The BFW model introduced by Bohman, Frieze, and Wormald [Random Struct. Algorithms, 25, 432 (2004)], and recently investigated in the framework of discontinuous percolation by Chen and D'Souza [Phys. Rev. Lett. 106, 115701 (2011)], is studied on the square and simple-cubic lattices. In two and three dimensions, we find numerical evidence for a strongly discontinuous transition. In two dimension...

  Background & Objectives: Cancer is a serious problem for human being and is becoming a serious problem day-by-day .A prerequisite for any therapeutic modality is early diagnosis. Automated cancer diagnosis by automatic image feature extraction procedures can be used as a feature extraction in the field of fractal dimension. The aim of this survey was to introduce a quantitative and objective...

There are several methods for estimating the fractal dimension of a time series of data such as the box counting method and the correlation method [DeGrauwe, Dewachter and EmbrechtS, 1993] [peitgen and Saupe, 1988]. The application of these methods are often demanding in computing time and require expert interaction for interpreting the calculated fractal dimension. Artificial neural nets (ANN)...

This paper is concerned with the development of a computational methodology based on fractal geometry for determining 3D structure of protein with imagery projection operations. In this investigation, the density-map image is a 2D projection of the 3D electron density map according to its depth of the density distribution along the projection direction. We extract fractal features of the densit...

Three aspects of texture are considered by the fractal geometry: Fractal Dimension (FD), Lacunarity and Succolarity. Fractal Dimension has been well studied; a great number of approaches have been presented to extract it from images. It can be computed from black-white to multi-band image. There are many approaches also, from the simple Box-Dimension to the most complex Hausdorff Dimension. The...

In present paper the effect of noise on fractal dimension of digital images has been tested. Since fractal dimension is a measure of texture which is property of neighbourhood, it is interesting to check how noise affects the values of fractal dimension. For this purpose, three standard digital images have been used and Gaussian noise, salt and pepper noise and speckle noise have been applied t...

A novel printed octagonal fractal microstrip antenna with semi-elliptical ground plane is presented for ultra wide band applications. The proposed antenna has a compact size of 20×20×1 mm³. The measured result of the antenna exhibits the ultra wide band characteristics from 2/9 to 14/2 GHz. In this paper, reducing antenna’s size by 35%, the same results were achieved, while small dimension frac...

The presence of correlated randomness in EEG time series signal buried in random noise was analyzed with the Higuchi fractal algorithm. The signal recognition algorithm design was built on the fact that the theoretical fractal dimension value of 2 is an indicator for a white noise time series and correlated randomness would alter the fractal dimension value from 2. However, the limited number o...

The paper deals with an algorithm for Hausdorff dimension estimation based on box-counting dimension calculation. The main goal of the paper is to propose a new approach to box-counting dimension calculation with less computational demands. Streszczenie. W artykule opisano algorytm estymacji wymiaru Hausdorffa oparty o wyznaczanie wymiaru pudełkowego. Głównym celem pracy jest zaproponowanie now...

phenomena in two dimensions. I spent most of the academic years 2013-2015 in Bonn, Germany (at the Max-Planck Institut and then the Hausdorff Center). In general, the Hausdorff dimension of a product is at least the sum of the dimensions of the two spaces. Does equality hold if one space is Euclidian? So let be. I find this discussion in Wikipedia very good: Fractal dimension Imagine a particul...