FRACTAL CURVE GENERATION THROUGH A GENERAL BINARY 6-POINT INTERPOLATING SUBDIVISION SCHEME WITH DUAL SHAPE CONTROL PARAMETERS

Abdul Ghaffar (), Tooba Bukhsh (), Salem Alkhalaf (), S. Abdel-Khalek (), Shahram Rezapour, Ghulam Mustafa () and Mustafa Inc
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Abdul Ghaffar: Department of Mathematics, Ghazi University, D G Khan 32200, Pakistan
Tooba Bukhsh: Department of Mathematics, Ghazi University, D G Khan 32200, Pakistan
Salem Alkhalaf: ��Department of Computer Engineering, College of Computer, Qassim University, Buraydah, Saudi Arabia
S. Abdel-Khalek: ��Department of Mathematics and Statistics, College of Science, Taif University, 11099, Taif 21944, Saudi Arabia
Shahram Rezapour: �Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam¶Department of Medical Research, China Medical University, 40402, Taichung, Taiwan
Ghulam Mustafa: ��Department of Mathematics, The Islamia University of Bahawalpur, Bahawapur 63100, Pakistan
Mustafa Inc: *Department of Mathematics, Science Faculty, Firat University, 23119, Elazig, Turkiye††Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602105, Tamil Nadu, India‡‡Department of Computer Engineering, Biruni University, 34010, Istanbul, Turkiye

FRACTALS (fractals), 2025, vol. 33, issue 06, 1-14

Abstract: In this paper, we introduce a novel approach to analyze the fractal properties of a general six-point binary interpolatory subdivision scheme with two shape parameters. This generalized scheme encompasses several well-known subdivision schemes, showcasing its versatility and adaptability in computer-aided geometric design, algorithms, and computational models. By exploring the influence of shape parameters on the fractal behavior of generated curves, we establish a method for creating fractals within specific parameter ranges. This research contributes to the understanding of fractal geometry and provides practical applications in computer-aided design and algorithmic modeling for efficient generation of complex models.

Keywords: Interpolatory Subdivision Scheme; Binary Six-Point Scheme; Continuity; Generation of Fractal Dimensions; Fractal; Algorithms; Computational Models; Curvature (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25401140

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