recent studies on wavelet transform and fractal modeling applied on mammograms for the detection of cancerous tissues indicate that microcalcifications and masses can be utilized for the study of the morphology and diagnosis of cancerous cases. it is shown that the use of fractal modeling, as applied to a given image, can clearly discern cancerous zones from noncancerous areas. in this paper, f...

By employing an embedding result due to Mañé, and its recent strengthening due to Foias & Olson it is shown that a global attractor with finite fractal (box counting) dimension d lies within an arbitrarily small neighbourhood of a smooth graph over the space spanned by the first [[2d+1]] Fourier-Galerkin modes. The proof is, however, non-constructive.

Since the end of the Seventies, following work of the French mathematician Mandelbrot, We are witnessing the true exploitation of the interest expressed by the scientific community for the fractals objects. The aim of this paper is to introduce the fractal theory by the calculation of the fractal dimension in the radiographic images. We implement for that, the box counting method for the segmen...

In this paper, we have developed a method to compute fractal dimension (FD) of discrete time signals, in the time domain, by modifying the box-counting method. The size of the box is dependent on the sampling frequency of the signal. The number of boxes required to completely cover the signal are obtained at multiple time resolutions. The time resolutions are made coarse by decimating the signa...

Most of the existing box-counting methods for measuring fractal features are only applicable to square images or images with each dimension equal to the power of 2 and require that the box at the top of the box stack of each image block is of the same height as that of other boxes in the same stack, which gives rise to inaccurate estimation of fractal dimension. In this paper, we propose a more...

Box-counting dimension is one of the most widely used fractal dimensions, because it is relatively easy for empirical estimation. Unfortunately, the task is simple only if one operates on oneor twodimensional data. Otherwise, the amount of computation grows exponentially with the number of space coordinates.A newmethod of estimation of the box-counting dimension of multivariate objects using sp...

A new method for calculating fractal dimension is developed in this paper. The method is based on the box dimension concept; however, it involves direct estimation of a suboptimal covering of the data set of interest. By finding a suboptimal cover, this method is better able to estimate the required number of covering elements for a given cover size than is the standard box counting algorithm. ...

In this paper, the dynamical behavior of different optimal iterative schemes for solving nonlinear equations with increasing order, is studied. The tendency of the complexity of the Julia set is analyzed and referred to the fractal dimension. In fact, this fractal dimension can be shown to be a powerful tool to compare iterative schemes that estimate the solution of a nonlinear equation. Based ...

background: amiodarone is a drug that is used for treatment of cardiac arrhythmia after cardiac ischemia. this drug as b blocker decreases arrhythmia rate but it has many side effects on different tissues. since there are rare reports about changes of lacrimal glands, this research has been carried out to study the morphological and ultrastructural changes of lacrimal gland cells after amiodaro...

It has been observed many times, both in the Monthly and elsewhere, that the set of all quotients of prime numbers is dense in the positive real numbers. In this short note we answer the related question: “Is the set of all quotients of Gaussian primes dense in the complex plane?” Quotient sets {s/t : s, t ∈ S} corresponding to subsets S of the natural numbers have been intensely studied in the...