Acta mathematica scientia,Series A ›› 2005, Vol. 25 ›› Issue (7): 1030-1039.

• Articles • Previous Articles     Next Articles

Generalized Julia Sets From a Nonanalytic Complex Mapping

 WANG Xin-Yuan, Luo Chao   

  • Online:2005-12-30 Published:2005-12-30
  • Supported by:

    国家自然科学基金(69974008)及辽宁省教育厅高等学校科学技术研究计划(20040081)资助

Abstract:

The method constructing the Julia sets from a simple nonanalytic mapping developed by Michelitsch and Rossler is expanded. According to the complex mapping expanded by the author, a series of the generalized Julia sets for real index number are constructed. Using the experimental mathematics method and combining the theory of analytic functions of one complex variable with computer aided drawing, the fractal features and evolutions of the generalized Julia sets are studied. The results show: (i) the geometry structure of the generalized Julia sets depends on the parameters of α,R and c; (ii) the generalized Julia sets have symmetry and fractal feature; (iii) the generalized Julia sets for decimal index number have discontinuity and collapse, and their evolutions depend on the choice of the principal range of the phase angle.

Key words: Nonanalytic mapping, The generalized Julia sets, Fractal, evolution

CLC Number: 

  • 28A80
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