The Theory Of Generating Fractal Pictures And Practice

This paper studies generating fractal picture by computer, especially we give a detailed study of generating fractal picture by L-system.A L-system first produce a sequences of words over a finite alphabet, the geo-metric realization of these words give finer and finer approximation of a fractal sets. This is an important method of producing fractal pictures.However, the mathematical theory of L-system is not rigorous. In this paper, we introduce a notion of consistence condition, which will make the theory rigorous. We show that only when a L-system satisfies the consistence condition, it will produce a sequence of sets convergent to a fractal. Indeed, we determine the iterated function system(IFS) of a L-system satisfying the consistence condition.We also point out that a L-system with several generation is corresponding to a graph-directed IFS.