计算机工程与应用 ›› 2007, Vol. 43 ›› Issue (5): 30-32.

• 学术探讨 • 上一篇    下一篇

逃逸时间法生成Julia集的算法分析和具体实现

秦宣云 任波   

  1. 中南大学 应用数学与应用软件系 中南大学数学科学与计算技术学院
  • 收稿日期:2006-06-08 修回日期:1900-01-01 出版日期:2007-02-11 发布日期:2007-02-11
  • 通讯作者: 任波

Arithmetic analysis and idiographic realization of creating the Julia set by the Escape Time Algorithm

XuanYun Qin Bo Ren   

  • Received:2006-06-08 Revised:1900-01-01 Online:2007-02-11 Published:2007-02-11
  • Contact: Bo Ren

摘要: 逃逸时间算法是生成Julia集最常用的算法,本文针对非线性复映射f(z)=zm+c为迭代函数的情形进行讨论。首先,根据逃逸时间算法的基本原理给出相应的算法步骤;然后,对迭代函数f(z)=zm+c进行了详细研究,从而合理地确定了算法中需要控制的变量Rmax和B(Rmax:判断({fn(z0)}有界与否的界限值;B:初始迭代点z0的取值范围)的取值,这样就大大地减少了迭代次数,从而提高了算法的运算效率。

关键词: 迭代函数, Julia集, 逃逸时间算法, 控制变量

Abstract: The familiar algorithm of creating the Julia set is the Escape Time Algorithm. In allusion to the state that the nonlinear complex mapping f(z)=zm+c is used as the iteration function, this paper firstly gives the corresponding algorithm-process according to the rationale of the escape time algorithm, then studies the iteration function f(z)=zm+c detailedly. Finally, the controlling variables Rmax and B (Rmax:the limitation of justifying if ({fn(z0)} is bounded; B:the range of the initial point z0) are made certain, therefore the number of iteration is reduced and the computing efficiency of the algorithm is improved too.

Key words: iteration function, Julia set, escape time algorithm, controlling variable