非解析复映射构造IFS的参数研究

发布时间：2018-11-06 09:09

【摘要】：为了采用非解析复映射构造分形或奇怪吸引子,研究了复映射f(z)=e~(iπ/2)z~n+c的广义M集的1周期参数对构造非线性IFS的影响.在该复映射的M集1周期区域随机选取参数;根据M集的对称性,用与所选参数在M集中对称位置的参数构成迭代函数系;在动力平面上构造出迭代函数系中的所有迭代函数的充满Julia集以及它们的公共吸引域;将随机选出参数所构造出的迭代函数的吸引不动点作为初始迭代点,通过在迭代函数系中连续随机选取一个迭代函数,跟踪这个吸引不动点在动力平面上的公共吸引域内的迭代轨道.通过实验,找到了可以生成分形的非线性IFS的参数选取方法.结果表明:当n取不同值时,非解析复映射族f(z)=e~(iπ/2)z~n+c的广义M集的1周期参数可以用于构造非线性IFS,这种IFS可以大量生成分形山以及具有Z_(n+1)和D_(n+1)对称特性的新分形.
[Abstract]:In order to construct fractal or strange attractor by using nonanalytic complex mappings, the effect of 1-period parameters of generalized M sets of complex mapping f (z) = e ~ (I 蟺 / 2) znc on the construction of nonlinear IFS is studied. According to the symmetry of the M set, the iterative function system is constructed by using the parameters in the symmetric position of the selected parameter in the M set. The full Julia sets of all iterative functions in the system of iterative functions and their common regions of attraction are constructed on the dynamic plane. The attraction fixed point of the iterative function constructed by randomly selected parameters is taken as the initial iteration point, and a random iterative function is selected continuously in the iterative function system. Track the iterative orbits of the fixed point of attraction in the common domain of attraction on the dynamic plane. Through experiments, the parameter selection method of nonlinear IFS which can generate fractal is found. The results show that the 1-period parameter of the generalized M set of nonanalytic complex mapping family f (z) = e ~ (I 蟺 / 2) znc can be used to construct nonlinear IFS, when n takes different values. This IFS can generate a large number of fractal mountains and new fractals with symmetric properties of Z _ (n _ 1) and D _ (n _ 1).
【作者单位】：沈阳建筑大学信息与控制工程学院;
【基金】：国家自然科学基金(61272253)
【分类号】：O189

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