New Julia Sets of Ishikawa Iterates

Chauhan, Yashwant Singh; Rana, Rajeshri; Negi, Ashish

doi:10.5120/1321-1675

Cited by 23 publications

(19 citation statements)

References 14 publications

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“…Similar investigations to those presented in this paper can be carried out for complex fractals (Julia and Mandelbrot sets) and biomorphs. Some aspects of such investigations have been reported in the literature [9,[32][33][34]. Another interesting direction rely on replacing complex numbers by more general: dual and double numbers used in [35] for defining the Q-Systems Fractals.…”

Section: Discussionmentioning

confidence: 99%

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Polynomiography Based on the Nonstandard Newton-Like Root Finding Methods

Gdawiec

Kotarski

Lisowska

2015

Abstract and Applied Analysis

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A survey of some modifications based on the classic Newton's and the higher order Newton-like root finding methods for complex polynomials is presented. Instead of the standard Picard's iteration several different iteration processes, described in the literature, which we call nonstandard ones, are used. Kalantari's visualizations of root finding process are interesting from at least three points of view: scientific, educational, and artistic. By combining different kinds of iterations, different convergence tests, and different colouring we obtain a great variety of polynomiographs. We also check experimentally that using complex parameters instead of real ones in multiparameter iterations do not destabilize the iteration process. Moreover, we obtain nice looking polynomiographs that are interesting from the artistic point of view. Real parts of the parameters alter symmetry, whereas imaginary ones cause asymmetric twisting of polynomiographs.

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Section: Discussionmentioning

confidence: 99%

“…When we look at (40), then we can see that this is the function used by Pickover in (32). Another way to modify the tests is to add some weights in the metric function.…”

Section: Convergence Testsmentioning

confidence: 99%

Polynomiography Based on the Nonstandard Newton-Like Root Finding Methods

Gdawiec

Kotarski

Lisowska

2015

Abstract and Applied Analysis

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“…Julia sets are defined by iterating a function of a complex number. Julia sets have been studied for quadratic [4,5,8,9], cubic [4,5,7] and also for higher degree polynomials. Pick appoint in the complex plane (i.e., a complex number; this can be represented as a point z = (x,y) in the plane).…”

Section: Introductionmentioning

confidence: 99%

Julia Set with Trigonometric Function

2019

ijrte

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Julia sets are generated by initializing a complex number z = x + yi where z is then iterated using the iteration function fc (z)= zn 2 + c, where n indicates the number of iteration and c is a constant complex number. Recently, study of cubic Julia sets was introduced in Noor Orbit (NO) with improved escape criterions for cubic polynomials. In this paper, we investigate the complex dynamics of different functions and apply the iteration function to generate an entire new class of Julia sets. Here, we introduce different types of orbits on cubic Julia sets with trigonometric functions. The two functions to investigate from Julia sets are sine and cosine functions.

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“…Julia sets are defined by iterating a function of a complex number. Julia sets have been studied for quadratic (Ishikawa et al, 1974 andChauhan et al, 2010) and also for higher degree polynomials. Pick a point in the complex plane (i.e.., a complex number; these can be represented as a point z = (x,y) in the plane).…”

Section: Introductionmentioning

confidence: 99%

Cubic and Quadratic Polynomial on Julia Set With Trigonometric Function

Titaley¹,

Manurung²,

Titaley³

2018

JIS

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CUBIC AND QUADRATIC POLYNOMIAL ON JULIA SET WITH TRIGONOMETRIC FUNCTIONABSTRACTJulia set are defined by iterating a function of a complex number and is generated from the iterated function . We investigate in this paper the complex dynamics of different functions and applied iteration function system to generate an entire new class of julia set. The purpose of this research is to make variation of Cubic and Quadratic polynomial on Julia Set and the two obvious to investigate from julia set are Sine and Cosine function. The results thus obtained are innovative and studies about different behavior of two basic trigonometry.Keywords : Julia Set, trigonometric function, polynomial function POLINOMIAL KUBIK DAN KUADRATIK PADA HIMPUNAN JULIA DENGAN FUNGSI TRIGONOMETRI ABSTRAKHimpunan Julia didefiniskan oleh fungsi iterasi dari bilangan kompleks dan dibangkitkan dari fungsi iterasi . Kami melakukan penelitian dalam penulisan ini tentang sistem dinamik kompleks dari fungsi yang berbeda dengan iterasi yang diterapkan untuk menghasilkan kelas baru dari himpunan Julia. Tujuan dari penelitian ini adalah untuk membuah kelas baru himpunan Julia dengan fungsi polinomial kubik dan kuadratik dengan fungsi sinus dan kosinus. Hasil akhir dari penelitian ini ada menemukan inovatif baru dari himpunan Julia dengan menggunakan dua fungsi trigonometri.Kata kunci: Julia set, fungsi trigonometri, fungsi polinomial

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New Julia Sets of Ishikawa Iterates

Abstract: We investigate in this paper the dynamics and the method of generating fractal images for Ishikawa iteration procedure. The geometry of relative superior Julia sets are explored for Ishikawa iteration.

Cited by 23 publications

References 14 publications

Polynomiography Based on the Nonstandard Newton-Like Root Finding Methods

Polynomiography Based on the Nonstandard Newton-Like Root Finding Methods

Julia Set with Trigonometric Function

Cubic and Quadratic Polynomial on Julia Set With Trigonometric Function

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