Mapping Fatou-Julia Iterations

AKHMET M., Fen M. O., Alejaily E. M.

10th International Conference on Information Management and Engineering (ICIME), Manchester, England, 22 - 24 September 2018, pp.64-67 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Doi Number: 10.1145/3285957.3285993
  • City: Manchester
  • Country: England
  • Page Numbers: pp.64-67
  • Keywords: Fatou-Julia iterations, Julia and Mandelbrot sets, Fractal mapping theorem
  • TED University Affiliated: Yes


A new method of fractals construction based on Fatou-Julia iteration is proposed. We develop a non-ordinary way to map fractal into a new fractal, where the mapping function is involved in the dynamics of the generated formula such that the modification does not violate the Julia and Fatou recipe for creating fractals. The method is applied for both Mandelbrot and Julia sets, and we follow the same technique of determining the fractal set using in the original iteration. The results of this paper are expected to have beneficial effects on many fields such as computer graphics and 3D printing technologies.