A fractal approach is used to analyze financial time series, applying different degrees of time resolution, and the results are interrelated. Some fractal properties of foreign exchange (FX) data are found. In particular, the mean size of the absolute values of price changes follows a “fractal” scaling law (a power law) as a function of the analysis time interval ranging from a few minutes up t...

Today Fractal geometry is completely new area of research in the field of computer science and engineering. It has wide range of applications. Fractals in nature are so complicated and irregular that it is hopeless to model them by simply using classical geometry objects. Benoit Mandelbrot, the father of fractal geometry, from his book The Fractal Geometry of Nature, 1982. This paper explor var...

Hexagonal regions are optimal for subdividing the plane in the sense that the regions are as close as possible to the disk shape while still providing a tessellation of the plane. It is however not possible to do recursive subdivisions, i.e. to divide a hexagon into smaller hexagons. In this paper, hexagon-like fractal regions will be presented. It is possible to decompose a hexagon-like fracta...

The recovery of cadmium, lead and copper with the brown alga Fucus vesiculosus was characterized and quantified. The biosorption data fitted the pseudo-second order and Langmuir isotherm models, but did not adjust to the intraparticle diffusion model. The metal uptakes deduced from the pseudo-second order kinetic model and the Langmuir isotherm model followed a similar sequence: Cu>Cd approxima...

A fractal set which corresponds to the six-vertex model has been obtained and a relationship between the free energy of the six-vertex model and the fractal dimension of the fractal set was established. Notions which correspond to the transfer matrix and the n-equivalence has been found in the area of the fractal geometry. This correspondence can be generalized to the case of the models suitabl...

A novel texture detecting analysis for medical pathological tissue images was developed by fractal Brown model. According to fractal Brown random field model, a discrete fractal random field for image texture detection on a definite scale could be derived from the Brown model. Using fractal dimensions in partial region of the image and gray difference between adjacent pixels and relevant Hurst ...

Polyominoes, shapes made up of squares connected edge-to-edge, provide a rich source of prototiles for edge-toedge fractal tilings. We give examples of fractal tilings with 2-fold and 4-fold rotational symmetry based on prototiles derived by dissecting polyominoes with 2-fold and 4-fold rotational symmetry, respectively. A systematic analysis is made of candidate prototiles based on lower-order...

In this paper we estimate the fractal dimension of stochastic processes with 1/f-like spectra by applying a recently-introduced multiresolution framework. This framework admits an efficient likelihood function evaluation, allowing us to compute the maximum likelihood estimate of this fractal parameter with relative ease. In addition to yielding results that compare well to other proposed method...

Fractality has emerged as a feature of the organization of some complex natural systems. Several biological secretions show fractal-like patterns for their crystallization phenomena but their presence in crystallizations of bovine cervical mucus (BCM) is yet unknown. In order to assess the fractality of BCM crystallization, samples of this fluid were taken from heifers at oestrus, their crystal...

In visualizing very long DNA sequences, including the complete genomes of several bacteria, yeast and segments of human genes, we encounter fractal-like patterns underlying these biological objects of prominent importance. The method used here to visualize genomes of organisms may well be used as a convenient tool to trace, e.g., evolutionary relatedness of species. We describe the method and e...