基于城市异速生长与分形维数的地理空间
Geographical space based on urban allometry and fractal dimension
AI总结：
本文通过将城市异速生长分为纵向、横向和等值线三类，推导出三组分形维数，并据此将城市地理空间划分为实际空间、相空间和有序空间，从而为解释城市分形维数和拓展地理空间分析理论提供统一框架。
摘要：
传统的地理空间概念主要指向基于景观、地图和遥感影像的实际空间。然而，这种空间概念不足以解释城市不同类型的分形维数。由齐普夫定律和时间序列分析得到的分形维数并不属于传统地理空间。根据数据集的性质，城市异速生长可分为三种类型：表示时间的纵向异速生长、表示等级体系的横向异速生长以及表示空间的等值线异速生长。依据量纲一致性原理，异速生长标度指数必须是一个分形维数与另一个分形维数之比。从上述三种异速生长模型中，我们可以推导出三组分形维数。根据这三组分形维数和维数唯一性原理，城市地理空间可分为三类：基于等值线异速生长和空间分布的实际空间、基于纵向异速生长和时间序列的相空间，以及基于横向异速生长和位序—规模分布的有序空间。这种广义空间不仅有助于解释城市各种分形维数，还可用于发展新的地理空间分析理论和方法。
英文摘要：
The conventional concept of geographical space is mainly referred to actual space based on landscape, maps, and remote sensing images. However, this notion of space is not enough to interpret different types of fractal dimension of cities. The fractal dimensions derived from Zipf's law and time series analysis do not belong to the traditional geographical space. Based on the nature of the datasets, the urban allometry can be divided into three types: longitudinal allometry indicating time, transversal allometry indicating hierarchy, and isoline allometry indicating space. According to the principle of dimension consistency, an allometric scaling exponent must be a ratio of one fractal dimension to another. From abovementioned three allometric models, we can derive three sets of fractal dimension. In light of the three sets of fractal dimension and the principle of dimension uniqueness, urban geographical space falls into three categories, including the real space based on isoline allometry and spatial distribution, the phase space based on longitudinal allometry and time series, and order space based on transversal allometry and rank-size distribution. The generalized space not only helps to explain various fractal dimensions of cities, but also can be used to develop new theory and methods of geospatial analysis.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
