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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Bibliographic Details
Published in:Research in mathematics (Philadelphia, Pa.) Vol. 11; no. 1
Main Authors: Shahzeen, Sundus, Muslim, Humaira, Ali, Asad, Akgül, Ali, Hassani, Murad Khan
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis Ltd 31.12.2024
Subjects:
Algorithms
Computer graphics
Convexity
Criteria
Encryption
Fractals
Image compression
Iterative algorithms
Nonlinear systems
Polynomials
ISSN:2768-4830, 2768-4830
Online Access:Get full text
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Summary: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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ISSN:2768-4830
2768-4830
DOI:10.1080/27684830.2024.2401324