Julia集的反函数迭代算法

Inverse Function Iterative Algorithm for the Julia Set

在研究二次函数等简单幂函数的Ju lia(朱利亚)集过程中,发现传统的逃逸时间算法耗费机时,并且得到的是Ju lia集的填充集而不是Ju lia集的吸引子。该文介绍了Ju lia集的反函数迭代基本算法和基于IFS(函数迭代系)反函数迭代算法。并且在反函数迭代的基本算法的基础上,提出了通过对迭代顺序的改变,以减少在迭代过程中对内存空间的需求。文中将反函数迭代算法与传统的Ju lia集的逃逸时间算法进行了仿真对比,表明利用反函数迭代算法可以极大的减少机时,并且利用该算法可以得到Ju lia集的吸引子。

In studying the simple quadratic function of the Julia set, we found it was time consuming and only got the Julia set＇s filled set but not its attractor by using the traditional escape time arithmetic. This paper introduces the basic arithmetic and IFS（ Iterated Function System） arithmetic using inverse function iteration method to draw the Julia set. Based on the basic arithmetic, this paper develops a new iteration order for reducing the demand for memory. In this paper, by comparing and contrasting the inverse function iteration arithmetic with the traditional escape time arithmetic, we find the inverse function iteration arithmetic can greatly decrease working time, and we can get the Julia set＇s attractor.