复映射族f(Z)=aZ^2+ti构成迭代函数系统的条件

The Condition of Complex Mapping Family f(Z)=aZ^2+ti to Become an IFS

IFS 是基于压缩映射理论的,而目前图形学中常用的是基于仿射变换的线性IFS,由非线性变换引起的非线性IFS 相对于线性IFS 具有更大的灵活性和更强的建模能力。笔者给出了复映射族f(Z)=aZ2+ti的定义,绘制出其作为非线性IFS 的吸引子图像;说明了映射压缩因子不是一个常数,而与迭代点有关;求出了复映射族构成IFS 的条件为迭代初始点在所有映射所形成的填充Julia 集的交集内,讨论了初始点选取与生成的迭代吸引子的关系。

IFS is based on contractive mapping. While the linear IFS, which is frequently used in computer graphics, is based on affine transformations. Compared with LIFS, the NIFS based on nonlinear function can provide more flexibility and enhanced ability of modeling. This paper gives the definition of the complex mapping family f(Z)=aZ2+ti; draws its attractor image as NIFS; explains that the contractive factor is not a constant and relates to iteration point; figures out the condition of complex mapping family to become an IFS, which is the initial iteration point locates in the intersection of all the mapping’s fill Julia set; and the paper also discusses the relationship between initial point choosing and iteration attractor.