From 1 dimension to N dimensions-fractal in automated cartographic generalization

Automated cartographic generalization has been an intensive research topic in cartography for decades. Some problems associated with this topic could be resolved to a certain extent using fractal analysis and fractal dimension. This paper investigates the fundamental theories and operational methods of generalization. Among others, methods of calculating fractal dimensions of curves and even complicated 3-dimensional geographic objects are explained. Fractal dimensions can be used as an objective criterion for both scaling the natural geographic objects and economical computer storage. More important is that the generalization algorithms based on fractal dimensions can be performed automatically.