Mandel-Bar Sets of Inverse Complex Function

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

doi:10.5120/1358-1834

Cited by 6 publications

(4 citation statements)

References 17 publications

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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%

“…Here, the imaginary component will increase, while the real component will remain. are thus declared as topologically complete [4]. We introduce in this paper trigonometric functions of the type {sin (z*) + z} and {cos (z*) + z} withz* z 3 + mz + nand applied iterated function system to develop an entirely new class of Julia set which gives the escape criterion for cubic polynomial.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Julia Set with Trigonometric Function

2019

ijrte

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“…In 1918, French mathematician Gaston Julia [1] investigated the iteration process of a complex function intensively and attained a Julia set, which is a landmark in the field of fractal geometry. The Julia set defines the boundary between prisoner set and escape set [2]. The prisoner set is a collection of points inside the Mandelbrot set and escape set is a collection of points outside the orbit of Mandelbrot set.…”

Section: Introductionmentioning

confidence: 99%

Construction of 3D Mandelbrot Set and Julia Set

Negi¹,

Garg²,

Agrawal³

2014

IJCA

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Today Fractal geometry is completely new area of research in the field of computer science and engineering. It has wide range of applications. Fractals in nature are so complicated and irregular that it is hopeless to model them by simply using classical geometry objects. Benoit Mandelbrot, the father of fractal geometry, from his book The Fractal Geometry of Nature, 1982. This paper present construction of famous fractal images-Mandelbrot set and Julia set using 3D iterated function system which gives real look and feel of complex natural fractal images.

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“…In 1918, French mathematician Gaston Julia [10] investigated the iteration process of a complex function intensively and attained a Julia set, which is a landmark in the field of fractal geometry. The Julia set defines the boundary between prisoner set and escape set [4]. The prisioner set is a collection of points inside the mendelbrot set and escape set is a collection of points out side the orbit of mendelbrot set.…”

Section: Introductionmentioning

confidence: 99%

A Review on Natural Phenomenon of Fractal Geometry

Negi¹,

Garg²,

Agrawal³

2014

IJCA

Self Cite

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Today Fractal geometry is completely new area of research in the field of computer science and engineering. It has wide range of applications. Fractals in nature are so complicated and irregular that it is hopeless to model them by simply using classical geometry objects. Benoit Mandelbrot, the father of fractal geometry, from his book The Fractal Geometry of Nature, 1982. This paper explor various concepts of fractal i.e. fractal dimension, various techniques to generate fractal, their characteristics and their application in real life.

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Mandel-Bar Sets of Inverse Complex Function

Abstract: We introduce in this paper the dynamics of Relative Superior Mandel-bar sets of inverse complex function for Ishikawa iteration. The z plane fractal images generated from the generalized transformation

Cited by 6 publications

References 17 publications

Julia Set with Trigonometric Function

Julia Set with Trigonometric Function

Construction of 3D Mandelbrot Set and Julia Set

A Review on Natural Phenomenon of Fractal Geometry

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