分形理论在地理学中的应用研究进展

Advancement of Applied Studies of Fractal Theory in Geography

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。

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; finally the problems concerned are discussed and future applications of it are also prospected