Related papers: Fractal Dimension for Fractal Structures: A Hausdo…
Fractal dimension is defined on the base of entropy, including macro state entropy and information entropy. The generalized correlation dimension of multifractals is based on Renyi entropy. However, the mathematical transform from entropy…
This paper introduces the concept of Fractal Frenet equations, a set of differential equations used to describe the behavior of vectors along fractal curves. The study explores the analogue of arc length for fractal curves, providing a…
This article presents the construction of a non-affine hypersurface on an $n$-simplex in $\mathbb{R}^n$. Additionally, fractal dimension of the graph of a non-affine multivariate real-valued fractal function is estimated under certain…
Several two-dimensional studies in spiral galaxies show that HII star formation regions have a fractal distribution, with a fractal dimension of approximately 2.3. In this work, the fractal dimension is calculated through the box-counting…
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…
Given a set in the plane, the average length of its projections over all directions is called Favard length. This quantity measures the size of a set, and is closely related to metric and geometric properties of the set such as…
We introduce the notion of fractal index associated with the universal class $h$ of particles or quasiparticles, termed fractons, which obey specific fractal statistics. A connection between fractons and conformal field…
We consider the {\it fractal von Neumann entropy} associated with the {\it fractal distribution function} and we obtain for some {\it universal classes h of fractons} their entropies. We obtain also for each of these classes a {\it…
There are many research papers dealing with fractal dimension of real-valued fractal functions in the recent literature. The main focus of the present paper is to study fractal dimension of complex-valued functions. This paper also…
A simple multifractal coarsening model is suggested that can explain the observed dynamical behavior of the fractal dimension in a wide range of coarsening fractal systems. It is assumed that the minority phase (an ensemble of droplets) at…
Fractals are geometric shapes that can display complex and self-similar patterns found in nature (e.g., clouds and plants). Recent works in visual recognition have leveraged this property to create random fractal images for model…
Given a fractal $\mathcal{I}$ whose Hausdorff dimension matches with the upper-box dimension, we propose a new method which consists in selecting inside $\mathcal{I}$ some subsets (called quasi-Cantor sets) of almost same dimension and with…
In this paper, we study the fractal dimension of the graph of a fractal transformation and also determine the quantization dimension of a probability measure supported on the graph of the fractal transformation. Moreover, we estimate the…
There are many research available on the study of real-valued fractal interpolation function and fractal dimension of its graph. In this paper, our main focus is to study the dimensional results for vector-valued fractal interpolation…
\emph{Fractal percolation} or \emph{Mandelbrot percolation} is one of the most well studied families of random fractals. In this paper we study some of the geometric measure theoretical properties (dimension of projections and structure of…
Urban form has been empirically demonstrated to be of scaling invariance and can be described with fractal geometry. However, the rational range of fractal dimension value and the relationships between various fractal indicators of cities…
In this study, we present a method to measure changes over time of fractal dimension. We confirmed that our method can calculate the fractal dimension with the same precision as conventional methods, and tracking performance of our method…
As for the remarkable study on the estimate of the Hausdorff dimension of a self-similar set due to weak contractions (Kitada A. et al. Chaos, Solitons & Fractals 13 (2002) 363-366), we present a mathematically simplified form which will be…
Singular vectors are those for which the quality of rational approximations provided by Dirichlet's Theorem can be improved by arbitrarily small multiplicative constants. We provide an upper bound on the Hausdorff dimension of singular…
In this paper we study multi-parameter projection theorems for fractal sets. With the help of these estimates, we recover results about the size of $A \cdot A+...+A \cdot A$, where $A$ is a subset of the real line of a given Hausdorff…