Related papers: Fractal dimension analysis of spatio-temporal patt…
Scaling properties of Yang-Mills fields are used to show that fractal structures are expected to be present in system described by those theories. We show that the fractal structure leads to recurrence formulas that allow the determination…
This work proposes a novel technique for the numerical calculus of the fractal dimension of fractal objects which can be represented as a closed contour. The proposed method maps the fractal contour onto a complex signal and calculates its…
We introduce a generalization of Higuchi's estimator of the fractal dimension as a new way to characterize the multifractal spectrum of univariate time series. The resulting multifractal Higuchi dimension analysis (MF-HDA) method considers…
Fractal behavior and long-range dependence are widely observed in measurements and characterization of traffic flow in high-speed computer networks of different technologies and coverage levels. This paper presents the results obtained when…
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…
First, let the fractal dimension D=n(integer)+d(decimal), so the fractal dimensional matrix was represented by a usual matrix adds a special decimal row (column). We researched that mathematics, for example, the fractal dimensional linear…
We study several fractal properties of the Weierstrass-type function \[ W(x)=\sum_{n=0} ^\infty \lambda (x) \lambda(\tau x) \cdots \lambda (\tau ^{n-1}x)\, g(\tau ^n x), \] where $\tau :[0,1)\to[0,1)$ is a cookie cutter map with possibly…
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…
Although geographic features, such as mountains and coastlines, are fractal, some studies have claimed that the fractal property is not universal. This claim, which is false, is mainly attributed to the strict definition of fractal…
Fractal structures emerge from statistical and hierarchical processes in urban development or network evolution. In a class of efficient and robust geographical networks, we derive the size distribution of layered areas, and estimate the…
An algorithm for calculating generalized fractal dimension of a time series using the general information function is presented. The algorithm is based on a strings sort technique and requires $O(N \log_2 N)$ computations. A rough estimate…
We consider the time-dependent statistical distributions of diffusive processes in relaxation to a stationary state for simple, two dimensional chaotic models based upon random walks on a line. We show that the cumulative functions of the…
The image fractal analysis is actively used in all science branches. In particular in materials science the fractal analysis is applied to study microstructure of deformed metals because its structure can be interpreted as the fractal…
For a long time, many methods are developed to make temporal signal analyses based on time series. However, for geographical systems, spatial signal analyses are as important as temporal signal analyses. Nonstationary spatial and temporal…
In this paper, we prove the identity $\dim_{\textrm H}(F)=d\cdot \dim_{\textrm H}(\alpha^{-1}(F))$, where $\dim_{\textrm H}$ denotes Hausdorff dimension, $F\subseteq \mathbb{R}^d$, and $\alpha:[0,1]\to [0,1]^d$ is a function whose…
We develop a hierarchical structure (HS) analysis for quantitative description of statistical states of spatially extended systems. Examples discussed here include an experimental reaction-diffusion system with Belousov-Zhabotinsky…
Fractal dimension is widely adopted in spatial databases and data mining, among others as a measure of dataset skewness. State-of-the-art algorithms for estimating the fractal dimension exhibit linear runtime complexity whether based on…
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…
A stochastic model relating the parameters of astrophysical structures to the parameters of their granular components is applied to the formation of hierarchical, large-scale structures from galaxies assumed as point-like objects. If the…
We consider the effects of spatial correlations in a two-dimensional site percolation model. By generalizing the Newman-Ziff Monte Carlo algorithm to include spatial correlations, percolation thresholds and fractal dimensions of percolation…