Multi-alpha fractal iteration algorithm
In numerous domains, such as an image compression or encryption, art, research, and many more, complex visualizations of nonlinear dynamical systems play an important role. Antifractals have recently become a popular topic of study. We generate them by applying an iteration to an initial point in th...
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| Vydáno v: | Research in mathematics (Philadelphia, Pa.) Ročník 11; číslo 1 |
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| Jazyk: | angličtina |
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Abingdon
Taylor & Francis Ltd
31.12.2024
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| ISSN: | 2768-4830, 2768-4830 |
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| Abstract | In numerous domains, such as an image compression or encryption, art, research, and many more, complex visualizations of nonlinear dynamical systems play an important role. Antifractals have recently become a popular topic of study. We generate them by applying an iteration to an initial point in the complex plane. The main aim is to explore the dynamics of antifractals such as Julia sets, tricorns, and multicorns of polynomials using a multi-alpha fractal iteration algorithm (python code). In this study we develop an Ali-algorithm that can be used not only to generate more antifractals by using different values but generate new antifractals by changing the values in the iteration. The scheme used is the CR iteration with s-convexity. The escape criterion is vital in generating antifractals, which are at the center of various image encryption and computer graphics applications. We determine a generic form of such criterion in CR orbit. Many stunning aesthetic patterns are generated for antipolynomials of complex plane $\bar{\varphi}^2+\bar{\varphi}+c$ |
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| AbstractList | In numerous domains, such as an image compression or encryption, art, research, and many more, complex visualizations of nonlinear dynamical systems play an important role. Antifractals have recently become a popular topic of study. We generate them by applying an iteration to an initial point in the complex plane. The main aim is to explore the dynamics of antifractals such as Julia sets, tricorns, and multicorns of polynomials using a multi-alpha fractal iteration algorithm (python code). In this study we develop an Ali-algorithm that can be used not only to generate more antifractals by using different values but generate new antifractals by changing the values in the iteration. The scheme used is the CR iteration with s-convexity. The escape criterion is vital in generating antifractals, which are at the center of various image encryption and computer graphics applications. We determine a generic form of such criterion in CR orbit. Many stunning aesthetic patterns are generated for antipolynomials of complex plane $\bar{\varphi}^2+\bar{\varphi}+c$ |
| Author | Shahzeen, Sundus Ali, Asad Hassani, Murad Khan Muslim, Humaira Akgül, Ali |
| Author_xml | – sequence: 1 givenname: Sundus surname: Shahzeen fullname: Shahzeen, Sundus organization: Department of Software Engineering, The University of Lahore, Lahore, Pakistan – sequence: 2 givenname: Humaira surname: Muslim fullname: Muslim, Humaira organization: Department of Mathematics and Statistics, The University of Lahore, Pakistan – sequence: 3 givenname: Asad surname: Ali fullname: Ali, Asad organization: Engineering Management Group, University of Wollongong Dubai, UAE – sequence: 4 givenname: Ali orcidid: 0000-0001-9832-1424 surname: Akgül fullname: Akgül, Ali organization: Art and Science Faculty, Department of Mathematics, Siirt University, Siirt, Turkey, Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon – sequence: 5 givenname: Murad Khan surname: Hassani fullname: Hassani, Murad Khan organization: Department of Mathematics, Ghazni University, Afghanistan |
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| Cites_doi | 10.1016/j.cam.2010.12.022 10.1088/0951-7715/2/4/003 10.7551/mitpress/2426.001.0001 10.1155/2015/417167 10.5120/1322-1676 10.4236/ajcm.2012.24048 10.1090/psapm/039/1010237 10.1109/ACCESS.2019.2892013 10.1201/9780429492563 10.1007/BF03024816 10.1006/jmaa.2000.7042 10.1016/j.matcom.2023.08.017 10.14445/22312803/IJCTT-V43P115 10.1142/S0218127403008259 10.1016/j.jde.2019.07.009 |
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| SubjectTerms | Algorithms Computer graphics Convexity Criteria Encryption Fractals Image compression Iterative algorithms Nonlinear systems Polynomials |
| Title | Multi-alpha fractal iteration algorithm |
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