Fractal Generation via CR Iteration Scheme with S-Convexity

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

doi:10.1109/ACCESS.2019.2919520

Fractal Generation via CR Iteration Scheme with S-Convexity

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

Research output: Contribution to journal › Article › peer-review

31 Citations (Scopus)

Abstract

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.

Original language	English
Article number	8723471
Pages (from-to)	69986-69997
Number of pages	12
Journal	IEEE Access
Volume	7
DOIs	https://doi.org/10.1109/ACCESS.2019.2919520
Publication status	Published - 2019
Externally published	Yes

Keywords

escape criterion
Iteration schemes
Julia set
Mandelbrot set
s-convexity

ASJC Scopus subject areas

General Computer Science
General Materials Science
General Engineering

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10.1109/ACCESS.2019.2919520

Cite this

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title = "Fractal Generation via CR Iteration Scheme with S-Convexity",

abstract = "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.",

keywords = "escape criterion, Iteration schemes, Julia set, Mandelbrot set, s-convexity",

author = "Kwun, \{Young Chel\} and Shahid, \{Abdul Aziz\} and Waqas Nazeer and Mujahid Abbas and Kang, \{Shin Min\}",

note = "Publisher Copyright: {\textcopyright} 2013 IEEE.",

year = "2019",

doi = "10.1109/ACCESS.2019.2919520",

language = "English",

volume = "7",

pages = "69986--69997",

journal = "IEEE Access",

issn = "2169-3536",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

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T1 - Fractal Generation via CR Iteration Scheme with S-Convexity

AU - Kwun, Young Chel

AU - Shahid, Abdul Aziz

AU - Nazeer, Waqas

AU - Abbas, Mujahid

AU - Kang, Shin Min

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - escape criterion

KW - Iteration schemes

KW - Julia set

KW - Mandelbrot set

KW - s-convexity

UR - https://www.scopus.com/pages/publications/85067238307

U2 - 10.1109/ACCESS.2019.2919520

DO - 10.1109/ACCESS.2019.2919520

M3 - Article

AN - SCOPUS:85067238307

SN - 2169-3536

VL - 7

SP - 69986

EP - 69997

JO - IEEE Access

JF - IEEE Access

M1 - 8723471

ER -

Fractal Generation via CR Iteration Scheme with S-Convexity

Abstract

Keywords

ASJC Scopus subject areas

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