2003 , Vol. 22 >Issue 4: 426 - 436

• 河南大学环境与规划学院,开封475001

修回日期: 2003-06-01

网络出版日期: 2003-07-24

Advancement of Applied Studies of Fractal Theory in Geography

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• College of Environment and Planning, Henan University, Henan, Kaifeng 475001

Revised date: 2003-06-01

Online published: 2003-07-24

### 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:Nn =C/rn DWhere Nn is the number of the objects whose measurement scale is rn,C is ration and D is fractal dimensionIn 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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