分形维数基于DLA模型的算法改进

A New Method to Calculate Fractal Dimension of DLA Model

现阶段的分形动力学生长模型多采用DLA模型,而维数的计算多依赖于盒计数法。但是由于盒计数法研究对象的数学局限性及计算的复杂、烦琐,使得其应用具有局限性,动力学机理不明确。为此,通过改进盒计数法得到了DLA模型的点维数di,并与盒计数法的结果相对比,验证了本方法在DLA模型图形维数计算方面的适用性、可靠性以及简单可操作性,并证明了点维数具有分形动力学特性,为以后利用盒计数法实现盒子转化点,点转化线长,直至构建出基于线和动力学关系的分形维数公式作理论探讨和准备。

DLA model is often adopted in the fractal dynamics growth models, and the box dimension calculation method is often used to calculate the dimension. Because of limitations of the applicability of the box dimension in mathematics and complicated calculations involved, a wide application of the box dimension is difficult and the description of dynamics mechanism will contain factors of uncertainty. To overcome those difficulties, point dimension d~ of DLA model is obtained by improving the calculation method of box dimension in this paper, and the result is compared with that of box dimension, and it is shown that point dimension does have fractal dynamics characteristics and can be used to calculate the dimension of DLA model, with reliability and efficiency, and easy to be implemented. To transform from the box to the point, from the point to the line and to obtain the dimension formulas for the line and dynamics, this paper provides some theoretical basis.