Switched Processes Generalized Mandelbrot Sets for Complex Index Number
-
摘要: 基于作者提出的开关复映射,阐述了开关广义Mandelbrot集(简称开关广义M集)的构造方法,并构造出一系列复数阶的开关广义Mandelbrot集.通过分析广义M集的构造算法,阐述了广义M集的结构特点.在此基础上对在开关映射作用下复C平面上初始点的轨道进行了研究,发现开关广义M集具有分形结构,其结构特征依赖于复指数w及开关变量r0,其断裂的原因是主幅角选取的不连续性.Abstract: According to the switched complex mapping proposed by the author, the method constructing the switched processes generalized M (Mandelbrot ) sets was elaborated, and a series of the switched processes generalized M sets for complex index number were constructed. The construction characteristics of the generalized M sets were expounded according to the analysis of the algorithm constructing the generalized M sets. On the basis of what has already been achieved, the trajectories of a starting point in the complex C-plane under the switched mapping were researched into. The results show that the switched processesgeneralized M sets hare te fractal feature the construction characteristics of the switched processes generalized M sets are dependent on the complex index number w and the switched variable r0, and the reason which results in the discontinuity of the switched processes generalized M sets is the discontinuity of choice of the principal range of the phase angle.
-
Key words:
- complex mapping /
- switched processes generalized M sets /
- fractal /
- evolution
-
[1] Peitgen H O,Saupe D.The Science of Fractal Images[M].Berlin:Springer-Verlag,1998.137-218. [2] Lakhtakia A,Varadan V V,Messier R,et al.On the symmetries of the Julia sets for the processz←zp+c[J].J Phys A:Math Gen,1987,20:3533-3535. [3] Gujar U G,Bhavsar V C,Vangala N.Fractals images from z←za+c in the complex z-plane[J].Computers & Graphics,1992,16(1):45-49. [4] WAGN Xing-yuan,LIU Xiang-dong,ZHU Wei-yong,et al.Analysis of C-plane fractal images from z←za+c for α＜0[J].Fractals,2000,8(3):307-314. [5] 王兴元,刘向东,朱伟勇.由复映射z←za+c(α＜0)所构造的广义M集的研究[J].数学物理学报,1999,19(1):73-79. [6] 王兴元,刘向东,朱伟勇.广义M集演化的研究[J].东北大学学报(自然科学版),1999,20(4):355-358. [7] Falconer K J.分形几何--数学基础及其应用[M].曾文曲,刘世耀译.沈阳:东北大学出版社,1991.238-245. -
计量
- 文章访问数: 2355
- HTML全文浏览量: 134
- PDF下载量: 548
- 被引次数: 0
下载:
渝公网安备50010802005915号