Related papers: Iterated Function Systems: A Comprehensive Survey
This paper contains four main results associated with an attractor of a projective iterated function system (IFS). The first theorem characterizes when a projective IFS has an attractor which avoids a hyperplane. The second theorem…
In this article, we study the novel concept of non-stationary iterated function systems (IFSs) introduced by Massopust in 2019. At first, using a sequence of different contractive operators, we construct non-stationary $\alpha$-fractal…
In nature, there are many phenomena with both irregularity and uncertainty. Therefore, a fuzzy-valued fractal interpolation is more useful for modeling them than fuzzy interpolation or fractal interpolation. We construct fractal…
Many graph algorithms can be viewed as sets of rules that are iteratively applied, with the number of iterations dependent on the size and complexity of the input graph. Existing machine learning architectures often struggle to represent…
We investigate whether the Hutchinson operator associated with the iterated function system (IFS) is continuous. It clarifies several partial results scattered across recent literature. While the main example for IFS with strict attractor…
Let C be a closed subset of a topological space X, and let f : C --> X. Let us assume that f is continuous and f(x) lies in C for every x in the boundary of C. How many times can one iterate f? This paper provides estimates on the number of…
This paper introduces Fourier duality for a class of affine iterated function systems (IFS) T_i. These systems are determined by a finite family of contractive affine maps in R^d. Our Fourier duality applies to the resulting probability…
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.…
We study invariant measures for random countable (finite or infinite) conformal iterated function systems (IFS) with arbitrary overlaps. We do not assume any type of separation condition. We prove, under a mild assumption of finite entropy,…
In this paper, we present a new feature selection method that is suitable for both unsupervised and supervised problems. We build upon the recently proposed Infinite Feature Selection (IFS) method where feature subsets of all sizes…
The term "overlapping" refers to a certain fairly simple type of piecewise continuous function from the unit interval to itself and also to a fairly simple type of iterated function system (IFS) on the unit interval. A correspondence…
We give a systematic account of iterated function systems (IFS) of weak contractions of different types (Browder, Rakotch, topological). We show that the existence of attractors and asymptotically stable invariant measures, and the validity…
Under suitable conditions, with respect to some property on a random iterated function system(RIFS), it is shown how the system satisfies in this property almost surely.
A powerful statistical interpolating concept, which we call \emph{fully lifted} (fl), is introduced and presented while establishing a connection between bilinearly indexed random processes and their corresponding fully decoupled (linearly…
We study the concept of a code (or shift) space for a generalized iterated function system (GIFS in short). We prove that relations between GIFSs and their code spaces are analogous to the case of classical IFSs. As an application, we…
We study the minimality of almost every orbital branch of minimal iterated function systems (IFSs). We prove that this kind of minimality holds for forward and backward minimal IFSs generated by orientation-preserving homeomorphisms of the…
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…
This paper is the first paper of three papers in a series, which intend to provide a systematic treatment for the space-filling curves of self-similar sets. In the present paper, we introduce a notion of \emph{linear graph-directed IFS}…
We study probabilistic iterated function systems (IFS), consisting of a finite or infinite number of average-contracting bi-Lipschitz maps on R^d. If our strong open set condition is also satisfied, we show that both upper and lower bounds…
We construct a converging geometric iterated function system on the moduli space of ordered triangles, for which the involved functions have geometric meanings and contain a non-contraction map under the natural metric.