Effect of Stochastic Noise on Superior Julia Sets

Julia sets are considered one of the most attractive fractals and have wide range of applications in science and engineering. The strong physical meaning of Mandelbrot and Julia sets is broadly accepted and nicely connected by Christian Beck (Physica D 125(3–4):171–182, 1999) to the complex logistic...

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Main Authors:	Mamta, Rani, Agarwal, Rashi
Format:	Article
Language:	English
Published:	Springer US 2010
Subjects:	QA75 Electronic computers. Computer science T Technology (General)
Online Access:	http://umpir.ump.edu.my/id/eprint/12404/ http://umpir.ump.edu.my/id/eprint/12404/ http://umpir.ump.edu.my/id/eprint/12404/ http://umpir.ump.edu.my/id/eprint/12404/1/Effect%20of%20stochastic%20noise%20on%20superior%20julia%20sets.pdf

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spelling	ump-124042016-03-22T07:26:03Z http://umpir.ump.edu.my/id/eprint/12404/ Effect of Stochastic Noise on Superior Julia Sets Mamta, Rani Agarwal, Rashi QA75 Electronic computers. Computer science T Technology (General) Julia sets are considered one of the most attractive fractals and have wide range of applications in science and engineering. The strong physical meaning of Mandelbrot and Julia sets is broadly accepted and nicely connected by Christian Beck (Physica D 125(3–4):171–182, 1999) to the complex logistic maps, in the former case, and to the inverse complex logistic map, in the latter. Argyris et al. (Chaos Solitons Fractals 11(13):2067–2073, 2000) have studied the effect of noise on Julia sets and concluded that Julia sets are stable for noises of low strength, and a small increment in the strength of noise may cause considerable deterioration in the configuration of the Julia sets. It is well-known that the method of function iterates plays a crucial role in discrete dynamics utilizing the techniques of fractal theory. However, recently Rani and Kumar (J. Korea Soc. Math. Edu. Ser. D: Res. Math. Edu. 8(4):261–277, 2004) introduced superior iterations as a generalization of function iterations in the study of Julia sets and studied superior Julia sets. This technique is further utilized to study effectively new Mandelbrot sets and related properties (see, for instance, Negi and Rani, Chaos Solitons Fractals 36(2):237–245, 2008; 36(4):1089–1096, 2008, Rani and Kumar, J. Korea Soc. Math. Edu. Ser. D: Res. Math. Edu. 8(4):279–291, 2004). The intent of this paper is to study certain effects of noise on superior Julia sets. We find that the superior Julia sets are drastically more stable for higher strength of noises than the classical Julia sets. Finally, we make a humble attempt to discuss some applications of superior orbit in discrete dynamics and of superior Julia sets in particle dynamics. Springer US 2010 Article PeerReviewed application/pdf en http://umpir.ump.edu.my/id/eprint/12404/1/Effect%20of%20stochastic%20noise%20on%20superior%20julia%20sets.pdf Mamta, Rani and Agarwal, Rashi (2010) Effect of Stochastic Noise on Superior Julia Sets. Journal of Mathematical Imaging and Vision, 36. p. 63. ISSN 0924-9907 http://dx.doi.org/10.1007/s10851-009-0171-0 doi:10.1007/s10851-009-0171-0
repository_type	Digital Repository
institution_category	Local University
institution	Universiti Malaysia Pahang
building	UMP Institutional Repository
collection	Online Access
language	English
topic	QA75 Electronic computers. Computer science T Technology (General)
spellingShingle	QA75 Electronic computers. Computer science T Technology (General) Mamta, Rani Agarwal, Rashi Effect of Stochastic Noise on Superior Julia Sets
description	Julia sets are considered one of the most attractive fractals and have wide range of applications in science and engineering. The strong physical meaning of Mandelbrot and Julia sets is broadly accepted and nicely connected by Christian Beck (Physica D 125(3–4):171–182, 1999) to the complex logistic maps, in the former case, and to the inverse complex logistic map, in the latter. Argyris et al. (Chaos Solitons Fractals 11(13):2067–2073, 2000) have studied the effect of noise on Julia sets and concluded that Julia sets are stable for noises of low strength, and a small increment in the strength of noise may cause considerable deterioration in the configuration of the Julia sets. It is well-known that the method of function iterates plays a crucial role in discrete dynamics utilizing the techniques of fractal theory. However, recently Rani and Kumar (J. Korea Soc. Math. Edu. Ser. D: Res. Math. Edu. 8(4):261–277, 2004) introduced superior iterations as a generalization of function iterations in the study of Julia sets and studied superior Julia sets. This technique is further utilized to study effectively new Mandelbrot sets and related properties (see, for instance, Negi and Rani, Chaos Solitons Fractals 36(2):237–245, 2008; 36(4):1089–1096, 2008, Rani and Kumar, J. Korea Soc. Math. Edu. Ser. D: Res. Math. Edu. 8(4):279–291, 2004). The intent of this paper is to study certain effects of noise on superior Julia sets. We find that the superior Julia sets are drastically more stable for higher strength of noises than the classical Julia sets. Finally, we make a humble attempt to discuss some applications of superior orbit in discrete dynamics and of superior Julia sets in particle dynamics.
format	Article
author	Mamta, Rani Agarwal, Rashi
author_facet	Mamta, Rani Agarwal, Rashi
author_sort	Mamta, Rani
title	Effect of Stochastic Noise on Superior Julia Sets
title_short	Effect of Stochastic Noise on Superior Julia Sets
title_full	Effect of Stochastic Noise on Superior Julia Sets
title_fullStr	Effect of Stochastic Noise on Superior Julia Sets
title_full_unstemmed	Effect of Stochastic Noise on Superior Julia Sets
title_sort	effect of stochastic noise on superior julia sets
publisher	Springer US
publishDate	2010
url	http://umpir.ump.edu.my/id/eprint/12404/ http://umpir.ump.edu.my/id/eprint/12404/ http://umpir.ump.edu.my/id/eprint/12404/ http://umpir.ump.edu.my/id/eprint/12404/1/Effect%20of%20stochastic%20noise%20on%20superior%20julia%20sets.pdf
first_indexed	2023-09-18T22:14:01Z
last_indexed	2023-09-18T22:14:01Z
_version_	1777415216638722048

Effect of Stochastic Noise on Superior Julia Sets

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