Related papers: Fractal dimension for a class of complex-valued fr…
The structure of the large scale distribution of the galaxies have been widely studied since the publication of the first catalogs. Since large redshift samples are available, their analyses seem to show fractal correlations up to the…
We present an overview of a theory of complex dimensions of self-similar fractal strings, and compare this theory to the theory of varieties over a finite field from the geometric and the dynamical point of view. Then we combine the several…
The primary objectives of this paper are to present the construction of bivariate fractal interpolation functions over triangular interpolating domain using the concept of vertex coloring and to propose a double integration formula for the…
The main goal of this paper has a double purpose. On the one hand, we propose a new definition in order to compute the fractal dimension of a subset respect to any fractal structure, which completes the theory of classical box-counting…
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…
This work presents an analysis of fractional derivatives and fractal derivatives, discussing their differences and similarities. The fractal derivative is closely connected to Haussdorff's concepts of fractional dimension geometry. The…
Complexity measures are designed to capture complex behavior and quantify *how* complex, according to that measure, that particular behavior is. It can be expected that different complexity measures from possibly entirely different fields…
In this paper, we first present a simple lemma which allows us to estimate the box dimension of graphs of given functions by the associated oscillation sums and oscillation vectors. Then we define vertical scaling matrices of generalized…
It is known that there exists a function interpolating a given data set such that the graph of the function is the attractor of an iterated function system which is called fractal interpolation function. We generalize the notion of fractal…
In this paper, we explore some significant properties associated with a fractal operator on the space of all continuous functions defined on the Sierpi\'nski Gasket (SG). We also provide some results related to constrained approximation…
Fractal geometry proved to be an effective mathematical tool for exploring real geographical space based on digital maps and remote sensing images. Whether the fractal theory tool can be applied to abstract geographical space has not been…
Dimension theory lies at the heart of fractal geometry and concerns the rigorous quantification of how large a subset of a metric space is. There are many notions of dimension to consider, and part of the richness of the subject is in…
A multifractal analysis is performed on a three-dimensional grayscale image associated with a complex system. First, a procedure for generating 3D synthetic images (2D image stacks) of a complex structure exhibiting multifractal behaviour…
Due to the fractal nature of retinal blood vessels, the retinal fractal dimension is a natural parameter for researchers to explore and has garnered interest as a potential diagnostic tool. This review aims to summarize the current…
Hausdorff dimension of level sets of generic continuous functions defined on fractals can give information about the "thickness/narrow cross-sections" "network" corresponding to a fractal set, $F$. This lead to the definition of the…
In this article, we investigate the fractal dimension of the graph of the mixed Riemann-Liouville fractional integral for various choice of continuous functions on a rectangular region. We estimate bounds for the box dimension and the…
We determine the Hausdorff and box dimension of the fractal graphs for a general class of Weierstrass-type functions of the form $f(x) = \sum_{n=1}^\infty a_n \, g(b_n x + \theta_n)$, where $g$ is a periodic Lipschitz real function and…
This work is an analytical and numerical study of the composition of several fractals into one and of the relation between the composite dimension and the dimensions of the component fractals. In the case of composition of standard IFS with…
The Interstellar Medium seems to have an underlying fractal structure, which can be characterized through its fractal dimension (Df). However, several factors may affect the determination of Df, such as distortions due to projection, low…
The fractal structure of real world objects is often analyzed using digital images. In this context, the compression fractal dimension is put forward. It provides a simple method for the direct estimation of the dimension of fractals stored…