Tricorns and Multicorns of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:math>-Iteration Scheme

Kang, Shin Min; Rafiq, Arif; Latif, Abdul; Shahid, Abdul Aziz; Kwun, Young Chel

doi:10.1155/2015/417167

Cited by 26 publications

(22 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Some types of fractals like Mandelbrot and Julia sets via different explicit iterations studied and generalized in [14]- [18] and [19], Iterated Function System fractals studied in [20] and [21], V-variable fractals and super-fractals demonstrated in [21] and [22], inversion fractals discussed in [23] and fractals arising from the root finding methods presented in [24]- [26] and [27]. The threshold escape radii for Jungck-Mann, Jungck-Ishikawa and Jungck-Noor iterations with the combination of s-convex function in second sense were proved in [28], [29]. The biological resembled images were demonstrated in [30]- [33] and [34] and Modified results for Julia sets and Mandelbrot were established in [35].…”

Section: Introductionmentioning

confidence: 94%

Fixed Point Results for Fractal Generation in Extended Jungck–SP Orbit

Tanveer

Abbas

et al. 2019

IEEE Access

Self Cite

View full text Add to dashboard Cite

In this paper, we extend Jungck-SP iteration with s-convexity in second sense and define its orbit. We prove the fixed point results for fractal generation via extended iteration and utilize these results to develop algorithms for fractal visualization. Moreover, we present some complex graphs of Julia and Mandelbrot sets in Jungck-SP orbit with s-convexity. We also present some examples to show the variation in images with involved parameters.

show abstract

Section: Introductionmentioning

confidence: 94%

Fixed Point Results for Fractal Generation in Extended Jungck–SP Orbit

Tanveer

Abbas

et al. 2019

IEEE Access

Self Cite

View full text Add to dashboard Cite

show abstract

“…The modified Ishikawa process, S-iteration, was employed by Kang et al [24,25] to study relative superior Mandelbrot sets, tricorn and multicorns. The S-orbit, for any x 0 ∈ C, is a sequence {x i } given by…”

Section: Definition 2 ([6]mentioning

confidence: 99%

Generation of Julia and Mandelbrot Sets via Fixed Points

2020

View full text Add to dashboard Cite

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.

show abstract

“…Moreover, the Jungck-type iterations were used in [31]- [37]. Various iterations were also used to generate biomorphs in [38], [39] and multi-corns in [40], [41].…”

Section: Introductionmentioning

confidence: 99%

Anti Mandelbrot Sets via Jungck-M Iteration

Tanveer

Saleem

et al. 2020

IEEE Access

View full text Add to dashboard Cite

Complex fractals achieved the highest popularity in the last ten years. Researchers used the fixed point iterations to visualize the fractals and compared the image generation times to check the efficiencies of iterations. This paper explores the behavior of Jungck-M iteration in the generation of anti-Mandelbrot sets. We define the orbit of Jungck-M iteration and prove its escape criteria. We establish the algorithm for anti-Mandelbrot set and visualize some graphs via proposed iteration. We calculate the image generation times for the generation of anti-Mandelbrot sets in proposed orbit and present the comparison with Jungck-CR iteration. We also discuss the variations in images at different values of the input parameters. Moreover, we present the graphs to show the escape time depends on input parameters.

show abstract

Tricorns and Multicorns ofS-Iteration Scheme

Cited by 26 publications

References 7 publications

Fixed Point Results for Fractal Generation in Extended Jungck–SP Orbit

Fixed Point Results for Fractal Generation in Extended Jungck–SP Orbit

Generation of Julia and Mandelbrot Sets via Fixed Points

Anti Mandelbrot Sets via Jungck-M Iteration

Contact Info

Product

Resources

About