JOURNAL ARTICLE

FRACTAL PROPERTIES OF THE GENERALIZED MANDELBROT SET WITH COMPLEX EXPONENT.

  • Published In: Fractals, 2024, v. 32, n. 4. P. 1 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: LIU, SHUAI; XU, XIYU; SRIVASTAVA, GAUTAM; SRIVASTAVA, HARI M. 3 of 3

Abstract

Mandelbrot set, which was provided as a highlight in fractal and chaos, is studied by many researchers. With the extension of Mandelbrot set to generalized M set with different kinds of exponent k (k − M set), properties are hard to understand when k is a complex number. In this paper, fractal property of generalized M set with complex exponent z is studied. First, a relation is constructed between generalized M set with complex and real exponent. Then, distribution of z − M set on complex plane is researched. Meanwhile, symmetry of generalized M set is proved. Finally, graphics, generated by escape time algorithm, are the validated results of this paper. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:Fractals. 2024/05, Vol. 32, Issue 4, p1
  • Document Type:Article
  • Subject Area:Mathematics
  • Publication Date:2024
  • ISSN:0218-348X
  • DOI:10.1142/S0218348X23401217
  • Accession Number:177608744
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