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Mandelbrot and Julia Sets of Complex Polynomials Involving Sine and Cosine Functions via Picard–Mann Orbit

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Abstract

The purpose of this paper is to generate fractals of sine and cosine functions for a complex polynomial \(z^k +c\) via Picard–Mann iterations. To generate Mandelbrot and Julia sets, escape criteria are established and proven for \(\sin z^k+c\) and \(\cos z^k+c\) for Picard–Mann iterations. Various input parameters for different k are used to compare images between sine and cosine. generation time and average number of iterations of the generated Mandelbrot and Julia sets are presented.

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Authors and Affiliations

  1. College of Engineering, Al Ain University, Abu Dhabi, UAE

    Nuha Hamada & Faten Kharbat

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  1. Nuha Hamada
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  2. Faten Kharbat
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Contributions

N.H contributed to the algorithm and prove the theorem. F.K. implemented the algorithm and produced the images. F.K also contributed to format the manuscript scoring to the journal All Authors wrote and reviewed the manuscript

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Correspondence to Faten Kharbat.

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Communicated by Palle Jorgensen.

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Hamada, N., Kharbat, F. Mandelbrot and Julia Sets of Complex Polynomials Involving Sine and Cosine Functions via Picard–Mann Orbit. Complex Anal. Oper. Theory 17, 13 (2023). https://doi.org/10.1007/s11785-022-01312-w

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  • DOI: https://doi.org/10.1007/s11785-022-01312-w

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