Fractal properties of interpolatory subdivision schemes and their application in fractal generation

In this paper, we present a novel method to analyze the fractal properties of the 4-point binary and the 3-point ternary interpolatory subdivision schemes. The relationship between the parameter and the fractal behavior of the limit curve of the two schemes is obtained, respectively. As an application of the obtained results, the generation of fractal curves and surfaces is discussed. Many examples show that the results presented in this paper offer a direct means for a fast generation of fractals.