由复映射z←zα+c(α<0)所构的广义M-集的研究

数学物理学报 ›› 1999, Vol. 19 ›› Issue (1): 73-79.

由复映射z←zα+c(α<0)所构的广义M-集的研究

(东北大学信息科学与工程学院 |沈阳 110006)
|(东北大学计算中心 |沈阳 110006)

出版日期:1999-02-01 发布日期:1999-02-01

Reserches on General Mandelbrot Sets from Complex Map z←zα+c(α<0)

(School of Information Science &|Engineering, Northeastern University, Shenyang 110006) |
(Computation Center, Northeastern University, Shenyang 110006)

Online:1999-02-01 Published:1999-02-01

摘要/Abstract

摘要：

阐述了构造复映射z←z^α+c(α<0)所产生的广义Mandelbrot-集(简称M-集或M-分形图) 的逃逸时间算法. 通过改变参数α，作出了一系列有趣的分形图.这些分形图为若干卫星群环绕中央恒星的星群结构.定量地研究了恒星和卫星群的几何结构，并对α取非整数时分形图的结构特点和卫星群胚胎出现的原因进行了分析. 最后给出几点结论.

关键词: 逃逸时间算法, 复映射, 广义Ｍ集．

Abstract:

This paper expounds the escape time algorithm of constructing general Mandelbrot sets from the complex mapping z←z^α+c(α<0). A series of interesting and rich families of fractal images are generated by changing a single parameter α. The fractal images consist of planetary structures with a central planet surrounded by satellite structures. The positions and sizes of the planet and satellite structures are analytically estimated. The embryonic satellite structure arising for non-integer values of α are also analysed. In the end, a few conclusions are reached.

Key words: Ｅｓｃａｐｅｔｉｍｅａｌｇｏｒｉｔｈｍ, Ｃｏｍｐｌｅｘｍａｐｐｉｎｇ, ＧｅｎｅｒａｌＭｓｅ

中图分类号:

&alpha

王兴元刘向东朱伟勇. 由复映射z←zα+c(α<0)所构的广义M-集的研究[J]. 数学物理学报, 1999, 19(1): 73-79.

Wang xingyuan Liu Xiangdong Zhu Weiyong . Reserches on General Mandelbrot Sets from Complex Map z←zα+c(α<0)[J]. Acta mathematica scientia,Series A, 1999, 19(1): 73-79.