Geometric Modelling of a Class of Sierpinski-type Fractals and Their Geometric Constructions

摘要

Study on properties of Sierpinski-type fractals, including dimension, measure, Lipschitz equivalence, etc is very interesting. It is well know that studying fractal theory relies on in-depth observation and analysis to topological structures of fractals and their geometric constructions. But most works of simulating fractals are for graphical goal and often done by non-mathematical researchers. This makes them difficult for most mathematical researchers to understand and application. In [22], the authors simulated a class of Sierpinski-type fractals and their geometric constructions in Matlab environment base on iterative algorithm for the purpose of mathematical research. In this paper, we continue such investigation by adding certain rotation structure. Our results may be used for any graphical goal, not only for mathematical reasons.