Dimension estimation of subdivision fractal and its application

In this paper, we evaluate fractal dimension of the fractal curve generated by the 3-point ternary interpolatory subdivision scheme. A formula between the subdivision parameter and the fractal dimension of the limit fractal curve is obtained. As an application of the obtained results, the generation of fractal curves and surfaces is discussed. The presented results in this paper can also be used to generate fractal curves with fractal dimension bounded above. Many examples demonstrate that the results presented in this paper offer a direct means for an effective generation of fractals.