论地理系统的空间与维度
On the Spaces and Dimensions of Geographical Systems
摘要：
为了消除不同地理空间和维度概念的混乱，本文提出了一个新的空间理论框架。基于三组分形维数，将地理空间分为三类：实空间（R-空间）、相空间（P-空间）和序空间（O-空间）。真实空间是具体的或可视的空间，其分形维数可以通过数字地图或遥感影像来计算。相空间和序空间都是抽象空间，其分维值不能用一两幅图或图像来估计。相空间的维数可以用时间序列来计算，序空间的维数可以用某一时刻的截面数据来确定。通过三个实例说明了地理系统的三种空间类型和分维。新空间理论可以用来解释城市异速生长律的标度指数和基于Horton河流定律的分维等地理标度律参数。
英文摘要：
To remove the confusion of concepts about different sorts of geographical space and dimension, a new framework of space theory is proposed in this paper. Based on three sets of fractal dimensions, the geographical space is divided into three types: real space (R-space), phase space (P-space), and order space (O-space). The real space is concrete or visual space, the fractal dimension of which can be evaluated through digital maps or remotely sensed images. The phase space and order space are both abstract space, the fractal dimension values of which cannot be estimated with one or two maps or images. The dimension of phase space can be computed by using time series, and that of order space can be determined with cross-sectional data in certain time. Three examples are offered to illustrate the three types of spaces and fractal dimension of geographical systems. The new space theory can be employed to explain the parameters of geographical scaling laws, such as the scaling exponent of the allometric growth law of cities and the fractal dimension based on Horton's laws of rivers.
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