Visualizing Space-Time Dynamics in Scaling Systems
Visualizing Space-Time Dynamics in Scaling Systems
复制标题
DOI：
10.1002/cplx.20342
复制
发表时间：
2010-11-01
期刊：
影响因子：
2.3
通讯作者：
Batty, Michael
中科院分区：
文献类型：
--
作者：
Batty, Michael
人类系统中缩放的特征是众所周知的幂律，其关键特征是物体的尺寸分布在空间和时间上表现出自相似性。在许多系统中，例如这里用作示例的城市、公司和高层建筑，幂律代表了其等级规模分布的肥尾或重尾的近似值，在时间上显得稳定，在数十年甚至数百年的时间里其尺度几乎没有变化。然而，当检查它们的排名随时间变化的详细动态时，会发现这种分布存在相当大的波动性。为了探索这种微波动性，我们引入了随空间和时间变化的等级移动的测量，并使用“等级时钟”的概念可视化大小分布。我们以 1300 年至 1861 年间意大利城镇的人口来说明这一点，然后将此分析与公元前 430 年以来的世界城市规模分布、1790 年以来的美国、1901 年以来的英国（英格兰、苏格兰、威尔士）和 1950 年以来的以色列进行比较。当我们将此分析扩展到 1955 年以来的美国公司以及纽约市和世界各地的高层建筑的分布时1909 年，我们生成了丰富的时空动力学组合，这增加了我们对不同系统如何在面对微观波动时在宏观层面表现出稳定性和规律性的理解。 (C) 2010 年 Wiley 期刊公司。复杂性 16：51-63，2010 年
The signature of scaling in human systems is the well-known power law whose key characteristic is that the size distributions of their objects display self-similarity in space and time. In many systems such as cities, firms, and high buildings used here as examples, power laws represent an approximation to the fat or heavy tails of their rank-size distributions, appearing stable in time with little change in their scaling over tens or even hundreds of years. However, when the detailed dynamics of how their ranks shift in time is examined, there is considerable volatility in such distributions. To explore this microvolatility, we introduce measures of rank shift over space and time and visualize size distributions using the idea of the "rank clock." We illustrate this for populations of Italian towns between 1300 and 1861 and then compare this analysis with city-size distributions for the world from 430 B.C.E., the United States from 1790, Great Britain (England, Scotland, Wales) from 1901, and Israel from 1950. When we extend this analysis to the distribution of US firms from 1955 and high buildings in New York City and the world from 1909, we generate a rich portfolio of space-time dynamics that adds to our understanding of how different systems can display stability and regularity at the macro level in the face of considerable volatility at the micro. (C) 2010 Wiley Periodicals, Inc. Complexity 16: 51-63, 2010