Related papers: Accuracy analysis of the box-counting algorithm
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…
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…
By viewing the covers of a fractal as a statistical mechanical system, the exact capacity of a multifractal is computed. The procedure can be extended to any multifractal described by a scaling function to show why the capacity and…
Fractal nests are sets defined as unions of unit $n$-spheres scaled by a sequence of $k^{-\alpha}$ for some $\alpha>0$. In this article we generalise the concept to subsets of such spheres and find the formulas for their box counting…
In this paper, we discuss the Higuchi algorithm which serves as a widely used estimator for the box-counting dimension of the graph of a bounded function $f : [0,1] \to \R$. We formulate the method in a mathematically precise way and show…
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…
Fractal dimension constitutes the main tool to test for fractal patterns in Euclidean contexts. For this purpose, it is always used the box dimension, since it is easy to calculate, though the Hausdorff dimension, which is the oldest and…
This work presents a new Visual Basic 6.0 application for estimating the fractal dimension of images, based on an optimized version of the box-counting algorithm. Following the attempt to separate the real information from noise, we…
Least box number coverage problem for calculating dimension of fractal networks is a NP-hard problem. Meanwhile, the time complexity of random ball coverage for calculating dimension is very low. In this paper we strictly present the upper…
We show that for sets with the Hausdorff--Besicovitch dimension equal zero the box counting algorithm commonly used to calculate Renyi exponents ($d_q$) can exhibit perfect scaling suggesting non zero $d_q$'s. Properties of these…
We show that when the standard techniques for calculating fractal dimensions in empirical data (such as the box counting) are applied on uniformly random structures, apparent fractal behavior is observed in a range between physically…
We study algorithmic problems on subsets of Euclidean space of low fractal dimension. These spaces are the subject of intensive study in various branches of mathematics, including geometry, topology, and measure theory. There are several…
The study addresses the problem of precision in floating-point (FP) computations. A method for estimating the errors which affect intermediate and final results is proposed and a summary of many software simulations is discussed. The basic…
The computational cost of a Monte Carlo algorithm can only be meaningfully discussed when taking into account the magnitude of the resulting statistical error. Aiming for a fixed error per particle, we study the scaling behavior of the…
It is shown that fractal dimension can be estimated seeking a solution of functional equation defined for areas of coverages of different scales. The method proposed is compared with widely known way to estimate fractal dimension via linear…
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and…
Fractal geometry deals mainly with irregularity and captures the complexity of a structure or phenomenon. In this article, we focus on the approximation of set-valued functions using modern machinery on the subject of fractal geometry. We…
We study various box-size scaling techniques to obtain the multifractal properties, in terms of the singularity spectrum f(alpha), of the critical eigenstates at the metal-insulator transition within the 3-D Anderson model of localisation.…
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…
We show that fractality in complex networks arises from the geometric self-similarity of their built-in hierarchical community-like structure, which is mathematically described by the scale-invariant equation for the masses of the boxes…