4): 150691.
BATTY M, MILTON R. A new framework for very large-scale urban modelling[J]. Urban Studies, 2021, 58(15): 3071-3094.
Centre for Cities. CfC cities data tool[EB/OL]. [2025-03-29]. https://www.centreforcities.org/data-
tool/#graph=map&city=show-all.
BETTENCOURT L M. Introduction to urban science:
evidence and theory of cities as complex systems[M].
Cambridge: The MIT Press, 2021.
BERRY B J L. Cities as systems within systems of cities[J]. Papers of the Regional Science Association, 1964, 13: 146-163.