Fractals

Some useful models in the earthquake description are supposed to have a stress distribution, which is usually modeled by means of a cellular automaton with homogeneous distribution. Geological evidence has shown that the Earth's crust during an earthquake is broken into fragments in a scale range that goes from millimeters to hundred of kilometers having a fractal-like structure. In this work, we use an automaton with a fractal structure proposed by Barriere and Turcotte to describe a seismic fault, but we change the definition of event magnitude. We have obtained the general features obtained in other models, especially the Gutenberg-Richter law. We also analyze other properties that have been observed in actual seismic faults.

A fractal relative permeability model is derived which takes into account the capillary pressure difference effect. The proposed model is expressed as a function of saturation, fractal dimensions, fluid properties and capillary pressure difference, and there is no empirical constant introduced in the proposed model. The effect of the capillary pressure difference on the relative permeability is analyzed, and the results indicate that the capillary pressure difference has the significant influence on the relative permeability at low saturation. The predicted relative permeabilities are compared with the available experimental data. Good agreement is found between the present model predictions and the available experimental data.

This paper reports a study on multidimensional fractal behavior of pions emitted in ¹⁶O-AgBr interactions at 2.1 and 60 AGeV by dividing the full bin range into different sub-bin ranges. Analysis is performed in (X_η - X_ϕ) space following two-dimensional factorial moment methodology using the concept of Hurst exponent, which takes into account the anisotropy of phase space. Different scaling behavior is observed in different bins at two different energies. The data show a positive evidence of change of fluctuation pattern from self-similarity to self-affinity with increase of energy. Multifractal dimensions have been calculated in each case and it is observed that pions at both energies exhibit multifractal behavior.

Group behavior emergent from the systems composed of two types of agents are investigated. The agents are defined on a two-dimensional grid system and move under the influence of the attractive and/or repulsive interactions. Depending on the intensity and the sense of the interactions, a wide variety of spatiotemporal patterns emerge on the system. Those patterns are discussed in terms of the well-known phenomena in real systems such as the residential segregation in cities, cell sorting in multicellular system, self-running droplet, group behavior of a fish school under the attack of a predator and the fission in a cell division process.

This short note describes a development of the traditional Pythagorean tree fractal that produces three-dimensional structures based on cubes rather than squares. Adding a 90° rotation at each bifurcation encourages three-dimensional growth, creating increasingly artistic shapes as the branching angle decreases.

The geometric features of the square and triadic Koch snowflake drums are compared using a position entropy defined on the grid points of the discretizations (prefractals) of the two domains. Weighted graphs using the geometric quantities are created and random walks on the two prefractals are performed. The aim is to understand if the existence of narrow channels in the domain may cause the "localization" of eigenfunctions.

In this paper, the human fingerprint, which is independent of rotation and scaling, is recognized. The multiple classification technique, based on wavelet and fractal analysis, is used. It is shown that systematic incorporation of decision from various classifiers leads to a better decision rather than simply fusing them. Multiple classifiers can serve as a means of enhancing the performance of pattern recognition problems. Multiple classifier system design involves the problem of classifier fusion. This paper deals with multi-classifier systems in which each classifier uses its own representation of the input pattern, based on features collected from multiple sources. The multiple feature sources considered here are multi-fractals, wavelets and fast Fourier transforms coefficients. A clustering algorithm is used to observe the efficacy of the feature sources. The multiple sources were graded according to their effectiveness of providing more non-overlapping clusters for different groups into which the samples are to be separated. This approach first considers the best source for the feature parameters. If this feature classifies the test sample into more than one cluster, then the feature next to the best is summoned to finish up the remaining part of the classification process. The continuation of this process along with the judicious selection of classifiers succeeds in identifying a single cluster for the test sample. The results obtained after the experiments on a set of fingerprint images shows that this novel technique can go a long way in avoiding ambiguity and thus limiting the need for use of soft-computing tools for making decisions. Our method provides a hard, concrete and accurate solution to pattern recognition problems employing multiple classifiers.

This paper investigates the Weierstrass type function in local fields whose graph is a chaotic repelling set of a discrete dynamical system, and proves that their exists a linear connection between the orders of its p-adic calculus and the dimensions of the corresponding graphs.

We consider calculation of the dimensions of self-affine fractals and multifractals that are the attractors of iterated function systems specified in terms of upper-triangular matrices. Using methods from linear algebra, we obtain explicit formulae for the dimensions that are valid in many cases.