高次复多项式的Mandelbrot-Julia集

Mandelbrot-Julia Sets of the High Degree Complex Polynomials

阐述了高次复多项式的 Mandelbrot-Julia 集(简称 M-J 集)理论,给出了高次复多项式 M-J 集的定义,并利用逃逸时间算法构造出一系列高次复多项式的 M-J 集。利用复变函数理论和计算机制图相结合的实验数学的方法,对 M-J 集的分形结构进行了深入研究,结果表明: 从理论上分析了 M 集的对称性; 通过定性地建立 M 集上 J 集的整体刻画,发现 M 集包含了 J 集构造的大量信息。

In this paper the theory of Mandelbrot-Julia sets of high degree complex polynomials is introduced, a series of the Mandelbrot-Julia sets of high degree complex polynomials is constructed through escape-time technique. After deeply research on Mandelbrot-Julia sets, the authors have done innovated work as follows: ① Theoretical analyze the nature of symmetry of generalized Mandelbrot-Julia sets; ② We find that Mandelbrot sets contain abundant information of structure of Julia sets by founding the whole portray of Julia sets based on Mandelbrot sets qualitatively.