| INFLUENCE OF SERIES OF SQUARE GRIDS ON FRACTAL DIMENSIONS—A Case Study of Mountains of China＇s Mainland |
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| 作者姓名： | ZHUXiao-hua CAIYun-long |
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| 作者单位： | DepartmentofResourcesandEnvironmentalGeosciences／KeyLaboratoryforEarthSurfaceProcessesundertheMinistryofEducation,PekingUniversity,Beijing100871,P.R.China |
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| 摘 要： | 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 by the box-counting method, the quantitative influence of series of square grids on them is ignored. The issue is systematically discussed as a case study of the mountains of China‘s Mainland in this paper. And some significant conclusions are drawn as follows: 1) Although the fractal character objectively exists in the mountains of China‘s Mainland, and it does not vary with the changes of series of square grids, the fractal dimensions of the mountains of China‘s Mainland are different with these changes. 2) The fractal dimensions of the mountains of China‘s Mainlandvary with the average lengths of sides of series of square grids. The fractal dimension of the mountains of China‘s Mainland is the function of the average length of side of square grid. They conform to the formula D=f(r) (where D is the fractal dimension, and r is the average length of side of square grid). 3) Different dots of data collection can affect the fractal dimension of the mountains of China‘s Mainland. 4) The same range of length of side of square grid and dots of data collection can ensure the comparison of fractal dimensions of the mountains of China‘ s Mainland. The research is helpful to get the more understanding of fractal and fractal dimension, and ensure that the fractal studies would be scientific.
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| 关 键 词： | 不规则碎片形 海岸线 地理学 中国大陆 |
| 收稿时间： | 18 May 2003 |
Influence of series of square grids on fractal dimensions |
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| ZHUXiao-hua CAIYun-long.Influence of series of square grids on fractal dimensions[J].Chinese Geographical Science,2004,14(1):9-14. |
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| Authors: | Zhu Xiao-hua Cai Yun-long |
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| Institution: | (1) Department of Resources and Environmental Geosciences/Key Laboratory for Earth Surface Processes under the Ministry of Education, Peking University, 100871 Beijing, P. R. China |
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| 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 by the box-counting method, the quantitative influence of series of square grids on them is ignored. The issue is systematically discussed as a case study of the mountains of China’s Mainland in this paper. And some significant conclusions are drawn as follows: 1) Although the fractal character objectively exists in the mountains of China’s Mainland, and it does not vary with the changes of series of square grids, the fractal dimensions of the mountains of China’s Mainland are different with these changes. 2) The fractal dimensions of the mountains of China’s Mainland vary with the average lengths of sides of series of square grids. The fractal dimension of the mountains of China’s Mainland is the function of the average length of side of square grid. They conform to the formula D=f(r) (where D is the fractal dimension, and r is the average length of side of square grid). 3) Different dots of data collection can affect the fractal dimension of the mountains of China’s Mainland. 4) The same range of length of side of square grid and dots of data collection can ensure the comparison of fractal dimensions of the mountains of China’s Mainland. The research is helpful to get the more understanding of fractal and fractal dimension, and ensure that the fractal studies would be scientific. |
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| Keywords: | fractal fractal dimension series of square grids China’ s Mainland |
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