Annina Iseli, Kevin Wildrick · Conformal Geometry and Dynamics of the American Mathematical Society · 2017
We consider a class of iterated function systems (IFSs) of contracting similarities of <inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper R Superscript n"><mml:semantics><mml:msup><mml:mrow class="MJX-TeXAtom-ORD"><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mi>n</mml:mi></mml:msup><mml:annotation encoding="application/x-tex">\mathbb {R}^n</mml:annotation></mml:semantics></mml:math></inline-formula>, introduced by Hutchinson, for which the invariant set possesses a natural Hölder continuous parameterization by the unit interval. When such an invariant set is homeomorphic to an interval, we give necessary conditions in terms of the similarities alone for it to possess a quasisymmetric (and as a corollary, bi-Hölder) parameterization. We also give a related necessary condition for the invariant set of such an IFS to be homeomorphic to an interval.
Cited by 1Open access
Pavel V. Moskalev, Alexey G. Bukhovets and Tatyana Ya. Biruchinskay · 2012
Pointwise generation and display of attractors (prefractals) of the random iterated function system (RIFS) for various combinations of probabilistic and geometric parameters of some fixed point sets (protofractals), described by Bukhovets A.G. (2012) <<a href="https://doi.org/10.1134%2FS0005117912020154" target="_top">doi:10.1134/S0005117912020154</a>>.
Cited by 2Open access
Ai Hua Fan, Ka‐Sing Lau · Journal of Mathematical Analysis and Applications · 1999
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Dan Dumitru · 2013
The aim of this paper is to prove that the union of a Peano space and a segment with whose intersection is nonempty is the attractor of a topological iterated function system formed by three functions.
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Cheng–Der Fuh · 2004
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D.S. Broomhead, J. P. Huke, Mark Muldoon et al. · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · 2004
This paper introduces a new class of models of digital communications channels. Physically, these models take account of the digital nature of the input. Mathematically, they are iterated function systems. As a consequence of making explicit assumptions about the role of discreteness in the models, it is possible to make general statements about the behaviour of these channels without needing to assume that they are linear. We provide the mathematical background necessary to understand the behaviour of these models and prove a number of results about their observability. We also provide a number of examples intended to demonstrate their connection with linear state–space models, and to suggest how the nonlinear theory might be developed towards applications.
Cited by 9
Adrian Petruşel · Journal of Numerical Analysis and Approximation Theory · 2004
The aim of this paper is to study the properties of the fractal and the multi-fractal operator generated by some iterated function system satisfying to a locally contractive type condition.
Cited by 5Open access
Young-Il Jun, Soon-Hyouk Lee, Gee-Yeon Lee et al. · 1994
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NTUR (臺灣機構典藏) · 2007
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Amol Potgantwar, Sunil Bhirud · 2009
Biometrics has been used for person identification since long time. Till today, researchers, neuroscientists and engineers working on the how human brain works for identification of the person. Hence it is a very interesting topic to do the work on it. Every individual has unique fingerprint and it does not changes throughout the lifetime. So it is the most widely used technique. But the face is most natural, non intrusive biometric and the cost of the system is low as compared with the other biometric system. Many conventional methods of face recognition depend solely on appearance and model based. But there is inbuilt degree of self similarity in the image of faces which can be efficiently utilized through representation exploiting self-transformations, known as Iterated Function System (IFS). Interestingly, virtually all images of natural or man-made objects, show region wise self similarity although they may not be globally self similar. Such objects can be represented by Partitioned Iterated Function System (PIFS) very compactly. Hence, the goal is to carry out the face recognition using Partitioned Iterated Function System. This approach has been tested upon the 106 images of 27 persons. It is giving the good results under the variance, rotation and scaling. In this approach we carried out face recognition based on PIFS representation and matching carried out in the PIFS code domain, which is more efficient than correlation in the image domain. The recognition method is attractive from the view point of execution time as the PIFS code of reference faces are built off-line and recognition of query object involves only comparison of its PIFS code with those in the database.
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F. G. Horowitz · 1996
: Iterated Function Systems (IFS) raster compression techniques achieve their results by identifying self-similarities in the source image. However, not all source images contain exploitable self-similarity. We describe a compression technique that combines a Karhunen-Loeve basis set (for non self-similar aspects of an image) with a block based IFS. 1. INTRODUCTION Iterated Function Systems (IFS), popularized in Barnsley [1], provide a concise way of coding certain classes of interscale (fractal or self-similar) redundancies. The Block IFS technique of Jacquin [2,3] was the first (published) automated solution to determining an IFS code for any given image. Jacquin&apos;s technique partitions an image into (large) domain blocks and (small) range blocks, and then finds best fitting mappings from the domains to the ranges. Currently, most practical IFS encodings are descended from Jacquin&apos;s pioneering technique. These descendents all share mappings with the following schema: data from a do...
Cited by 2
Amol Potgantwar, Sunil Bhirud · 2009
Many conventional methods of face recognition depend solely on appearance and model based. But there is inbuilt degree of self similarity in the image of faces which can be efficiently utilized through representation exploiting self-transformations, known as iterated function system (IFS). Interestingly, virtually all images of natural or man-made objects, show region wise self similarity although they may not be globally self similar. Such objects can be represented by partitioned iterated function system (PIFS) very compactly. Hence, the goal is to carry out the face recognition using partitioned iterated function system. This approach has been tested upon the 106 images of 27 persons. It is giving the good results under the variance, rotation and scaling. In this approach we carried out face recognition based on PIFS representation and matching carried out in the PIFS code domain, which is more efficient than correlation in the image domain. The recognition method is attractive from the view point of execution time as the PIFS code of reference faces are built off-line and recognition of query object involves only comparison of its PIFS code with those in the database. (5 pages)
Cited by 0
Judy Yangjun Lin, Huoxia Liu · Journal of Theoretical Probability · 2024
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Rice, Jonathan, Informatique et Mathematiques Appliquees de Grenoble (IMAG), 38 - Saint-Martin-d'Heres (France). Atelier de Recherches sur les Techniques Mathematiques et Informatiques de Systemes (ARTEMIS), Grenoble-1 Univ., 38 - Saint-Martin-d'Heres (France). Atelier de Recherches sur les Techniques Mathematiques et Informatiques des Systemes (ARTEMIS) et al. · OpenGrey (Institut de l'Information Scientifique et Technique) · 1995
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Mujahid Abbas, Talat Nazir · 2018
The purpose of this chapter is to construct the fractal set of iterated function system, a certain finite collection of mappings defined on a metric space that induce compact-valued mappings defined on a family of compact subsets of a metric space. We prove that Hutchinson operator defined with the help of a finite family of F -contraction mappings on a complete metric space is itself generalized F -contraction mapping on a family of compact subsets of X . We then obtain a final fractal obtained by successive application of a generalized F − Hutchinson operator. We also construct a fractal with the help of a finite family of generalized F -contraction mappings, a class of mappings more general than contraction mappings, defined in the setup of b-metric space. Consequently, we obtain a variety of results for iterated function system satisfying a different set of contractive conditions. Some examples are presented to support the results proved herein.
Cited by 3
Corey de Wit · ArXiv.org · 2025
This paper describes the celebrated aperiodic hat tiling by Smith et al. [Comb. Theory 8 (2024), 6] as generated by an overlapping iterated function system. We briefly introduce and study infinite sequences of iterated function systems that converge uniformly in each component, and use this theory to model the hat tiling's associated imperfect substitution system.
Cited by 0Open access
Michael F. Barnsley, Andrew Vince · arXiv (Cornell University) · 2012
We investigate the topological and metric properties of attractors of an iterated function system (IFS) whose functions may not be contractive. We focus, in particular, on invertible IFSs of finitely many maps on a compact metric space. We rely on ideas Kieninger and McGehee and Wiandt, restricted to what is, in many ways, a simpler setting, but focused on a special type of attractor, namely point-fibred minimal (locally) invariant sets. This allows us to give short proofs of some of the key ideas.
Cited by 7Open access
Pier Luigi Sacco, Marco Sandri · 1994
We reconsider the input-output model in the light of a new mathematical formalism, namely the so called Iterated Function Systems (IFS), that, in spite of the linearity of the structure of the system, allows a greatly complex dynamical behavior. The basic theory is presented and some analytical results are provided, together with some simulations (at least partly) based on empirical data.
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Xingyuan Wang, Li Fan-ping · Nonlinear Analysis · 2008
Cited by 14
Kifayat Ullah, S. K. Katiyar · Topological Algebra and its Applications · 2022
Abstract In this article, we are considering the cyclic weak ϕ -contraction and prove that the result is also true in Hausdorff metric space. We are constructing a cyclic weak ϕ iterated function system (IFS), which gives the self-referential set or attractor, called the fractal.
Cited by 4Open access