Mapping Fatou-Julia Iterations

Date

2018-01-01

Author

Akhmet, Marat
Fen, Mehmet Onur
Alejaily, Ejaily Milad

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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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.

Subject Keywords

Fatou-Julia iterations, Julia and Mandelbrot sets, Fractal mapping theorem

URI

https://hdl.handle.net/11511/47259

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Department of Mathematics, Conference / Seminar