| 分形理论在地理学中的应用研究进展 |
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| 引用本文： | 秦耀辰,刘凯.分形理论在地理学中的应用研究进展[J].地理科学进展,2003,22(4):426-436. |
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| 作者姓名： | 秦耀辰 刘凯 |
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| 作者单位： | 河南大学环境与规划学院,开封475001 |
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| 基金项目： | 国家自然科学基金(49471025) |
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| 摘 要： | 美国数学家Mandelbrot提出的分形理论为解决复杂性问题提供了有效方法。地理学的复杂性问题已成为分形理论的重要实证研究领域。本文根据国内已有的文献,在概括分形理论主要内容的基础上,对地理学各分支领域的应用研究现状及有关问题进行了评述,并就地理学分形研究的前景作了展望。
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| 关 键 词： | 地理学 分形理论 分形维数 进展 |
| 文章编号： | 1007-6301(2003)04-0426-11 |
| 收稿时间： | 2003-06-01 |
| 修稿时间： | 6/1/2003 12:00:00 AM |
Advancement of Applied Studies of Fractal Theory in Geography |
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| QIN Yaochen,LIU Kai.Advancement of Applied Studies of Fractal Theory in Geography[J].Progress in Geography,2003,22(4):426-436. |
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| Authors: | QIN Yaochen LIU Kai |
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| Institution: | College of Environment and Planning, Henan University, Henan, Kaifeng 475001 |
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| Abstract: | American mathematician B B Mandelbrot introduced fractal theory in the middle of 1970s and it is an effective method for sophisticated problems Before 1975 mathematicians had found already some fractals, for examples, the Canter ternary and Peano curves Since then,it has been applied in almost every field of natural science and social science successfully Especially in recent years, fractal theory has aroused a great amount of interest and attention from scientists So called "fractal" means "irregular, fractional, fragmental" and its core is self similarity To characterize fractal, different dimensions are defined according to methods to calculate it Examples include Hausdorff dimension, capacity dimension,correlation dimension, etc Fractal theory describes irregular (fractal) objects in quantitative manner The property of fractals can be mathematically expressed by self simility and self affinity suggesting that the structural phenomena exist at any scale Fractal dimension as a measure provides geometric property of fractals In 1986, B B Mandelbrot proposed: "the shape whose components are similar to its entirety is called fractal" and "fractal is inflexibility under nonlinear transformations" We can define a fractal assemble as:Nn =C/rn DWhere Nn is the number of the objects whose measurement scale is rn,C is ration and D is fractal dimensionIn this paper, the main contents of fractal theory are introduced firstly; then based on a great number of correlative papers the domestic conditions of applications of fractal theory in geography are reviewed. |
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| Keywords: | fractal theory fractal dimension geography advancement |
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