Fractal Generation via CR Iteration Scheme With S-Convexity

The visual beauty, self-similarity, and complexity of Mandelbrot sets and Julia sets have made an attractive field of research. One can find many generalizations of these sets in the literature. One such generalization is the use of results from fixed-point theory. The aim of this paper is to provid...

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Bibliographic Details
Published inIEEE access Vol. 7; pp. 69986 - 69997
Main Authors Kwun, Young Chel, Shahid, Abdul Aziz, Nazeer, Waqas, Abbas, Mujahid, Kang, Shin Min
Format Journal Article
LanguageEnglish
Published Piscataway IEEE 2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Convexity
Education
escape criterion
Extraterrestrial measurements
Fractals
Image coding
Iteration schemes
Julia set
Mandelbrot set
Orbits
s-convexity
Self-similarity
Space vehicles
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Summary:The visual beauty, self-similarity, and complexity of Mandelbrot sets and Julia sets have made an attractive field of research. One can find many generalizations of these sets in the literature. One such generalization is the use of results from fixed-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.
ISSN:2169-3536
2169-3536
DOI:10.1109/ACCESS.2019.2919520