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Koch类方波曲线中特征角序列函数的一种求法

发表时间:2009-07-15  浏览量:1446  下载量:525
全部作者: 郝五零,郝军军
作者单位: 云南大学物理系非线性复杂系统中心
摘 要: 通过讨论Koch类方波曲线第1次生成曲线时的特征角序列函数H的生成条件,找到了一个简化的特征角序列函数H′,并运用待定系数法求出了此函数。然后,运用归纳法求出了第n次生成曲线时的简化的特征角序列函数H′,更便于求出Koch类方波曲线的解析表达式,从而为研究生成元为2n(n是整数)段的严格自相似的规则分形曲线提供了一种更为有效的方法。
关 键 词: 几何学;分形;特征角序列函数;待定系数法;Koch类方波曲线
Title: One method for getting the characteristic angle sequence function of square wave Koch-like curve
Author: HAO Wuling, HAO Junjun
Organization: Center for Nonlinear Complex Systems, Department of Physics,Yunnan University
Abstract: This paper deals with the formation conditions of the characteristic angle sequence function H of square wave Koch-like curve obtained at the first time iteration. And it achieves a simpler characteristic angle sequence function H′ by analyzing the formation conditions of H based on the method of undetermined coefficient. Moreover, the paper obtains the simplified characteristic angle sequence function H′ at the nth time iteration on the basis of inductive method. Thus, the analytic expressions of the square wave Koch-like curve can be calculated more easily and a more effective method for studying the rigorously self-similar and regular fractal curves which generators have 2n pieces (n is an integer) is presented.
Key words: geometry; fractal; characteristic angle sequence function; method of undetermined coefficient; square wave Koch-like curve
发表期数: 2009年7月第13期
引用格式: 郝五零,郝军军. Koch类方波曲线中特征角序列函数的一种求法[J]. 中国科技论文在线精品论文,2009,2(13):1341-1344.
 
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