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Contracting similarity fixed point of a class of self-affine fractal

Shanhui Sun, Hong Li, Qun Ning, Bingqiu Zhang

By constructing a kind of self-affine fractal, contracting similarity fixed point of this kind of fractal is studied. The paper introduces the basic concept of the self-affine fractal, and compares it with the self-similar fractal to show their connection and difference. Then the paper introduces the definition of the contracting similarity fixed point and shows the application and importance of it. Through the mathematical model depiction of self-affine fractal, combined with the newly-defined eigenfunction, the paper gives the contracting mapping function of contracting similarity fixed point. Based on the contracting mapping function, the paper shows the formula of the contracting similarity fixed point of the selfaffine fractal. As an application, the paper finally presents two relevant examples.