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

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