FRACTAL CURVE GENERATION THROUGH A GENERAL BINARY 6-POINT INTERPOLATING SUBDIVISION SCHEME WITH DUAL SHAPE CONTROL PARAMETERS - Ghaffar, Abdul; Bukhsh, Tooba; Alkhalaf, Salem; Abdel-Khalek, S.; Rezapour, Shahram; Mustafa, Ghulam; İnç, Mustafa (World Scientific Publ Co Pte Ltd, 2025)
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