Fractal generation via CR iteration scheme with s-convexity

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Authors

Kwun, Young Chel
Shahid, Abdul Aziz
Nazeer, Waqas
Abbas, Mujahid
Kang, Shin Min

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Institute of Electrical and Electronics Engineers

Abstract

The visual beauty, self-similarity, and complexity of Mandelbrot sets and Julia sets have made an attractive eld of research. One can nd many generalizations of these sets in the literature. One such generalization is the use of results from xed-point theory. The aim of this paper is to provide escape criterion and generate fractals (Julia sets and Mandelbrot sets) via CR iteration scheme with s-convexity. Many graphics of Mandelbrot sets and Julia sets of the proposed three-step iterative process with s-convexity are presented. We think that the results of this paper can inspire those who are interested in generating automatically aesthetic patterns.

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Keywords

Iteration schemes, Julia set, Mandelbrot set, Escape criterion, S-convexity

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Citation

Kwun, Y.C., Shahid, A.A., Nazeer, W. et al. 2019, 'Fractal generation via CR iterations scheme with s-convexity', IEEE Access, vol. 7, pp. 69986-69997.