Related papers: Sphractal: Estimating the Fractal Dimension of Sur…
This paper develops a technical and practical reinterpretation of the real interval [a,b] under the paradigm of fractal countability. Instead of assuming the continuum as a completed uncountable totality, we model [a,b] as a layered…
The implementation of fractional differential calculations can give new possibilities for image processing tools, in particular for those that are devoted to astronomical images analysis. As discussed in arxiv:0910.2381, the fractional…
We investigate fractal aspects of elliptical polynomial spirals; that is, planar spirals with differing polynomial rates of decay in the two axis directions. We give a full dimensional analysis of these spirals, computing explicitly their…
Using Monte Carlo simulations we study the distributions of the 3-block mass $N_3$ in 4d, 5d, and 6d percolation systems. Because the probability of creating large 3-blocks in these dimensions is very small, we use a ``go with the winners''…
Here we study a class of second-order nonautonomous differential equations, and the corresponding planar and spatial systems, from the point of view of fractal geometry. The fractal oscillatority of solutions at infinity is measured by…
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…
High energy impacts at joint locations often generate highly fragmented, or comminuted, bone fractures. Current approaches for treatment require physicians to decide how to classify the fracture within a hierarchy fracture severity…
The small-angle scattering (SAS) from the Cantor surface fractal on the plane and Koch snowflake is considered. We develop the construction algorithm for the Koch snowflake, which makes possible the recurrence relation for the scattering…
We have investigated the fractal characteristics and shape complexity of the fracture surfaces of swelled isotactic polypropylene Y1600 in supercritical carbon dioxide fluid through the consideration of the statistics of the islands in…
We investigate the influence of fractal structure on material properties. We calculate the statistical correlation functions of fractal media defined by level-cut Gaussian random fields. This allows the modeling of both surface fractal and…
Fractured metal fragments with rough and irregular surfaces are often found at crime scenes. Current forensic practice visually inspects the complex jagged trajectory of fractured surfaces to recognize a ``match'' using comparative…
A novel fractal analysis of the cosmic web structure is carried out, employing the Sloan Digital Sky Survey, data release 7. We consider the large-scale stellar mass distribution, unlike other analyses, and determine its multifractal…
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…
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…
In this article a definition of optimal cover for fractal structures is proposed. Expression for Minkowsky dimension is rewritten in terms of functional equation on areas of covers that constructed for different scales.Given the definition,…
Fractal sets, by definition, are non-differentiable, however their dimension can be continuous, differentiable, and arithmetically manipulable as function of their construction parameters. A new arithmetic for fractal dimension of polyadic…
A fractal approach to numerical analysis of electromagnetic space-time crystals, created by three standing plane harmonic waves with mutually orthogonal phase planes and the same frequency, is presented. Finite models of electromagnetic…
A type of fractal dimension definition is based on the generalized entropy function. Both entropy and fractal dimension can be employed to characterize complex spatial systems such as cities and regions. Despite the inherent connect between…
The curves of scaling behavior is a significant concept in fractal dimension analysis of complex systems. However, the underlying rationale of this kind of curves for fractal cities is not yet clear. The aim of this paper is at researching…
A class of simplified measures is constructed to capture the key features of generic spatio-temporally chaotic systems. A combined analytical and numerical investigation allows us to extablish the scaling beahviour of the fractal dimension…