Multi-alpha fractal iteration algorithm

• 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
• DOI: 10.1080/27684830.2024.2401324

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 $\bar{\varphi}^2+\bar{\varphi}+c$