Original Articles

Advancement of Applied Studies of Fractal Theory in Geography

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

Received date: 2003-06-01

  Revised date: 2003-06-01

  Online published: 2003-07-24


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.

Cite this article

QIN Yaochen, LIU Kai . Advancement of Applied Studies of Fractal Theory in Geography[J]. PROGRESS IN GEOGRAPHY, 2003 , 22(4) : 426 -436 . DOI: 10.11820/dlkxjz.2003.04.011