自仿射分形曲线标度指数的算法及其应用  

Algorithm for Scaling Exponent of Self-affine Fractal Curve and its Application

作　　者：汪富泉[1] 

机构地区：[1]广东石油化工学院继续教育学院,茂名525000

出　　处：《工程数学学报》2014年第5期728-732,共5页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(51179110);国家重点基础研究发展计划(2013cB036401)~~

摘　　要：分形曲线的自仿射性及其工程应用是一个重要研究课题.标度指数是刻画自仿射分形曲线的特征值,Matsushita、Nikora、Sapozhnikov等分别根据方差、测度和对数关联积分提出标度指数的算法.本文分析了上述算法的不足,使用坐标和测度建立了一个新算法.本算法符合分形原理,可较好反映曲线的自仿射性和纵横方向的不同变化特征,计算过程简单明了,便于工程应用.最后,我们应用上述四种算法计算了中国下荆江河道的标度指数,揭示了河道的自仿射性和横向摆动特征,对河道整治工程具有重要参考意义.Self-affnity of fractal curves and its application are important research topics. The Scaling exponent is used to describe the eigenvalues of the self-affine fractal curve. Matsushita, Nikora and Sapozhnikov et al have proposed different algorithms of scaling exponent according to variance, measurement and logarithmic correlation integral, respectively. In this paper, we propose a new algorithm by analyzing the demerits of their methods. This new algorithm, based on the fractal theory, may better disclose the self-affinity and variable features of fractal curves in vertical and horizontal directions, and the calculating process is also simple and clear, which can be effectively applied to engineering. Moreover, the self-affine scaling exponent of Lower Jingjiang channel is simulated by the above four algorithms, so as to reveal the self-affinity and lateral oscillation features of waterway, which is of great value to channel improvement engineering.

关 键 词：自仿射分形 标度指数 下荆江 

分 类 号：O213[理学—概率论与数理统计]