Skip to content
Free planNo credit card requiredStart writing
AI for Research home
AI for Research home
Dashboard
Sign inGet started

Search 250 million research papers

Read the abstract, see who wrote it and who cites it, and get the citation in APA, MLA, Chicago or Harvard.

About 1,644 papers for “iterated function systems”

Iterated Function Systems

Aimee Johnson, Kathleen Madden, Ayşe Şahı̇n · American Mathematical Society eBooks · 2017

Let {fi | 1 ≤ i ≤ n} be a finite set of n mappings from a complete metric space (E, d) onto itself; {pi | 1 ≤ i ≤ n} a discrete probability distribution, that is, a set of nonnegative real numbers such that \( \sum\nolimits_{i = 1}^n {pi} = 1 \) ; and F : E : E the mapping defined by x : F(x) = fi(x) with probability pi. The dynamical system ((E,d),F) is called an iterated function system or IFS.

Cited by 0

Discrete Iterated Function Systems

Mario Peruggia · 1993

Written for researchers and developers applying Integrated Function Systems in the creation of fractal images, this book presents a modification of a widely used probabilistic algorithm for generating IFS-encoded images. The book also includes a discussion of how IFS techniques can be applied to produce animated motion pictures.

Cited by 33

Forward Iterated Function Systems

Linda Keen, Nikola Lakic · 2003

We consider the iterated function system Fn = fn ◦... ◦ f2 ◦ f1 formed from the holomorphic functions in the family H(∆,Ω). The analog of stable behavior for such systems is that the limit functions be constant. We prove that a necessary and sufficient condition for stable behavior for all iterated function systems formed from H(∆,Ω) is that Ω be a proper subset of ∆. We also prove that for a given iterated function system the constant limit functions are unique if and only if Ω is relatively compact in ∆. 1

Cited by 0

Tiling Iterated Function Systems

Michael F. Barnsley, Louisa F. Barnsley, Andrew Vince · arXiv (Cornell University) · 2020

This paper presents a detailed symbolic approach to the study of self-similar tilings. It uses properties of addresses associated with graph-directed iterated function systems to establish conjugacy properties of tiling spaces. Tiles may be fractals and the tiled set may be a complicated unbounded subset of $\mathbb{R}^{M}$.

Cited by 0Open access

Quantum iterated function systems

Artur Łoziński, Karol Życzkowski, Wojciech Słomczyński · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 2003

An iterated function system (IFS) is defined by specifying a set of functions in a classical phase space, which act randomly on an initial point. In an analogous way, we define a quantum IFS (QIFS), where functions act randomly with prescribed probabilities in the Hilbert space. In a more general setting, a QIFS consists of completely positive maps acting in the space of density operators. This formalism is designed to describe certain problems of nonunitary quantum dynamics. We present exemplary classical IFSs, the invariant measure of which exhibits fractal structure, and study properties of the corresponding QIFSs and their invariant states.

Cited by 34Open access

On the relation between iterated function systems and partitioned iterated function systems

Dieter van Melkebeek, Adhemar Bultheel · Lirias (KU Leuven) · 1996

In this paper, we give a theoretically founded transition from Iterated Function Systems based on affine transformations to Partitioned Iterated Function Systems. We show that there are two essential steps, namely, restricting the affine transformations, and solving the evoked problem of ink dissipation.

Cited by 0Open access

Attractors of iterated function systems

P. F. Duvall, L. S. Husch · Proceedings of the American Mathematical Society · 1992

In this paper, the question of which compact metric spaces can be attractors of hyperbolic iterated function systems on Euclidean space is studied. It is shown that given any finite-dimensional compact metric <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper X"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding="application/x-tex">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, there is a Cantor set <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C"> <mml:semantics> <mml:mi>C</mml:mi> <mml:annotation encoding="application/x-tex">C</mml:annotation> </mml:semantics> </mml:math> </inline-formula> such that the disjoint union of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C"> <mml:semantics> <mml:mi>C</mml:mi> <mml:annotation encoding="application/x-tex">C</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper X"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding="application/x-tex">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is an attractor. In the process, it is proved that every such <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper X"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding="application/x-tex">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is the Lipschitz image of a Cantor set.

Cited by 30

Locally Contractive Iterated Function Systems

David Steinsaltz · The Annals of Probability · 1999

An iterated function system on $\mathscr{X}\subset\mathbb{R}^d$ is defined by successively applying an i.i.d.sequence of random Lipschitz functions from to $\mathscr{X}$ to $\mathscr{X}$. This paper shows how $F _n = f_1\circ\ldots\circ f_n$ may converge even in the absence of the strong contraction conditions, for instance, Lipschitz constant smaller than 1 on average,which earlier work has required. Instead, it is posited that there be a region of contraction which compensates for the noncontractive or even expansive part of the functions. Applications to queues, to self-modifying random walks and to random logistic maps are given.

Cited by 28Open access