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

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.