Results 31 to 40 of about 3,191,545 (316)

Dimension of invariant measures for affine iterated function systems [PDF]

Duke mathematical journal, 2019
Let $\{S_i\}_{i\in \Lambda}$ be a finite contracting affine iterated function system (IFS) on ${\Bbb R}^d$. Let $(\Sigma,\sigma)$ denote the two-sided full shift over the alphabet $\Lambda$, and $\pi:\Sigma\to {\Bbb R}^d$ be the coding map associated ...
De-Jun Feng
semanticscholar   +1 more source

The Effect of Learning Rate on Fractal Image Coding Using Artificial Neural Networks

Fractal and Fractional, 2022
The amount by which the artificial neural network weights are updated during the training process is called the learning rate. More precisely, the learning rate is an adjustable parameter used in training neural networks in which small values, often in ...
Rashad A. Al-Jawfi
doaj   +1 more source

Iterated function systems with super-exponentially close cylinders II [PDF]

Proceedings of the American Mathematical Society, 2019
Several important conjectures in Fractal Geometry can be summarised as follows: If the dimension of a self-similar measure in $\mathbb{R}$ does not equal its expected value, then the underlying iterated function system contains an exact overlap.
S. Baker
semanticscholar   +1 more source

Iterated Function Systems on Multifunctions [PDF]

, 2007
We introduce a method of iterated function systems (IFS) over the space of set-valued mappings (multifunctions). This is done by first considering a couple of useful metrics over the space of multifunctions F(X,Y). Some appropriate IFS-type fractal transform operators T:F(X,Y)->F(X,Y) are then defined which combine spatially-contracted and range ...
D. La Torre, F. Mendivil, E. Vrscay
openaire   +3 more sources

Attractor of Cantor Type with Positive Measure [PDF]

, 2017
We construct an iterated function system consisting of strictly increasing contractions $f,g\colon [0,1]\to [0,1]$ with $f([0,1])\cap g([0,1])=\emptyset$ and such that its attractor has positive Lebesgue ...
Morawiec, Janusz, Zürcher, Thomas
core   +3 more sources

IFSs consisting of generalized convex contractions

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2017
In this paper we introduce the concept of iterated function system consisting of generalized convex contractions. More precisely, given n ∈ ℕ*, an iterated function system consisting of generalized convex contractions on a complete metric space (X; d) is
Georgescu Flavian
doaj   +1 more source

Approximating distribution functions by iterated function systems [PDF]

Journal of Applied Mathematics and Decision Sciences, 2002
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
S.M. Iacus, D. La Torre
openaire   +3 more sources

Iterated Relation Systems on Riemannian Manifolds

Fractal and Fractional
For fractals on Riemannian manifolds, the theory of iterated function systems often does not apply well directly, as these fractal sets are often defined by relations that are multivalued or non-contractive.
Jie Liu, Sze-Man Ngai, Lei Ouyang
doaj   +1 more source

The absolute continuity of the invariant measure of random iterated function systems with overlaps

, 2009
We consider iterated function systems on the interval with random perturbation. Let $Y_\epsilon$ be uniformly distributed in $[1- \epsilon, 1 + \epsilon]$ and let $f_i \in C^{1+\alpha}$ be contractions with fixpoints $a_i$.
Barany, Balazs, Persson, Tomas
core   +2 more sources

The Chaos Game on a General Iterated Function System from a Topological Point of View [PDF]

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2010
We investigate combinatorial issues relating to the use of random orbit approximations to the attractor of an iterated function system with the aim of clarifying the role of the stochastic process during the generation of the orbit.
M. Barnsley, Krzysztof Leśniak
semanticscholar   +1 more source