Switched Processes Generalized Mandelbrot Sets for Complex Index Number
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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.
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Key words:
- complex mapping /
- switched processes generalized M sets /
- fractal /
- evolution
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