D4对称平面排列映射广义充满Julia集

Ceneral Filled-in Julia Sets from Plane Tiling Mapping with D4 Symmetry

为了更加直观、有效地在参数空间挑选参数构造出具有 D4对称特性的平面排列映射的混沌吸引子和广义充满 Julia集 ,在参数空间任选两个实参数构造参数断面 ,构造其上的广义 M集 .在这种广义 M集的周期区域中挑选参数 ,可以由计算机生成大量新颖的广义充满 Julia集 .为了揭示出这种广义充满 Julia集内部的复杂结构 ,给出了两种构造方法 .

In order to more visually and actively choose the parameters by which the symmetric chaos attractors and general filled-in Julia sets can be generated, the general M sets, which are on the parameter sections composed of any two real parameters chosen from the parameter space of the plane tiling mapping with D4 symmetry, are constructed. Choosing the parameters from the period region of the M set, many of the novel general filled-in Julia sets can be constructed by a computer. To reveal the complex structures in this kind of the general filled-in Julia sets we presents two kinds of constructing methods. Two new styles of art images are given for the visual research on the dynamical system with plane symmetry using a computer in this paper.