Applied Mathematics and Mechanics (English Edition) ›› 2003, Vol. 24 ›› Issue (1): 73-81.

• Articles • Previous Articles     Next Articles

SWITCHED PROCESSES GENERALIZED MANDELBROT SETS FOR COMPLEX INDEX NUMBER

WANG Xing-yuan   

  1. School of Electronic and Information Engineering, Dalian University of Technology, Dalian 116024, China
  • Received:2000-12-10 Revised:2002-09-20 Online:2003-01-18 Published:2003-01-18
  • Supported by:

    the National Natural Science Foundation of China(69974008);the Postdoctoral Science Foundation of China;the Natural Science Foundation of Liaoning Province(972194)

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.

2010 MSC Number: 

APS Journals | CSTAM Journals | AMS Journals | EMS Journals | ASME Journals