Fractal Dimension And Its Normalized Treatment For Application

This paper has made a summary of all kinds of classical fractal dimensions. At the same time, this article summarizes the normalized methods of dimension calculation which was offered by Sheng Zhongping.Fractal dimension is an important tool for scientific research. It is an effective way that used to describe the non-smooth and irregular geometric objects in the nature and nonlinear systems. There are many kinds of methods about calculating the fractal dimensions. Its application is greatly wide. This paper firstly studies and integrates these methods systematically: the simple Self-similarity dimension; the Hausdorff dimension basing on Hausdorff measure; the Box dimension. They all have many equivalent definitions. We have also introduced the relations between the various dimensions.It requires that the scale of the measurement tends to limit for many dimension calculation methods in the above. That's very difficult to achieve in reality .Because the structural level of the actual objects is finite. Furthermore the character of dimensions that was estimated in the many literatures is the character of measure in fact. Sheng Zhongping analyzes the mechanism of the dimension character. He also gives a series of new conceptions as well as two rules that the dimension character must have. Thereout he establishes the normalized methods. Based on the theorem of collage thinking and the actual significance, we have the fractal divided into several parts broadly similar. The core conceptions were the introduced of the normative precision dimension and the normative fitted dimension. As a dimension feature, they can be used for general fractal cluster study. It is compatible telescopic invariance and local invariance which is same with self-similar fractal.