Search results for "fractal dimension."

Monte Carlo Studies of Relations between Fractal Dimensions in Monofractal Data Sets

1998

Within the fractal approach to studying the distribution of seismic event locations, different fractal dimension definitions and estimation algorithms are in use. Although one expects that for the same data set, values of different dimensions will be different, it is usually anticipated that the direction of fractal dimension changes among different data sets will be the same for every fractal dimension. Mutual relations between the three most popular fractal dimensions, namely: the capacity, cluster and correlation dimensions, have been investigated in the present work. The studies were performed on the Monte Carlo generated data sets. The analysis has shown that dependence of the fractal …

Fractal dimension confidence interval estimation of epicentral distributions

1999

Estimates of the fractal dimension of hypocentral distributions require evaluating the range of independent variables in which fractal parameters exhibit a power law. Systematic and accidental errors are produced mainly by the subjective selection of this range, the insufficiency of data sets as well as by hypocenter mislocations. Therefore it is very important to determine the confidence intervals which are associated with fractal dimension estimates. The effects of various sources of errors are studied using different geometric clusters of epicenters, which have been synthetically generated using a multicluster algorithm with different hierarchical levels, so as to reproduce some characte…

A Random Walk Through Fractal Dimensions. VonB. H. Kaye. VCH Verlagsgesellschaft, Weinheim/VCH Publishers, New York 1989. XXV, 421 S., geb. DM 138.00…

1991

Fractal Dimension Logarithmic Differences Method for Low Voltage Series Arc Fault Detection

2021

Series arc faults introduce singularities in the current signal and changes over time. Fractal dimension can be used to characterize the dynamic behaviour of the current signal by providing a degree of signal chaos. This measure of irregularity exhibits changes in signal behaviour that can suitably be used as a basis for series arc fault detection. In this paper, an efficient low voltage series arc fault detection method based on the logarithmic differences of the estimate of the fractal dimension of the current signal using the multiresolution length-based method is presented. The discrete wavelet transform and the hard thresholding denoising with the universal threshold are also used. Exp…

Assessing forest landscape structure using geographic windows.

2001

Landscape structure, interpreted as indicator of functional processes, has become a main attribute of multiresource forest inventories, enhancing its value with respect to society needs. This approach implies effective use of earth observation techniques and geographic information systems to obtain a global view of the inventoried landscapes and to understand the ecological functions of large spatially-heterogeneous landscape mosaics. Landscape structure often reveal extremely complex patterns that can only be very roughly characterized by methods of Euclidean geometry. Conversely, fractals can be applied to adequately describe many of the irregular, fragmented patterns found in nature. In …

Bi- and three-dimensional fractal analysis of the brown seaweed Gongolaria montagnei and their relationship with gastropod molluscs assemblage

2022

Habitat complexity is one of the main influences on biodiversity in marine environments, particularly in coastal areas where foundation seaweeds provide substrate for highly diverse communities. We studied the 2D and 3D fractal dimensions of Gongolaria montagnei (Fucales) over the vegetative season and examine their relationship with the abundance, species richness and morpho-functional groups of the gastropod associated. Overall, the 3D fractal analysis method used here better describes seaweeds structural complexity compared to the traditional 2D fractal analysis, as highlighted by the higher relationship with gastropod assemblage associated to the alga in terms of abundance, number of sp…

Microstructure of Ag2BI4(B = Ag, Cd) superionics studied by SEM, impedance spectroscopy and fractal dimension analysis

2008

Two silver ion conducting solid electrolytes, Ag2HgI4 and Ag2CdI4, representing a wide class of AgI-based halogenide superionics have been the subjects of study by means of electrical impedance spectroscopy, SEM, porosity measurements and fractal dimension analysis. Even though both materials have been obtained by the same method under strictly identical conditions they were found to exhibit certain differences at the microstructural level. Thus, by the direct measurements of porosity and density it was found that the grain boundaries are better developed in silver mercuric iodide. On the assumption that pore geometry in the materials under study displays fractal character it was shown that…

Fractal dimension: A useful tool to describe the microgeometry of machined surfaces

1993

Abstract The authors have utilized some concepts of fractal geometry to describe the complexity of profiles surveyed from surfaces worked by cutting. In particular an experimental analysis was carried out to investigate the influence of the worked material, cutting speed and cutting operation on the “fractal dimension” parameter. The obtained results show that this parameter is able to describe the irregularities of the profile on a small scale, which is important for an overall understanding of the functional behaviour of machined surfaces. Such descriptions cannot be derived from the more commonly employed parameters.

Fractal geometry of higher derivative gravity

2019

We determine the scaling properties of geometric operators such as lengths, areas, and volumes in models of higher derivative quantum gravity by renormalizing appropriate composite operators. We use these results to deduce the fractal dimensions of such hypersurfaces embedded in a quantum spacetime at very small distances.

FLUCTUATION-INDUCED LOCAL OSCILLATIONS AND FRACTAL PATTERNS IN THE LATTICE LIMIT CYCLE MODEL

2003

The fractal properties of the Lattice Limit Cycle model are explored when the process is realized on a 2-dimensional square lattice support via Monte Carlo Simulations. It is shown that the structure of the steady state presents inhomogeneous fluctuations in the form of domains of identical particles. The various domains compete with one another via their borders which have self-similar, fractal structure. The fractality is more prominent, (fractal dimensions df < 2), when the parameter values are near the critical point where the Hopf bifurcation occurs. As the distance from the Hopf bifurcation increases in the parameter space the system becomes more homogeneous and the fractal dimens…