利用n维参数L系统构造超复数空间广义M-J集

The General Hypercomplex M-J Sets on the n-Dimensional Parametric L Systems

利用n维参数L系统描述了超复数空间广义Mandelbrot集和Julia集,给出了描述算法和实验所得图形,并对四元数广义M-J集的动力学特征进行了理论上的分析和探讨。经过实验发现,四元数广义M-J集在保留了复平面M-J集特征的基础上,还有一些特殊的性质,如广义M集在三维虚轴截面上的拓扑结构等同于球体,四元数Julia集在参数c同模同实部的情况下保持着结构的一致性。实验结果表明,n维参数L系统字母表较为简洁,包含信息量大,可以有效的描述诸如广义M-J集和四元数广义M-J集的分形集。

Parametric n-dimensional L systems are realized and extended to express more fractal sets such as general hypercomplex M-J sets. The algorithm and the fractal images it produces are presented, and the dynamic characters of the general quaternion M-J sets are discussed. It is found that quaternionic M-J sets not only keep the same properties with the complex M-J sets, but also have some new properties, such as the topology structure of the quaternionic M sets in the three image axes is homeomorphous to a sphere, and the quaternionic Julia sets with the parameter c of the same module and same real part share the same structure. It can be concluded that n-dimensional L systems, which have pithily alphabet but convey plentiful information, could depict such fractals as general hypercomplex M-J sets well.