The Technology Of Formal Fractal Modeling

Mandlebrot created fractal in the 1970s, irregular and unlimited fine structure of the self-similar are the most important features of the fractal , so the fractal can be well used to define and express the complex geometry which express difficultly by continental geometric.The generation algorithm of fractal graphics is one of the hottest research on fractal, and iterated function systems and L system in fractal modeling, simulating nature features have broad application prospects, but their shortcomings are difficult to predict and are complex to express .This thesis reviews the fractal development history and the generation algorithm of fractal graphics by iterated function systems and L system , and studies the formal modeling system fractal structure of the grammar, semantics and fomal expression. According to calculating process generated by IFS attractor, we propose symbol rewriting algorithm of IFS which makes a connction between IFS and L system,and give the algorithm examples of a suitable symbol rewriting system, and achieve fractal modeling system of symbol rewriting of IFS. The definition of symbol rewriting system, the conversion of IFS system, The descriptions and examples of IFS symbol rewriting algorithm show that it has a more capabilitiy of expression, modeling and intuitive interactivity than conventional IFS and L system.This thesis results provide a new way for fractal modeling technology. The axiomatic method and the use of formal methods greatly improve the realization of fractal graphics efficiency. It is very useful for nature scene simulating, flash making, architecture foiling and virtual reality etc.