Study On Fractal Modeling System Based On Graphic Rewriting

Fractal geometry is called " nature's geometry",which was born in the 1970s.it is mainly used to depict geometry shapes of irregular or rough. Many facts show that fractal widely exists in the nature, and spreads all over fields such as mathematics, physics, chemistry, material science, biology and medicine, geography, earthquake and astronomy, computer science and so on. With the development of fractal theory, increasingly importance has been attached to the fractal modeling.Nowadays, fractal modeling has been one of important research programs in computer graphic field.The main research object of the paper is a fractal modeling system based on graphic rewriting.This paper reviewed the birth of fractal theory and it's relation with the computer graphic, described the basic fractal theory used in the fractal modeling, including self-similarity and self-affinity, scaleless character, fractional dimension and the basic characteristics of the fractal. And two existing fractal modeling systems were researched thoroughly,including L-System and Iterated Function System.Finally,we consulted the original fractal modeling systems,including the expression of formal language, the visible modeling process of replacing graphic by graphic, built the fractal modeling system based on graphic rewriting.In line with the principle of replacing graphic by graphic, Graphic Rewriting System based on symbol is defined in this paper. There are a couple of possibilities in the process of replacing graphic by graphic of the new System,according to the complexity of Symbol system and application requirement, a classification of Graphic Rewriting System is made. The paper focus on analyzing context-free Graphic ewriting system, including its universal structures, processing methods and relationship with L-System and IFS.Compared with the Iterated Function System, The new system does not require that the transformation must be compressed,at the same time,the new system can control the fractal graphic of Recurrent Interated easily, Support the replacement of non-linear and unrestricted relations;the biggest difference with L-system is the use of Customizing symbols grammar, Makes the replacement process is no longer limited to the control of two-point geometry and the relevant processes, Support for arbitrary affine transformation and the specific non-linear transformation, support for basic graphics sets and modeling methods.The results show that Graphic Rewriting System is simpler than L-System and IFS. Furthermore, it has stronger modeling ability and more visible modeling process.