超复数系统中的高维广义M-J集  

The Hyperdimensional Generalized M-J Sets in Hypercomplex Number System

作　　者：金涛[1] 王兴元[2] 

机构地区：[1]齐齐哈尔大学计算机与控制工程学院,黑龙江齐齐哈尔161006 [2]大连理工大学计算机科学与技术学院,辽宁大连116024

出　　处：《计算机仿真》2013年第6期261-266,315,共7页Computer Simulation

基　　金：黑龙江省教育厅科学技术研究项目(12531761;12511602);齐齐哈尔大学青年教师科研启动支持计划项目(2012k-M17)

摘　　要：研究超复数算法优化问题,由于超复数系统中构造曼德勃罗-茱莉亚集(M-J集)的算法目前还停留在三元数和四元数水平,且仅实现了低维M-J集在2-D和3-D截面上的仿真。为了更深入研究分形结构的特征性质,使用倍增和截去方法建立了任意维的超复数系统,讨论了超复数系统中的加法和乘法运算是闭的前提条件,并给出了超复数系统中高维(任意偶数维)广义M-J集的定义及构造算法。通过选取不同参数,实现并绘制了不同维度广义M-J集的2-D截面,对2-D截面的分形结构特征进行分析,结果表明高维广义M-J集在不同水平上的自相似性,并理论证明了2-D截面的对称性。有关对称性的分析将有助于进一步研究超复数动力学。Hypercomplex algorithm optimization problem has been studied in this paper. In order to carry out a in - depth study on the characteristics and properties of the fractal structure, doubling and truncation techniques were used to generate a hypercomplex number system of any dimension, and the precondition of that addition and multipli- cation closed in hypercomplex number system was discussed, and the definition and constructing arithmetic of the hy- perdimensional（ any even -dimensional） generalized Mandelbrot- Julia sets in hypercomplex number system were listed out. Through choosing different parameters, the authors realized and drew the 2 - D cross sections of the differ- ent dimensions generalized M - J sets, and studied the fractal feature of 2 - D cross sections. The results show that the hyperdimensional generalized Mandelbrot - Julia sets were self similar in the different level. By using theories, the authors also have proved the symmetry of 2 - D cross sections. The analysis of symmetry in this paper can help to study the dynamics of hypercomplex number.

关 键 词：超复数系统 高维 广义曼德勃罗-茱莉亚集 分形 对称性 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术] TP391.9[自动化与计算机技术—计算机科学与技术]