Contracting Similarity Fixed Point of General Sierpinski Gasket

The article mainly studies the contracting similarity fixed point and the structure of the general Sierpinski gasket. Firstly, the paper analyzes the importance of contracting similarity fixed point in fractal geometry. Based on a series of definitions, the article studies the contracting similarity fixed point. Then, the paper researches on the structure of the general Sierpinski gasket, and describes it through function. Using a new characteristic function and other techniques, the article gives two important lemmas of the general Sierpinski gasket and the complete proof. By the proved lemmas, the article gets the formula of the contracting similarity fixed point of the Sierpinski gasket, and then proves that the aforementioned contracting similarity fixed points form a new fractal. As application, the paper classifies the above contracting similarity fixed points into three types and gives two examples.