Relevant bibliographies by topics / Iterated Function Systems (IFS)

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Iterated Function Systems (IFS)'

Author: Grafiati
Published: 4 June 2021
Last updated: 7 September 2023

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Journal articles on the topic "Iterated Function Systems (IFS)"

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Iacus, Stefano Maria, and Davide La Torre. "Approximating distribution functions by iterated function systems." Journal of Applied Mathematics and Decision Sciences 2005, no. 1 (January 1, 2005): 33–46. http://dx.doi.org/10.1155/jamds.2005.33.

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An iterated function system (IFS) on the space of distribution functions is built with the aim of proposing a new class of distribution function estimators. One IFS estimator and its asymptotic properties are studied in detail. We also propose a density estimator derived from the IFS distribution function estimator by using Fourier analysis. Relative efficiencies of both estimators, for small and moderate sample sizes, are presented via Monte Carlo analysis.
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Mohtashamipour, Maliheh, and Alireza Zamani Bahabadi. "Chaos in Iterated Function Systems." International Journal of Bifurcation and Chaos 30, no. 12 (September 30, 2020): 2050177. http://dx.doi.org/10.1142/s0218127420501771.

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In the present paper, we study chaos in iterated function systems (IFS), namely dynamical systems with several generators. We introduce weak Li–Yorke chaos, chaos in branch, and weak topological chaos to perceive the role of branches to create chaos in an IFS. Moreover, we define another type of chaos, [Formula: see text]-chaos, on an IFS. Further, we find the necessary conditions to create the chaotic iterated function systems.
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Balu, Rinju, and Sunil Mathew. "ON (n, m)-ITERATED FUNCTION SYSTEMS." Asian-European Journal of Mathematics 06, no. 04 (December 2013): 1350055. http://dx.doi.org/10.1142/s1793557113500551.

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One of the most common way to generate a fractal is by using an iterated function system (IFS). In this paper, we introduce an (n, m)-IFS, which is a collection of n IFSs and discuss the attractor of this system. Also we prove the continuity theorem and collage theorem for (n, m)-IFS.
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FRAME, MICHAEL, and NIAL NEGER. "FRACTAL VIDEOFEEDBACK AS ANALOG ITERATED FUNCTION SYSTEMS." Fractals 16, no. 03 (September 2008): 275–85. http://dx.doi.org/10.1142/s0218348x08003946.

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We demonstrate that videofeedback augmented with one or two mirrors can produce stationary fractal patterns obtained by an iterated function system (IFS) with two transformations (one with a reflection, one without), and with four transformations (two with reflections, one without, one with a 180° rotation). Camera placement yielding only a partial image in one or both mirrors can be achieved using IFS with memory. The IFS rules are obtained from the images of three non-collinear points in each of the principal pieces of the image.
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JONES, HUW. "ITERATED FUNCTION SYSTEMS FOR OBJECT GENERATION AND RENDERING." International Journal of Bifurcation and Chaos 11, no. 02 (February 2001): 259–89. http://dx.doi.org/10.1142/s0218127401002237.

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Iterated function systems (IFS) have been used since the mid 1980s in generating fractal forms and in image compression. They have the property of encoding complex structures as relatively simple and concise algorithms and data sets. The complete information for generation of an IFS structure, known as an "attractor", is held in the definition of a few transformation functions, typically affine transformations described by simple linear equations. These transform 2D or 3D objects by combinations of translation, scaling and rotation, preserving parallel lines. The process of generating an attractor using either of the two standard methods is straightforward, but the inverse problem of identifying the IFS for a particular attractor is more difficult. The paper introduces and reviews the uses of Iterated Function Systems, particularly for 2D image and 3D object generation. As well as a general exposition of the method, results developed by the author for creation of fractal objects are shown. Some are based on regular geometric structures, others mimic a number of naturally occurring forms. These deviate from normal practice in using nonaffine transformations in the IFS definition. A new method for synthesising images of smooth objects using IFS is developed and illustrated as an alternative to standard 3D rendering methods (see the cover picture), which are briefly described.
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Centore, P. M., and E. R. Vrscay. "Continuity of Attractors and Invariant Measures for Iterated Function Systems." Canadian Mathematical Bulletin 37, no. 3 (September 1, 1994): 315–29. http://dx.doi.org/10.4153/cmb-1994-048-6.

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AbstractWe prove the "folklore" results that both the attractor A and invariant measure μ of an N-map Iterated Function System (IFS) vary continuously with variations in the contractive IFS maps as well as the probabilities. This represents a generalization of Barnsley's result showing the continuity of attractors with respect to variations of a parameter appearing in the IFS maps. Some applications are presented, including approximations of attractors and invariant measures of nonlinear IFS, as well as some novel approximations of Julia sets for quadratic complex maps.
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Rajan, Pasupathi, María A. Navascués, and Arya Kumar Bedabrata Chand. "Iterated Functions Systems Composed of Generalized θ-Contractions." Fractal and Fractional 5, no. 3 (July 14, 2021): 69. http://dx.doi.org/10.3390/fractalfract5030069.

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The theory of iterated function systems (IFSs) has been an active area of research on fractals and various types of self-similarity in nature. The basic theoretical work on IFSs has been proposed by Hutchinson. In this paper, we introduce a new generalization of Hutchinson IFS, namely generalized θ-contraction IFS, which is a finite collection of generalized θ-contraction functions T1,…,TN from finite Cartesian product space X×⋯×X into X, where (X,d) is a complete metric space. We prove the existence of attractor for this generalized IFS. We show that the Hutchinson operators for countable and multivalued θ-contraction IFSs are Picard. Finally, when the map θ is continuous, we show the relation between the code space and the attractor of θ-contraction IFS.
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EROĞLU, KEMAL ILGAR, STEFFEN ROHDE, and BORIS SOLOMYAK. "Quasisymmetric conjugacy between quadratic dynamics and iterated function systems." Ergodic Theory and Dynamical Systems 30, no. 6 (November 24, 2009): 1665–84. http://dx.doi.org/10.1017/s0143385709000789.

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AbstractWe consider linear iterated function systems (IFS) with a constant contraction ratio in the plane for which the ‘overlap set’ 𝒪 is finite, and which are ‘invertible’ on the attractor A, in the sense that there is a continuous surjection q:A→A whose inverse branches are the contractions of the IFS. The overlap set is the critical set in the sense that q is not a local homeomorphism precisely at 𝒪. We suppose also that there is a rational function p with the Julia set J such that (A,q) and (J,p) are conjugate. We prove that if A has bounded turning and p has no parabolic cycles, then the conjugacy is quasisymmetric. This result is applied to some specific examples including an uncountable family. Our main focus is on the family of IFS {λz,λz+1} where λ is a complex parameter in the unit disk, such that its attractor Aλ is a dendrite, which happens whenever 𝒪 is a singleton. C. Bandt observed that a simple modification of such an IFS (without changing the attractor) is invertible and gives rise to a quadratic-like map qλ on Aλ. If the IFS is post-critically finite, then a result of A. Kameyama shows that there is a quadratic map pc (z)=z2 +c, with the Julia set Jc such that (Aλ,qλ) and (Jc,pc) are conjugate. We prove that this conjugacy is quasisymmetric and obtain partial results in the general (not post-critically finite) case.
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Vasisht, Radhika, Mohammad Salman, and Ruchi Das. "Variants of shadowing properties for iterated function systems on uniform spaces." Filomat 35, no. 8 (2021): 2565–72. http://dx.doi.org/10.2298/fil2108565v.

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In this paper, the notions of topological shadowing, topological ergodic shadowing, topological chain transitivity and topological chain mixing are introduced and studied for an iterated function system (IFS) on uniform spaces. It is proved that if an IFS has topological shadowing property and is topological chain mixing, then it has topological ergodic shadowing and it is topological mixing. Moreover, if an IFS has topological shadowing property and is topological chain transitive, then it is topologically ergodic and hence topologically transitive. Also, these notions are studied for the product IFS on uniform spaces.
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DEKKING, F. M., and P. VAN DER WAL. "THE BOUNDARY OF THE ATTRACTOR OF A RECURRENT ITERATED FUNCTION SYSTEM." Fractals 10, no. 01 (March 2002): 77–89. http://dx.doi.org/10.1142/s0218348x0200077x.

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We prove for a subclass of recurrent iterated function systems (also called graph-directed iterated function systems) that the boundary of their attractor is again the attractor of a recurrent IFS. Our method is constructive and permits computation of the Hausdorff dimension of the attractor and its boundary.
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Dissertations / Theses on the topic "Iterated Function Systems (IFS)"

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Gadde, Erland. "Stable iterated function systems." Doctoral thesis, Umeå universitet, Institutionen för matematik, teknik och naturvetenskap, 1992. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-100370.

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The purpose of this thesis is to generalize the growing theory of iterated function systems (IFSs). Earlier, hyperbolic IFSs with finitely many functions have been studied extensively. Also, hyperbolic IFSs with infinitely many functions have been studied. In this thesis, more general IFSs are studied. The Hausdorff pseudometric is studied. This is a generalization of the Hausdorff metric. Wide and narrow limit sets are studied. These are two types of limits of sequences of sets in a complete pseudometric space. Stable Iterated Function Systems, a kind of generalization of hyperbolic IFSs, are defined. Some different, but closely related, types of stability for the IFSs are considered. It is proved that the IFSs with the most general type of stability have unique attractors. Also, invariant sets, addressing, and periodic points for stable IFSs are studied. Hutchinson’s metric (also called Vaserhstein’s metric) is generalized from being defined on a space of probability measures, into a class of norms, the £-norms, on a space of real measures (on certain metric spaces). Under rather general conditions, it is proved that these norms, when they are restricted to positive measures, give rise to complete metric spaces with the metric topology coinciding with the weak*-topology. Then, IFSs with probabilities (IFSPs) are studied, in particular, stable IFSPs. The £-norm-results are used to prove that, as in the case of hyperbolic IFSPs, IFSPs with the most general kind of stability have unique invariant measures. These measures are ”attractive”. Also, an invariant measure is constructed by first ”lifting” the IFSP to the code space. Finally, it is proved that the Random Iteration Algorithm in a sense will ”work” for some stable IFSPs.

Diss. Umeå : Umeå universitet, 1992


digitalisering@umu
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Reid, James Edward. "Numerical Values of the Hausdorff and Packing Measures for Limit Sets of Iterated Function Systems." Thesis, University of North Texas, 2017. https://digital.library.unt.edu/ark:/67531/metadc1011825/.

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In the context of fractal geometry, the natural extension of volume in Euclidean space is given by Hausdorff and packing measures. These measures arise naturally in the context of iterated function systems (IFS). For example, if the IFS is finite and conformal, then the Hausdorff and packing dimensions of the limit sets agree and the corresponding Hausdorff and packing measures are positive and finite. Moreover, the map which takes the IFS to its dimension is continuous. Developing on previous work, we show that the map which takes a finite conformal IFS to the numerical value of its packing measure is continuous. In the context of self-similar sets, we introduce the super separation condition. We then combine this condition with known density theorems to get a better handle on finding balls of maximum density. This allows us to extend the work of others and give exact formulas for the numerical value of packing measure for classes of Cantor sets, Sierpinski N-gons, and Sierpinski simplexes.
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Alexander, Simon. "Multiscale Methods in Image Modelling and Image Processing." Thesis, University of Waterloo, 2005. http://hdl.handle.net/10012/1179.

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The field of modelling and processing of 'images' has fairly recently become important, even crucial, to areas of science, medicine, and engineering. The inevitable explosion of imaging modalities and approaches stemming from this fact has become a rich source of mathematical applications.

'Imaging' is quite broad, and suffers somewhat from this broadness. The general question of 'what is an image?' or perhaps 'what is a natural image?' turns out to be difficult to address. To make real headway one may need to strongly constrain the class of images being considered, as will be done in part of this thesis. On the other hand there are general principles that can guide research in many areas. One such principle considered is the assertion that (classes of) images have multiscale relationships, whether at a pixel level, between features, or other variants. There are both practical (in terms of computational complexity) and more philosophical reasons (mimicking the human visual system, for example) that suggest looking at such methods. Looking at scaling relationships may also have the advantage of opening a problem up to many mathematical tools.

This thesis will detail two investigations into multiscale relationships, in quite different areas. One will involve Iterated Function Systems (IFS), and the other a stochastic approach to reconstruction of binary images (binary phase descriptions of porous media). The use of IFS in this context, which has often been called 'fractal image coding', has been primarily viewed as an image compression technique. We will re-visit this approach, proposing it as a more general tool. Some study of the implications of that idea will be presented, along with applications inferred by the results. In the area of reconstruction of binary porous media, a novel, multiscale, hierarchical annealing approach is proposed and investigated.
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Reis, Glauco dos Santos. "Uma abordagem de compressão de imagens através de sistemas de funções iteradas." Universidade Presbiteriana Mackenzie, 2011. http://tede.mackenzie.br/jspui/handle/tede/1408.

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Made available in DSpace on 2016-03-15T19:37:38Z (GMT). No. of bitstreams: 1 Glauco dos Santos Reis.pdf: 1334999 bytes, checksum: d2d72d3f95a449c19482f55f82b7f61e (MD5) Previous issue date: 2011-08-22
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A new image compression technique is proposed, based on the affine transformations (ATs) that define an iterated function system (IFS). Previous related research in the field has shown that an image may be approximated by iteratively subjecting a set of sub-regions to a group of ATs. In this case, the original image should be partitioned in regions, and each one of the active pixels are transformed by the AT. The new transformed set should be approximated to other image regions. This iterated execution to find ATs for the best set of areas might result in smaller storage space since the similar areas might be replaced by AT coefficients. Despite this advantage, the technique is computationally intensive, because both the sub-regions and the corresponding ATs that have to be searched for. Here, a new form of similarity is proposed, based on the successive points generated by the iteration of affine transformations. By understanding an AT as a discrete dynamical system, with each image point represented by an iteration of the AT, the method captures similarities between these points, namely, those with the same color in the image; by saving the starting point and the transformations coefficients, the points can be iterated back, to reconstruct the original image. This results in lighter computational effort, since the comparison is made point by point, instead of region by region. Experiments were made on a group of 10 images, representing a broad set of distinct features and resolutions. The proposed algorithm competes in terms of storage size, when compared to JPEG, mainly when the image size is small, and the number of colors are reduced, as currently happens for most images used in the Internet. Although the proposed method is faster than the traditional method for IFS compression, it is slower than common file formats like JPEG.
Uma nova técnica para compressão de imagens é proposta, baseada em conjuntos de transformações afins (affine transformations - ATs), normalmente conhecidos como sistemas de funções iteradas (iterated function system -IFS). Pesquisas anteriores mostraram que uma imagem poderia ser aproximada pela aplicação de um grupo de ATs em conjuntos de sub-regiões da imagem, de forma iterativa. Através deste processo, a imagem original seria subdividida em regiões e sobre a coordenada de cada ponto habilitado de cada região seria aplicada uma transformação afim. O resultado representaria um novo conjunto de pontos similares a outras regiões da imagem. A execução de forma iterada deste processo de identificação das ATs para o maior conjunto de regiões similares de uma determinada imagem permitiria uma redução no armazenamento, já que as regiões similares poderiam ser armazenadas como os coeficientes das transformações afins. Apesar desta vantagem em termos de compressão, a técnica é computacionalmente intensiva, pela busca exaustiva de sub-regiões e das ATs geradoras, de forma a proporcionar o melhor preenchimento em outras regiões da imagem. Esta pesquisa propõe uma nova forma de compressão baseada em ATs, utilizando a sequência de pontos gerada pela iteração das ATs. Entendendo uma AT como um sistema dinâmico em tempo discreto, cada novo ponto identificado é consequência direta da iteração da AT sobre o ponto anterior, permitindo a captura de similaridades nesta sequência de pontos. Através do salvamento dos coeficientes das ATs e das coordenadas iniciais, é possível a reconstrução da imagem pela iteração da AT a partir do ponto inicial. Isto pode resultar em menor esforço computacional, pois apenas comparações simples de pontos são necessárias, ao invés de comparações entre os pontos de regiões da imagem. Foram feitos experimentos em um conjunto de 10 classes de imagens, representando um espectro de diferentes características gerais e resoluções. O algoritmo proposto rivaliza em termos de armazenamento quando comparado ao formato JPEG, principalmente para imagens de pequeno tamanho e com número de cores reduzidas, como as utilizadas com frequência na Internet. Apesar de ser mais rápido para a compressão do que outros métodos baseados em IFS, ele é mais lento do que métodos clássicos como o JPEG.
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Boore, Graeme C. "Directed graph iterated function systems." Thesis, University of St Andrews, 2011. http://hdl.handle.net/10023/2109.

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This thesis concerns an active research area within fractal geometry. In the first part, in Chapters 2 and 3, for directed graph iterated function systems (IFSs) defined on ℝ, we prove that a class of 2-vertex directed graph IFSs have attractors that cannot be the attractors of standard (1-vertex directed graph) IFSs, with or without separation conditions. We also calculate their exact Hausdorff measure. Thus we are able to identify a new class of attractors for which the exact Hausdorff measure is known. We give a constructive algorithm for calculating the set of gap lengths of any attractor as a finite union of cosets of finitely generated semigroups of positive real numbers. The generators of these semigroups are contracting similarity ratios of simple cycles in the directed graph. The algorithm works for any IFS defined on ℝ with no limit on the number of vertices in the directed graph, provided a separation condition holds. The second part, in Chapter 4, applies to directed graph IFSs defined on ℝⁿ . We obtain an explicit calculable value for the power law behaviour as r → 0⁺ , of the qth packing moment of μ[subscript(u)], the self-similar measure at a vertex u, for the non-lattice case, with a corresponding limit for the lattice case. We do this (i) for any q ∈ ℝ if the strong separation condition holds, (ii) for q ≥ 0 if the weaker open set condition holds and a specified non-negative matrix associated with the system is irreducible. In the non-lattice case this enables the rate of convergence of the packing L[superscript(q)]-spectrum of μ[subscript(u)] to be determined. We also show, for (ii) but allowing q ∈ ℝ, that the upper multifractal q box-dimension with respect to μ[subscript(u)], of the set consisting of all the intersections of the components of F[subscript(u)], is strictly less than the multifractal q Hausdorff dimension with respect to μ[subscript(u)] of F[subscript(u)].
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Vines, Greg. "Signal modeling with iterated function systems." Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/13315.

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Hardin, Douglas Patten. "Hyperbolic iterated function systems and applications." Diss., Georgia Institute of Technology, 1985. http://hdl.handle.net/1853/30864.

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Giles, Paul A. "Iterated function systems and shape representation." Thesis, Durham University, 1990. http://etheses.dur.ac.uk/6188/.

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We propose the use of iterated function systems as an isomorphic shape representation scheme for use in a machine vision environment. A concise description of the basic theory and salient characteristics of iterated function systems is presented and from this we develop a formal framework within which to embed a representation scheme. Concentrating on the problem of obtaining automatically generated two-dimensional encodings we describe implementations of two solutions. The first is based on a deterministic algorithm and makes simplifying assumptions which limit its range of applicability. The second employs a novel formulation of a genetic algorithm and is intended to function with general data input. Keywords: Machine Vision, Shape Representation, Iterated Function Systems, Genetic Algorithms.
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Kieninger, Bernd. "Iterated function systems on compact Hausdorff spaces /." Aachen : Shaker, 2002. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=010050648&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.

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Paul, Baldine-Brunel. "Video Compression based on iterated function systems." Diss., Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/13553.

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Books on the topic "Iterated Function Systems (IFS)"

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Discrete iterated function systems. Wellesley, Mass: A.K. Peters, 1993.

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1967-, Kornelson Keri A., and Shuman Karen L. 1973-, eds. Iterated function systems, moments, and transformations of infinite matrices. Providence, R.I: American Mathematical Society, 2011.

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Bratteli, Ola. Iterated function systems and permutation representations of the Cuntz algebra. Providence, R.I: American Mathematical Society, 1999.

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Canright, David. Estimating the spatial extent of attractors of iterated function systems. Monterey, Calif: Naval Postgraduate School, 1993.

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Tsoodol, Nyamkhuu. Geometric modeling of 3D fractal objects: Finding 3D Iterated function system of natural objects based on 2D IFS of 2D orthogonal parallel projections. VDM Verlag Dr. Müller, 2009.

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Peruggia. Iterated Function Systems CB. Jones and Bartlett Publishers, Inc, 1993.

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Iterated Function Systems for Real-Time Image Synthesis. London: Springer London, 2007. http://dx.doi.org/10.1007/1-84628-686-7.

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Nikiel, Slawomir. Iterated Function Systems for Real-Time Image Synthesis. Springer, 2007.

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Iterated Function Systems for Real-Time Image Synthesis. Springer, 2007.

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Nikiel, Slawomir. Iterated Function Systems for Real-Time Image Synthesis. Springer London, Limited, 2010.

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Book chapters on the topic "Iterated Function Systems (IFS)"

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Cuzzocrea, Alfredo, Enzo Mumolo, and Giorgio Mario Grasso. "Genetic Estimation of Iterated Function Systems for Accurate Fractal Modeling in Pattern Recognition Tools." In Computational Science and Its Applications – ICCSA 2017, 357–71. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-62392-4_26.

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Barnsley, Michael F., John H. Elton, and Douglas P. Hardin. "Recurrent Iterated Function Systems." In Constructive Approximation, 3–31. Boston, MA: Springer US, 1989. http://dx.doi.org/10.1007/978-1-4899-6886-9_1.

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Massopust, Peter. "Hypercomplex Iterated Function Systems." In Trends in Mathematics, 589–98. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-87502-2_59.

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Colapinto, Cinzia, and Davide La Torre. "Iterated Function Systems, Iterated Multifunction Systems, and Applications." In Mathematical and Statistical Methods in Insurance and Finance, 83–90. Milano: Springer Milan, 2008. http://dx.doi.org/10.1007/978-88-470-0704-8_11.

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Sokolov, Dmitry, Gilles Gouaty, Christian Gentil, and Anton Mishkinis. "Boundary Controlled Iterated Function Systems." In Curves and Surfaces, 414–32. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-22804-4_29.

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Rousseau, Christiane, and Yvan Saint-Aubin. "Image Compression Iterated Function Systems." In Mathematics and Technology, 1–42. New York, NY: Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-69216-6_11.

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Field, Michael. "Fractals and Iterated Function Systems." In Springer Undergraduate Mathematics Series, 329–47. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-67546-6_8.

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Gowrisankar, A., and D. Easwaramoorthy. "Local Countable Iterated Function Systems." In Trends in Mathematics, 169–75. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-01120-8_20.

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Pasupathi, R., A. K. B. Chand, and M. A. Navascués. "Cyclic Multivalued Iterated Function Systems." In Springer Proceedings in Mathematics & Statistics, 245–56. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-9307-7_21.

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Bezuglyi, Sergey, and Palle E. T. Jorgensen. "Iterated Function Systems and Transfer Operators." In Transfer Operators, Endomorphisms, and Measurable Partitions, 133–42. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-92417-5_12.

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Conference papers on the topic "Iterated Function Systems (IFS)"

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U, Yongsop, Ying Yu, Dong Han, and Jizhou Sun. "Research on Generation of Fractal Architecture Model Scheme via Iterated Function System (IFS)." In 2015 International Conference on Computer Science and Intelligent Communication. Paris, France: Atlantis Press, 2015. http://dx.doi.org/10.2991/csic-15.2015.18.

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Lu, Guojun, and Toon L. Yew. "Image compression using partitioned iterated function systems." In IS&T/SPIE 1994 International Symposium on Electronic Imaging: Science and Technology, edited by Majid Rabbani and Robert J. Safranek. SPIE, 1994. http://dx.doi.org/10.1117/12.173912.

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Mishra, Kunti, and Bhagwati Prasad. "Iterated function systems in Gb-metric space." In ADVANCEMENT IN MATHEMATICAL SCIENCES: Proceedings of the 2nd International Conference on Recent Advances in Mathematical Sciences and its Applications (RAMSA-2017). Author(s), 2017. http://dx.doi.org/10.1063/1.5008714.

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Soto-Villalobos, Roberto, Francisco Gerardo Benavides-Bravo, Filiberto Hueyotl-Zahuantitla, and Mario A. Aguirre-López. "A New Deterministic Gasket Fractal Based on Ball Sets." In WSCG 2023 – 31. International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision. University of West Bohemia, Czech Republic, 2023. http://dx.doi.org/10.24132/csrn.3301.34.

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Abstract:
In this paper, we propose a new gasket fractal constructed in a deterministic iterated function system (IFS) way by means of interacting ball and square sets in R^2. The gasket consists of the ball sets generated by the IFS, possessing also exact self-similarity. All this leads to a direct deduction of other properties and a clear construction methodology, including a dynamic geometry procedure with an open-source construction protocol. We also develop an extended version of the fractal in R^n. Some resulting configurations consisting of stacked 2D-fractals are plotted. We discuss about potential applications of them in some areas of science, focusing mainly on percolation models. Guidelines for future work are also provided.
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Cohen, H. A. "Deterministic scanning and hybrid algorithms for fast decoding of IFS (iterated function system) encoded image sets." In [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing. IEEE, 1992. http://dx.doi.org/10.1109/icassp.1992.226164.

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Goyal, Komal, and Bhagwati Prasad. "Generalized iterated function systems." In ADVANCED TRENDS IN MECHANICAL AND AEROSPACE ENGINEERING: ATMA-2019. AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0036922.

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Green, Simon G. "GPU-accelerated iterated function systems." In ACM SIGGRAPH 2005 Sketches. New York, New York, USA: ACM Press, 2005. http://dx.doi.org/10.1145/1187112.1187128.

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Hernández Ávalos, Pedro A., Claudia Feregrino Uribe, Roger Luis Velázquez, and René A. Cumplido Parra. "Watermarking Based on Iterated Function Systems." In 2009 Mexican International Conference on Computer Science. IEEE, 2009. http://dx.doi.org/10.1109/enc.2009.58.

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Kocsis, Steve. "Digital Compression And Iterated Function Systems." In 33rd Annual Techincal Symposium, edited by Andrew G. Tescher. SPIE, 1990. http://dx.doi.org/10.1117/12.962305.

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Ildikó, Somogyi, and Soós Anna. "Interpolation using local iterated function systems." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017). Author(s), 2018. http://dx.doi.org/10.1063/1.5044147.

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Reports on the topic "Iterated Function Systems (IFS)"

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Schwartz, Ira B., and Laurie Reuter. Background Simulation and Filter Design Using Iterated Function Systems. Fort Belvoir, VA: Defense Technical Information Center, February 1991. http://dx.doi.org/10.21236/ada232632.

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Doughty, Christine. Estimation of hydrologic properties of heterogeneous geologic media with an inverse method based on iterated function systems. Office of Scientific and Technical Information (OSTI), December 1995. http://dx.doi.org/10.2172/195663.

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Doughty, Christine A. Estimation of hydrologic properties of heterogeneous geologic media with an inverse method based on iterated function systems. Office of Scientific and Technical Information (OSTI), May 1996. http://dx.doi.org/10.2172/241577.

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