Related papers: Diameter Diminishing To Zero IFSs
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We study contraction conditions for an iterated function system of continuous maps on a metric space which are chosen randomly, identically and independently. We investigate metric changes, preserving the topological structure of the space,…
Most existing Image Restoration (IR) models are task-specific, which can not be generalized to different degradation operators. In this work, we propose the Denoising Diffusion Null-Space Model (DDNM), a novel zero-shot framework for…
Measures generated by Iterated Function Systems composed of uncountably many one--dimensional affine maps are studied. We present numerical techniques as well as rigorous results that establish whether these measures are absolutely or…
This article introduces the novel notion of dimension preserving approximation for continuous functions defined on $[0,1]$ and initiates the study of it. Restrictions and extensions of continuous functions in regards to fractal dimensions…
The primary objective of the present paper is to develop the theory of quantization dimension of an invariant measure associated with an iterated function system consisting of finite number of contractive infinitesimal similitudes in a…
An infinite iterated function system (IIFS) is a countable collection of contraction maps on a compact metric space. In this paper we study the conditions under which the attractor of a such system admits a parameterization by a continuous…
Moran-type iterated function systems (Moran-type IFS or MIFS) are defined by a sequence of iterated function systems, and their basic theoretical framework is established. We define Moran-type attractors and invariant probability measures…
This note presents some numerical examples worked out in order to show the reader how to implement, within a widely accessible computational setting, the methodology for achieving zero cancellation in linear multivariable systems discussed…
We study random independent and identically distributed iterations of functions from an iterated function system of homeomorphisms on the circle which is minimal. We show how such systems can be analyzed in terms of iterated function…
This preliminary paper presents initial explorations in rendering Iterated Function System (IFS) fractals using a differentiable rendering pipeline. Differentiable rendering is a recent innovation at the intersection of computer graphics…
We introduce new method of optimization for finding free parameters of affine iterated function systems (IFS), which are used for fractal approximation. We provide the comparison of effectiveness of fractal and quadratic types of…
Miculescu and Mihail in 2008 introduced the concept of a \emph{generalized iterated function system} (GIFS in~short), a particular extension of the classical IFS. The idea is that, instead of families of selfmaps of a metric space~$X$,…
We provide an overview of iterated function systems (IFS), where randomly chosen state-to-state maps are applied iteratively to a state. We aim to summarize the state of art and, where possible, identify fundamental challenges and…
For any ring we propose the construction of a cover which increases the finitistic dimension on one side and decreases the finitistic dimension to zero on the opposite side. This complements recent work of Cummings.
In this paper, we continue some work devoted to explicit zero-free discs for a large class of Dirichlet series. In a previous article, such zero-free regions were described using some spaces of functions which were defined with some…
The aim of this paper is to present an original approach that takes advantage from the geometric features of strictly convex functions to tackle the problem of finding the minimum from another perspective. The general idea is that near the…
In the present work, we study the attractors of iterated function systems (IFSs) on connected and compact metric spaces. We prove that the whole of the phase space of a forward minimal IFS, for which some map admits an attracting fixed…
We consider the dimension and measure of typical attractors of random iterated function systems (RIFSs). We define a RIFS to be a finite set of (deterministic) iterated function systems (IFSs) acting on the same metric space and, for a…
Intrinsic tame filling functions are quasi-isometry invariants that are refinements of the intrinsic diameter function of a group. The main purpose of this paper is to show that every finite presentation of a group has an intrinsic tame…