Fractal generation via Khan iteration: Escape criteria and dynamical analysis

Akansha Tyagi and Sachin Vashistha

Chaos, Solitons & Fractals, 2025, vol. 201, issue P1

Abstract: We introduce a novel fractal generation technique based on an iterative scheme for locating common fixed points. We derive the escape criterion for Khan iteration scheme by employing complex polynomials and rational functions. Several examples illustrating the Mandelbrot and Julia sets are obtained via the proposed method. To investigate the influence of iteration parameters on the fractal sets, we examine two numerical indicators: the average escape time and the non-escaping area index. Our analysis reveals a nonlinear relationship between these fractal characteristics and the iteration parameters.

Keywords: Escape criterion; Fractals; Julia set; Mandelbrot set (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:201:y:2025:i:p1:s096007792501197x

DOI: 10.1016/j.chaos.2025.117184

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