Generation of Mandelbrot and Julia sets for generalized rational maps using SP-iteration process equipped with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si197.svg" display="inline" id="d1e6347"><mml:mi>s</mml:mi></mml:math>-convexity

Rawat, Shivam; Prajapati, Darshana J.; Tomar, Anita; Gdawiec, Krzysztof

doi:10.1016/j.matcom.2023.12.040

Mathematics and Computers in Simulation

2024

DOI: 10.1016/j.matcom.2023.12.040

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Generation of Mandelbrot and Julia sets for generalized rational maps using SP-iteration process equipped with s-convexity

Shivam Rawat,

Darshana J. Prajapati,

Anita Tomar

et al.

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Cited by 3 publications

References 31 publications

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On the evolution and importance of the Fibonacci sequence in visualization of fractals

Sharma,

Tomar,

Padaliya

2025

Chaos, Solitons & Fractals

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On the evolution and importance of the Fibonacci sequence in visualization of fractals

Sharma,

Tomar,

Padaliya

2025

Chaos, Solitons & Fractals

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Fractals as Julia Sets for a New Complex Function via a Viscosity Approximation Type Iterative Methods

Almutlg,

Ahmad

2024

Axioms

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In this article, we examine and investigate various variants of Julia set patterns for complex exponential functions W(z)=αezn+βzm+logct, and T(z)=αezn+βzm+γ (which are analytic except at z=0) where n≥2, m,n∈N, α,β,γ∈C,c∈C∖{0} and t∈R,t≥1, by employing a viscosity approximation-type iterative method. We employ the proposed iterative method to establish an escape criterion for visualizing Julia sets. We provide graphical illustrations of Julia sets that emphasize their sensitivity to different iteration parameters. We present graphical illustrations of Julia sets; the color, size, and shape of the images change with variations in the iteration parameters. With fixed input parameters, we observe the intriguing behavior of Julia sets for different values of n and m. We hope that the conclusions of this study will inspire researchers with an interest in fractal geometry.

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Generation of Julia and Mandelbrot fractals for a generalized rational type mapping via viscosity approximation type iterative method extended with $ s $-convexity

Murali,

Muthunagai

2024

MATH

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<abstract><p>A dynamic visualization of Julia and Mandelbrot fractals involves creating animated representations of these fractals that change over time or in response to user interaction which allows users to gain deeper insights into the intricate structures and properties of these fractals. This paper explored the dynamic visualization of fractals within Julia and Mandelbrot sets, focusing on a generalized rational type complex polynomial of the form $ S_{c}(z) = a z^{n}+\frac{b}{z^{m}}+c $, where $ a, b, c \in \mathbb{C} $ with $ |a| > 1 $ and $ n, m \in \mathbb{N} $ with $ n > 1 $. By applying viscosity approximation-type iteration processes extended with $ s $-convexity, we unveiled the intricate dynamics inherent in these fractals. Novel escape criteria was derived to facilitate the generation of Julia and Mandelbrot sets via the proposed iteration process. We also presented graphical illustrations of Mandelbrot and Julia fractals, highlighting the change in the structure of the generated sets with respect to the variations in parameters.</p></abstract>

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Generation of Mandelbrot and Julia sets for generalized rational maps using SP-iteration process equipped with s-convexity

Cited by 3 publications

References 31 publications

On the evolution and importance of the Fibonacci sequence in visualization of fractals

On the evolution and importance of the Fibonacci sequence in visualization of fractals

Fractals as Julia Sets for a New Complex Function via a Viscosity Approximation Type Iterative Methods

Generation of Julia and Mandelbrot fractals for a generalized rational type mapping via viscosity approximation type iterative method extended with $ s $-convexity

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