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Following the work of Louisa and Michael Barnsley on results in tops of iterated function systems, we extend their work to graph-directed iterated function systems by investigating the relationship between top addresses and shift spaces.…

Dynamical Systems · Mathematics 2024-02-05 Grover Lancaster-Cole , Georgiana Lyall , Thomas Malcolm , Qiyu Zhou

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…

Dynamical Systems · Mathematics 2012-10-04 K. Igudesman , G. Shabernev

In this paper, we introduce a construction of hidden variable recurrent fractal interpolation functions (HVRFIF) with four function contractivity factors. In the fractal interpolation theory, it is very important to ensure flexibility and…

Dynamical Systems · Mathematics 2019-06-26 Chol-Hui Yun

The fast basin of an attractor of an iterated function system (IFS) is the set of points in the domain of the IFS whose orbits under the associated semigroup intersect the attractor. Fast basins can have non-integer dimension and comprise a…

Dynamical Systems · Mathematics 2015-10-19 Michael F. Barnsley , Andrew Vince

In the present paper, the notion of Lidstone Fractal Interpolation Function ($Lidstone \ FIF$) is introduced to interpolate and approximate data generating functions that arise from real life objects and outcomes of several scientific…

Dynamical Systems · Mathematics 2014-07-10 G. P. Kapoor , M. Sahoo

Within the new concept of a local iterated function system (local IFS), we consider a class of attractors of such IFSs, namely those that are graphs of functions. These new functions are called local fractal functions and they extend and…

Functional Analysis · Mathematics 2014-08-28 Peter Massopust

In this paper, the notion of dimension preserving approximation for real-valued bivariate continuous functions, defined on a rectangular domain $\rectangle$, has been introduced and several results, similar to well-known results of…

Classical Analysis and ODEs · Mathematics 2021-01-19 V. Agrawal , T. Som , S. Verma

We study a fractional differentiation operator for functions on the conjugate space to an infinite extension of a local field of zero characteristic which is a union of an increasing sequence of finite extensions. In particular, a…

Functional Analysis · Mathematics 2007-05-23 Anatoly N. Kochubei

Iterated Graph Systems (IGS) transplant ideas from fractal geometry into graph theory. Building on this framework, we extend Edge IGS from the primitive to the reducible setting. Within this broader context, we formulate rigorous…

Combinatorics · Mathematics 2026-05-13 Nero Ziyu Li , Frank Xin Hu , Thomas Britz

Our companion paper \cite{Stojnicnflgscompyx23} introduced a very powerful \emph{fully lifted} (fl) statistical interpolating/comparison mechanism for bilinearly indexed random processes. Here, we present a particular realization of such fl…

Probability · Mathematics 2023-12-01 Mihailo Stojnic

The aim of this paper is to 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…

General Mathematics · Mathematics 2016-06-17 Talat Nazir , Sergei Silvestrov , Xiaomin Qi

We consider functions $f$ of two real variables, given as trigonometric functions over a finite set $F$ of frequencies. This set is assumed to be closed under rotations in the frequency plane of angle $\frac{2k\pi}{M}$ for some integer $M$.…

Numerical Analysis · Mathematics 2016-12-02 Jean-Paul Gauthier , Dario Prandi

We study a wide class of fractal interpolation functions in a single platform by considering the domains of these functions as general attractors. We obtain lower and upper bounds of the box dimension of these functions in a more general…

Dynamical Systems · Mathematics 2024-10-07 R. Pasupathi

In this article, we construct the multivariate fractal interpolation functions for a given data points and explore the existence of $\alpha$-fractal function corresponding to the multivariate continuous function defined on $[0,1]\times…

Functional Analysis · Mathematics 2022-06-28 Vishal Agrawal , Megha Pandey , Tanmoy Som

We present an introduction to fractal interpolation beginning with a global set-up and then extending to a local, a non-stationary, and finally the novel quaternionic setting. Emphasis is placed on the overall perspective with references…

Functional Analysis · Mathematics 2021-09-01 Peter R Massopust

A simple, yet unifying method is provided for the construction of tilings by tiles obtained from the attractor of an iterated function system (IFS). Many examples appearing in the literature in ad hoc ways, as well as new examples, can be…

Metric Geometry · Mathematics 2013-10-24 Michael Barnsley , Andrew Vince

We investigate multifractal regularity for infinite conformal iterated function systems (cIFS). That is we determine to what extent the multifractal spectrum depends continuously on the cIFS and its thermodynamic potential. For this we…

Dynamical Systems · Mathematics 2014-06-16 Johannes Jaerisch , Marc Kesseböhmer

We construct interpolation operators for functions taking values in a symmetric space -- a smooth manifold with an inversion symmetry about every point. Key to our construction is the observation that every symmetric space can be realized…

Numerical Analysis · Mathematics 2016-05-24 Evan Gawlik , Melvin Leok

In our previous work, On the localization of Hutchinson-Barnsley fractals, Chaos Solitons Fractals, 173 (2023), 113-674, we presented a method for finding a finite family of closed balls whose union contains the attractor of a given…

Dynamical Systems · Mathematics 2023-11-17 Bogdan Anghelina , Radu Miculescu

We estimate a Box-counting dimension of fractal surfaces which are generated by iterated function systems with a vertical contraction factor function on an arbitrary data set over rectangular grids and can express well a lot of natural…

Dynamical Systems · Mathematics 2013-03-20 CholHui Yun , MunChol Kim