一类分形曲线的构造算法及维数

Algorithm and Dimension Research of Fractal Curves

以分形理论为依据,根据分形几何描绘自然景物的基本思想,论述了一类分形曲线的递归算法和生成过程,通过参数控制,研究了如何使一条直线段生成了3种不同结构的分形曲线,运用C++编程绘出3种不同结构的分形曲线的图形;同时对Hausdorff维数理论进行了深入的研究与探讨,并且以Hausdorff维数理论为依据分析了由直线分形演绎生成的分形曲线的维数,把维数理论与实践应用相结合。本研究为分形曲线的生成和实践应用提供了理论依据。

Based on fractal theory and basic thought that fractal geometry describes natural scenery, a recursion algorithm of a special kind of curve and its generating progress is discussed in detail. By controlling parameter, the problem how to generate three form of fractal curves from a straight line is studied. And then the dimension theory of Hausdorff is discussed and is used to analyze the dimensions of three curves. Finally, the dimension theory is applied to practice. The study provides a basis for both the generation and practical applications of fractal curves.