Most of the known methods for estimating the fractal dimension of fractal sets are based on the evaluation of a single geometric characteristic, e.g. the volume of its parallel sets. We propose a method involving the evaluation of several geometric characteristics, namely all the intrinsic volumes (i.e. volume, surface area, Euler characteristic etc.) of the parallel sets of a fractal. Motivate...

spatial analysis of aeolian landforms by fractal theory (case study: ardestan rig) abstract natural sciences face to a great revolution, nowadays. now, scientists think the world as a collection of complex systems which prediction of consequences of this complex systems is so difficult. in this situation the systems have rotational act so irregularly lead to regular and regularly lead to irregu...

Using sum-frequency vibrational spectroscopy, we found that water structure at nanoporous silica/water interfaces depended on the nanoporous film structure. For a periodic, self-assembled nanoporous film with monosized 2 nm pores occupying 20% of the top surface area, the surface vibrational spectrum was dominated by water in contact with silica, bare or covered by silane, at the top surface. I...

The dark silicon problem, which limits the power-growth of future computer generations, is interpreted as a heat energy transport problem when increasing the energy emitting surface area within a given volume. A comparison of two 3D-configuration models, namely a standard slicing and a fractal surface generation within the Menger sponge geometry is presented. It is shown, that for iteration ord...

Modern life style of women has made them more vulnerable to breast cancer and it is considered as the largest cause of mortality among women. This paper presents a novel method to classify mammograms into normal ones, with benign and malignant microcalcifications, and with malignant and benign tumors using fractal features derived from fractal dimension. Here, three fractal dimension estimation...

In this chapter, the main principles of the theory of fractals and multifractals are stated. A singularity spectrum is introduced for the random telecommunication traffic, concepts of fractal dimensions and scaling functions, and methods used in their determination by means of Wavelet Transform Modulus Maxima (WTMM) are proposed. Algorithm development methods for estimating multifractal spectru...

I introduce a simple continuous probability theory based on the Ginzburg-Landau equation that provides for the first time a common analytical basis to relate and describe the main features of two seemingly different phenomena of condensed-matter physics, namely self-organized criticality and multifractality. Numerical support is given by a comparison with reported simulation data. Within the th...

This poster is a review of the paper “Fractal-based analysis of optical coherence tomography data to quantify retinal tissue damage” by Somfai et al. (2014). The abstract is as follows: “The sensitivity of Optical Coherence Tomography (OCT) images to identify retinal tissue morphology characterized by early neural loss from normal healthy eyes is tested by calculating structural information and...