【摘要】 根据分形理论,应用网格法系统地探讨了中国大陆山系、断层系与水系的空间分形结构,并计算出中国大陆以及三大自然区山系、断层系与水系的空间维数,在此基础上还探讨了山系、断层系与水系空间维数在三大自然区的变化情况。得出的基本结论为:(1)中国大陆山系、断层系与水系的空间分形结构是客观存在的;(2)中国大陆山系的空间维数值为1.1513,中国大陆断层系的空间维数值为1.2507,中国大陆水系的空间维数值为1.4169;(3)在三大自然区中,山系、断层系空间维数值均以青藏高原区相对为最大,而以西北干旱区相对为最小,山系与断层系空间维数值的变化在空间上有着一致的对应关系,山系空间维数值较大,则断层系空间维数值亦较大,而水系空间维数值的大小依次为东部季风区水系、青藏高原区水系与西北干旱区水系;(4)中国大陆山系、断层系空间维数响应的关系为D_F=0.6884D_M+0.4446(式中:D_M为山系的空间维数,D_F为断层系的空间维数)。该式不仅为山系、断层系关系的定量化研究提供了全新的手段,而且还为山系、断层系内在密切关系的证实提供了全新的分形理论的证据;(5)整个中国大陆山系、断层系与水系的空间维数值并不等于三大自然区相应要素空间维数值的简单加和平均值;(6)进行山系等地貌现象的分形研究,应遵循相同的分维更多还原

【Abstract】 Mandelbrot enunciated the uncertainty of the length of a coastline in his paper" How long is the coastline of Britain?" published in " Science" in 1967. The fractal concept was presented for the first time in that paper and has been applied to many fields ever since. Although fractal dimensions of lots of phenomena were calculated , related studies on fractal character of mountains, faults and river basins of China continent are seldom seen. This issue is discussed in this paper. Some significant conclusions are drawn: (l)The fractal character objectively exists in mountains, faults and river basins of China continent. (2)The fractal dimensions of mountains and faults of China continent are 1.1513 and 1.2507 respectively by the box-counting method,that of river basins of China continent is 1.4169. (3)The change of fractal dimensions of mountains of China continent in three natural regions is accord with that of faults. (4)The relationship of fractal dimensions between mountains and faults of China continent may be expressed as DF = 0.6884DM + 0.4446 (Where DM is the fractal dimension of mountains, DF is the fractal dimension of faults) , there is a good correlation between them. Thus,a new fractal proof may be offered to prove the internal relation between mountains and faults. (5)The fractal dimension of mountains of China continent is unequal to the average fractal dimension of all its parts, as well as faults and river basins of China continent. (6)The same fractal method should be adopted for comparison of geomorphologic phenomena .更多还原