Escape Criteria for Generating Fractals of Complex Functions Using DK-Iterative Scheme-Reference-Cited by-同舟云学术

Escape Criteria for Generating Fractals of Complex Functions Using DK-Iterative Scheme

Published:2023-01-10 Issue:1 Volume:7 Page:76
ISSN:2504-3110
Container-title:Fractal and Fractional
language:en
Short-container-title:Fractal Fract

Author:

Tassaddiq Asifa¹^ORCID,Tanveer Muhammad²^ORCID,Azhar Muhammad³^ORCID,Arshad Muhammad²,Lakhani Farha⁴

Affiliation:

1. Department of Basic Sciences and Humanities, College of Computer and Information Sciences, Majmaah University, Al-Majmaah 11952, Saudi Arabia

2. Department of Mathemtics and Statistics, Sub-Campus Depalpur, University of Agriculture, Faisalabad 38040, Pakistan

3. Department of Mathemtics, Government College University Lahore, Lahore 54000, Pakistan

4. School of Computing, University of Leeds, Leeds LS2 9JT, UK

Abstract

Fractals are essential in representing the natural environment due to their important characteristic of self similarity. The dynamical behavior of fractals mostly depends on escape criteria using different iterative techniques. In this article, we establish an escape criteria using DK-iteration as well as complex sine function (sin(zm)+c;m≥2,c∈C) and complex exponential function (ezm+c;m≥2,c∈C). We use this to analyze the dynamical behavior of specific fractals namely Julia set and Mandelbrot set. This is achieved by generalizing the existing algorithms, which led to the visualization of beautiful fractals for m=2,3 and 4. Moreover, the image generation time in seconds using different values of input parameters is also computed.

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

Link

https://www.mdpi.com/2504-3110/7/1/76/pdf

Reference42 articles.

1. Kharbanda, M., and Bajaj, N. (2013, January 3–5). An exploration of fractal art in fashion design. Proceedings of the 2013 International Conference on Communication and Signal Processing, Melmaruvathur, India.

2. Cohen, N. (1997, January 6–8). Fractal antenna applications in wireless telecommunications. Proceedings of the Professional Program Proceedings. Electronic Industries Forum of New England, Boston, MA, USA.

3. A chaos-based image encryption technique utilizing Hilbert curves and H-Fractals;Zhang;IEEE Access,2019

4. Fractal image compression;Fisher;Fractals,1984

5. Kumar, S. (2006, January 23–25). Public key cryptographic system using Mandelbrot sets. Proceedings of the MILCOM 2006-2006 IEEE Military Communications Conference, Washington, DC, USA.

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