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 processes generalized M sets have the 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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Communicated by ZHANG Shi-sheng
Foundation items: the National Natural Science Foundation of China (69974008); the Postdoctoral Science Foundation of China; the Natural Science Foundation of Liaoning Province (972194)
Biography: WANG Xing-yuan (1964−), Associate Professor, Doctor E-mail: wanxy@dlut.edu.cn
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Xing-yuan, W. Switched processes generalized mandelbrot sets for complex index number. Appl Math Mech 24, 73–81 (2003). https://doi.org/10.1007/BF02439380
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DOI: https://doi.org/10.1007/BF02439380