广义Julia集关于迭代参数的对称性分析  

Analysis for the Symmetry of General J Sets to Iterated Parameters

作　　者：秦宣云[1] 管继虹[1] 任波[1] 韩旭里[1] 

机构地区：[1]中南大学数学科学与计算技术学院,长沙410083

出　　处：《计算机辅助设计与图形学学报》2007年第7期927-930,共4页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(50474052);湖南省青年骨干教师基金(2005)

摘　　要：由迭代函数fω,c(z)=zω+c(ω∈C,c∈C)构造了广义Julia集(简称广义J集),并通过对迭代函数fω,c(z)=zω+c(ω∈C,c∈C)中参数ω,c的改变,根据逃逸时间算法,利用VC++编程得到了相应的广义J集图形.通过图形对比,给出了仅随参数c变化所得图形对称性的一个重要结论,并从理论上给予了证明.类似地,通过对参数ω,c同时变化所得图形的分析,得到了相应的结论.The general Julia sets （the general J sets for short） are generated from the iterated functions system fω,c（z）=z^ω＋c（ω∈C,c∈C）. Based on the escape time algorithm, by changing the parameters ω,c in fω,c（z）=z^ω＋c（ω∈C,c∈C） , the corresponding fractal images of general J sets were produced with the platform of VC＋＋ . In comparison with output graphs, an important conclusion of the symmetry of general J sets by only changing parameter c is drawn and proved theoretically. Similarly, through the analysis to graphs of general J sets by the change of both ω and c, a corresponding conclusion is also given.

关 键 词：分形 广义J分形图 逃逸时间算法 

分 类 号：TP306[自动化与计算机技术—计算机系统结构]