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