在前期工作的基础上,对东北地区城市体系空间结构的分形维数进行了分省、分区计算,然后借助各种不同的分维数值对东北三省城市体系的地理结构进行了区域差异分析,进而总结了几种对于城市体系具有普遍意义的分形空间图式,最后对东北地区城市体系空间结构的分形优化提出了若干建议。文章为城市体系空间结构的分形研究提供了一个完整的范例。

A comprehensive study based on Northeast China is made of the fractal spatial structure of urban systems in the paper which can be used as a typical example on the geographical fractal researches in spatial structure of systems of cities and towns.
In the first part,the rudimentary knowledge on the urban geographical fractal theory advanced mainly by the authors is given as an introduction to the next part,and a series of new thoughts,view points,and concepts,etc,is presented to improve and consummate the previous theory,and in particular,the geographical meanings of the related fractal dimensions are made more clear than ever,and the relationships between the different fractional dimensions are systematized.
In the second part,the values of the fractal dimensions,including point-point correlation dimension,one-point correlation dimension,and aggregation dimension,of the urban systems in Northeast China are calculated according to different regions,especially,different provinces, namely,Liaoning,Jilin,and Heilongjiang,by means of ln-ln plots and the formula given in the preceding part which are transformed into another convenient expressions in due form,and the computed results are tabulated and graphed in order to analyse the fractal features of the spatial structure of the urban systems concerned.
In the third part,analyses are made as the climax of the study.Firstly,the values of the fractal dimensions of the spatial structure of the different urban systems which are divided chiefly in accordance with provincial boundaries are compared with one another,their characters are illustrated,their implications are interpreted,and the preliminary theory is propounded to account for the formation of the fractal urban systems.Secondly,the spatial patterns of the fractal structure of the studied urban systems are abstracted and classified into three basic types.Thirdly,some propositions are made to optimize the spatial structure of the urban systems of Northeast China.