Scaling of Geographic Space as a Universal Rule for Mapping or Cartographic Generalization

Mapping, or cartographic generalization in particular, is a process of producing maps at different levels of detail by retaining essential properties of the underlying geographic space. In this paper, we explore how mapping or cartographic generalization process can be guided by the underlying scaling of geographic space. Scaling refers to the fact that in a large geographic area small objects are far more common than large ones. In the corresponding probability density function, this scaling is reflected as a heavy tailed distribution such as a power law, lognormal, and exponential distribution. In essence, any heavy tailed distribution consists of the head of the distribution (with a low percentage of objects) and the tail of the distribution (with a high percentage of objects). We therefore suggest that the objective of the mapping process is to retain the objects in the head yet to eliminate those in the tail. We applied this selection principle to several generalization experiments, and found that the scaling of geographic space can indeed be a universal rule for mapping and cartographic generalization. We further relate the universal rule to T\"opfer's radical law (or trained cartographers' decision making in general), and illustrate several advantages of the universal rule compared to the radical law.