Medha Garg, Sumit Chandok · Applied General Topology · 2020
<p>In this paper, we define weak θ<sub>m</sub>− contraction mappings and give a new class of Picard operators for such class of mappings on a complete metric space. Also, we obtain some new results on the existence and uniqueness of attractor for a weak θ<sub>m</sub>− iterated multifunction system. Moreover, we introduce (α, β, θ<sub>m</sub>)− contractions using cyclic (α, β)− admissible mappings and obtain some results for such class of mappings without the continuity of the operator. We also provide an illustrative example to support the concepts and results proved herein.</p>
Cited by 3Open access
Hsueh‐Ting Chu, Chien-Chang Chen · Computers & Graphics · 2003
Cited by 16
Huoyun Wang, Xing Liao, Qing Liu et al. · Journal of Mathematical Analysis and Applications · 2020
Cited by 10
Çilingir, Figen · DergiPark (Istanbul University) · 2014
Bir dalm fonksiyonunun parametrik olmayan tahmin edicisi yinelenmi fonksiyon sistemleri kullanlarak elde edilebilmektedir.Bu ynteme gre
Cited by 0Open access
D.S. Mazel, A. Passamante · 2002
Iterated Function Systems (IFSs) are currently being used for computer graphics and data compression. In this paper, we expand the use of IFSs to the detection of data. We show that an IFS model of data yields a template of the data that, when transformed with an affine map, enhances noisy data and aids in detection. Applications to chaotic systems data and speech data are given.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
Cited by 1
A. K. B. Chand, N. Vijender, Ravi P. Agarwal · Advances in Difference Equations · 2014
In this paper we consider the (inverse) problem of determining the iterated function system (IFS) which produces a shaped fractal interpolant. We develop a new type of rational IFS by using functions of the form E i F i , where E i are cubics and F i are preassigned quadratics having 3-shape parameters. The fixed point of the developed rational cubic IFS is in C 1 , but its derivative varies from a piecewise differentiable function to a continuous nowhere differentiable function. An upper bound of the uniform error between the fixed point of a rational IFS and an original function C 4 is deduced for the convergence results. The automatic generations of the scaling factors and shape parameters in the rational IFS are formulated so that its fixed point preserves the positive/monotonic features of prescribed data. The presence of scaling factors provides additional freedom to the shape of the fractal interpolant over its classical counterpart in the modeling of discrete data.
Cited by 18Open access
Talat Nazir, Mujahid Abbas, Hira Haleem Lodhi · Applied General Topology · 2024
The aim of this paper is to study the sufficient conditions for the existence of attractor of a generalized cyclic iterated function system composed of a complete metric space and a finite collection of generalized cyclic F-contraction mappings. Some examples are presented to support our main results and concepts defined herein. The results proved in the paper extend and generalize various well known results in the existing literature.
Cited by 1Open access
Filip Strobin, Jarosław Swaczyna · Bulletin of the Australian Mathematical Society · 2012
Abstract We follow the idea of generalising the notion of classical iterated function systems, as presented by Mihail and Miculescu. We give their deliberations a more general setting and, using this general approach, study the generic aspect of the problem of existence of an attractor of a function system.
Cited by 68Open access
Journal of International Crisis and Risk Communication Research · 2009
We extend classical basis constructions from Fourier analysis to attractors for affine iterated function systems (IFSs). This is of interest since these attractors have fractal features, e.g., measures with fractal scaling dimension. Moreover, the spectrum is then typically quasi-periodic, but non-periodic, i.e., the spectrum is a "small perturbation" of a lattice. Due to earlier research on IFSs, there are known results on certain classes of spectral duality-pairs, also called spectral pairs or spectral measures. It is known that some duality pairs are associated with complex Hadamard matrices. However, not all IFSs X admit spectral duality. When X is given, we identify geometric conditions on X for the existence of a Fourier spectrum, serving as the second part in a spectral pair. We show how these spectral pairs compose, and we characterize the decompositions in terms of atoms. The decompositions refer to tensor product factorizations for associated complex Hadamard matrices.
Cited by 0Open access
Qiang Wang · 2023
A novel fractal encoding method based on minimum iterated function system was proposed in this study. First, we found that there existed a minimum domain block set (MDBS) which can complete the block-matching for all range blocks, and the definition of minimum iterated function system (MIFS) was introduced. The remaining domain blocks constitute the redundant domain block set (RDBS). Based on the characteristics of the range blocks coming from RDBS, the corresponding bock-matching operations can be optimized by removing the constraints on the scaling coefficients. Then, better block-matching effect can be achieved, and the decoded image quality can be improved as well. Finally, based on MIFS, the decoding process can be also accelerated effectively. Three fractal encoding methods were adopted to assess the performance of the proposed method. Experimental results show that compared the the previous methods, the proposed method can achieve better decoded image quality with slightly more computations and fewer computations in decoding process.
Cited by 0
Kaneko, Kunihiko · arXiv (Cornell University) · 2005
The dynamics of units (molecules) with slowly relaxing internal states is studied as an iterated function system (IFS) for the situation common in e.g. biological systems where these units are subjected to frequent collisional interactions. It is found that an increase in the collision frequency leads to successive discrete states that can be analyzed as partial steps to form a Cantor set. By considering the interactions among the units, a self-consistent IFS is derived, which leads to the formation and stabilization of multiple such discrete states. The relevance of the results to dynamical multiple states in biomolecules in crowded conditions is discussed.
Cited by 0Open access
Retno Wulandari, Kosala Dwidja Purnomo, Ahmad Kamsyakawuni · Jurnal EurekaMatika · 2022
The Pythagorean tree is a flat fractal composed of squares. A Pythagorean tree with two branches developed into three components is called a fractal tree. In this article, the author generates a fractal tree that has been expanded to have n branches using the Iterated Function Systems (IFS) method. The fractal tree will be caused by the IFS method using affine transformations, namely dilation, translation, and rotation on a square as the initial geometric object. The generation of a fractal tree begins with determining the basic shape of the branching. The choice of the primary form of branching will affect the body and characteristics of the resulting fractal tree. There are two primary forms of branching to produce a fractal tree that has several variations in the selection of angles: the same angle, a different angle, and a random angle.Keywords: Affine Transformation, Fractal, Fractal Tree, Iterated Function System Method.AbstrakPohon Pythagoras adalah sebuah fraktal datar yang tersusun dari bujur sangkar. Pohon Pythagoras yang memiliki dua percabangan dikembangkan menjadi tiga percabangan disebut dengan istilah pohon fraktal. Pada artikel ini, penulis membangkitkan pohon fraktal yang dikembangkan jumlah cabangnya sampai sebanyak menggunakan metode Iterated Function Systems (IFS). Pohon fraktal dibangkitkan dengan metode IFS menggunakan transformasi affine yaitu dilatasi, translasi, dan rotasi pada persegi sebagai objek geometri awal. Pembangkitan pohon fraktal dimulai dengan menentukan bentuk dasar percabangan. Pemilihan bentuk dasar percabangan akan berpengaruh pada bentuk dan karakteristik dari pohon fraktal yang dihasilkan. Ada dua macam bentuk dasar percabangan sehingga dapat menghasilkan pohon fraktal yang memiliki beberapa variasi pemilihan sudut yakni sudut sama, sudut berbeda, dan sudut random.
Cited by 0Open access
Dorin Ervin Dutkay, Palle E. T. Jørgensen · Mathematische Zeitschrift · 2008
Cited by 29Open access
E. Rezaali · JOURNAL OF ADVANCES IN MATHEMATICS · 2016
In this article, we are trying to see the Iterated function system or more generally a skew product as formation a semigroup action system. We will try to implement more semigroup action properties on itself. For this purpose, we introduce a semigroup action corresponding Iterated function system and explain more properties of itself then with considering Hutchitson operator on Iterated function system, we try consider the corresponding semigroup action for Iterated function system and achive more its properties.
Cited by 0Open access
Qi-Rong Deng · Bulletin of the Australian Mathematical Society · 2009
Abstract A reverse iterated function system is defined as a family of expansive maps { T 1 , T 2 ,…, T m } on a uniformly discrete set $M\subset \Bbb {R}^d$ . An invariant set is defined to be a nonempty set $F\subseteq M$ satisfying F =⋃ j =1 m T j ( F ). A computation method for the dimension of the invariant set is given and some questions asked by Strichartz are answered.
Cited by 8Open access
Rice, J., Trinity Coll., Dublin (Ireland). Dept. of Computer Science · OpenGrey (Institut de l'Information Scientifique et Technique) · 1996
Cited by 0
Medha, Sumit Chandok · 2019
Cited by 0
Tianxin Huang, Ruihuan Xue, Fengyi Xie et al. · 2023
Aiming at virtual applications, a prototype of affine transformation for designing patterns is proposed in this paper. Due to the capability of generating fractal geometry with self-similar and micro-fine structure by simple affine transformation, the iterative function system (IFS) is utilized to model the prototype, which is comprised of prototype the affine transform, computing the parameters of IFS ,designing and implementing iterative algorithms, and generating basic fractal sets as well. Simulation experiments has shown the validity of the proposed method.
Cited by 0
D.S. Mazel, Mary E. Farrell · 2005
Cited by 1
Maria Fernanda Barrozo, F. E. Levis, Claudia V. Ridolfi · Results in Mathematics · 2021
Cited by 1