Related papers: Set-Valued Fractal Approximation for Countable Dat…
We introduce two frameworks in order to deal with fractal and multi-fractal analysis for subset sum problems where some embedding into the $1$-dimensional Euclidean space plays an important role. As one of these frameworks, the notion of…
The complex dynamics of baker's map and its variants in an infinite-precision mathematical domain have been extensively analyzed in the past five decades. However, their real structure implemented in a finite-precision computer remains…
The area-perimeter scaling can be employed to evaluate the fractal dimension of urban boundaries. However, the formula in common use seems to be not correct. By means of mathematical method, a new formula of calculating the boundary…
Fractured surfaces carry unique details that can provide an accurate quantitative comparison to support comparative forensic analysis of those fractured surfaces. In this study, a statistical analysis comparison protocol was applied to a…
Fractal geometry provides a powerful tool for scale-free spatial analysis of cities, but the fractal dimension calculation results always depend on methods and scopes of study area. This phenomenon has been puzzling many researchers. This…
If our aesthetic preferences are affected by fractal geometry of nature, scaling regularities would be expected to appear in all art forms, including music. While a variety of statistical tools have been proposed to analyze time series in…
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…
We study new relations between countable iterated function systems (IFS) with overlaps, Smale endomorphisms and random systems with complete connections. We prove that stationary measures for countable conformal IFS with overlaps and…
We introduce the concept of fractels for functions and discuss their analytic and algebraic properties. We also consider the representation of polynomials and analytic functions using fractels, and the consequences of these representations…
The present work investigates the segmentation of textures by formulating it as a strongly convex optimization problem, aiming to favor piecewise constancy of fractal features (local variance and local regularity) widely used to model…
This paper presents a new approach of constructing $\alpha$-fractal interpolation functions (FIFs) using neural network operators, integrating concepts from approximation theory. Initially, we construct $\alpha$-fractals utilizing neural…
Fractals are self-repeating patterns which have dimensions given by fractions rather than integers. While the dimension of a system unambiguously defines its properties, a fractional dimensional system can exhibit interesting properties.…
Scale invariance of intrinsic patterns is an important concept in geology that can be observed in numerous geological objects and phenomena. These geological objects and phenomena are described as containing statistically selfsimilar…
In this report we present experimental results using \emph{Haussdorf-Besicovich} fractal dimension for performing morphological galaxy classification. The fractal dimension is a topological, structural and spatial property that give us…
We introduce the novel concept of a non-stationary iterated function system by considering a countable sequence of distinct set-valued maps $\{\mathcal{F}_k\}_{k\in \mathbb{N}}$ where each $\mathcal{F}_k$ maps $\mathcal{H}(X)\to…
In this article we treat a notion of continuity for a multi-valued function $F$ and we compute the descriptive set-theoretic complexity of the set of all $x$ for which $F$ is continuous at $x$. We give conditions under which the latter set…
Fractal dimensions have been used as a quantitative measure for structure of eigenstates of quantum many-body systems, useful for comparison to random matrix theory predictions or to distinguish many-body localized systems from chaotic…
In the process of measuring objects with local self-similarity, such as satellite images or coastlines, we obtain a data set with both local self-similarity and uncertainty. To better interpolate such data sets, an interpolation function…
We forge connections between the theory of fractal sets obtained as attractors of iterated function systems and process calculi. To this end, we reinterpret Milner's expressions for processes as contraction operators on a complete metric…
We study the kinetics of random sequential adsorption of a mixture of particles with continuous distribution of sizes for different deposition rules. It appears in the long time limit the resulting system can be described using the fractal…