Fixed point results in the generation of Julia and Mandelbrot sets

Nazeer, Waqas; Kang, Shin Min; Tanveer, Muhmmad; Shahid, Abdul Aziz

doi:10.1186/s13660-015-0820-3

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Definition 2 ([6]1

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2024

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Cited by 42 publications

(40 citation statements)

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“…Recently, M. Kumari et al [16] used a new iterative process (an example of four-step feedback process) for creating new Julia and Mandelbrot sets for quadratic, cubic and higher degree polynomials. Further, some researchers obtained fixed point results in the generation of Julia and Mandelbrot sets with s-convexity, see ( [15], [22], [28]).…”

Section: Introductionmentioning

confidence: 99%

Generation of New Fractals via SP Orbit with s-Convexity

Kumari¹,

Kumari²,

Chugh³

2017

IJET

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Section: Introductionmentioning

confidence: 99%

Generation of New Fractals via SP Orbit with s-Convexity

Kumari¹,

Kumari²,

Chugh³

2017

IJET

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“…Kang et al [28] introduced Julia and Mandelbrot sets in implicit Jungck Mann and Jungck Ishikawa orbits. Later, several researchers [27,29,[31][32][33] employed this implicit iterative process to generate graphs of such complex polynomials. In order to achieve this, they split the polynomial T into two functions T 1 (x) = x n + r and T 2 (x) = mx.…”

Section: Definition 2 ([6]mentioning

confidence: 99%

Generation of Julia and Mandelbrot Sets via Fixed Points

2020

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The aim of this paper is to present an application of a fixed point iterative process in generation of fractals namely Julia and Mandelbrot sets for the complex polynomials of the form T ( x ) = x n + m x + r where m , r ∈ C and n ≥ 2 . Fractals represent the phenomena of expanding or unfolding symmetries which exhibit similar patterns displayed at every scale. We prove some escape time results for the generation of Julia and Madelbrot sets using a Picard Ishikawa type iterative process. A visualization of the Julia and Mandelbrot sets for certain complex polynomials is presented and their graphical behaviour is examined. We also discuss the effects of parameters on the color variation and shape of fractals.

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“…Further, the cubic Julia sets and antifractals [3] were studied in the Noor orbit. Julia and Mandelbrot sets have been studied in Jungck orbit also (see [9] and references therein).…”

Section: Introductionmentioning

confidence: 99%