Popcorn fractals are instances of Integrated Fractal Systems involving trigonometric functions. In this paper, we study the effect of spherical, swirl and pseudo-horseshoe functions on popcorn fractals to produce talismanic and tantric designs. General Terms Fractal, Algorithm, Turbo C++, Program.

Connections between the analysis on fractals and the iteration of rational functions were discovered in the earliest publications on diffusion processes on certain self-similar sets, such as the Sierpiński gasket (see, for instance [3, 38]). The connection stems from the fact that time on the successive approximations of the fractal is modelled by a branching process. The relation of branching ...

It is known that the heterogeneity of scale-free networks helps enhancing the efficiency of trapping processes performed on them. In this paper, we show that transport efficiency is much lower in a fractal scale-free network than in non-fractal networks. To this end, we examine a simple random walk with a fixed trap at a given position on a fractal scale-free network. We calculate analytically ...

The behavioral responses of zebrafish (Danio rerio) to sublethal concentrations of sodium hypochlorite (NaClO)-based household bleach were quantified in order to index toxicity of the solution. The swimming behavior of zebrafish was captured using nonplanar 3D stereocameras in combination with 3D coordinate computation with perspective correction (3DCCPC) to compute for actual 3D coordinates. S...

1 I n t r o d u c t i o n The aim of geometric modeling is to model forms by manipulating or combining well-known shapes such as circles and boxes. In order to be convenient such a model should allow easy control and manipulation of the final shape. When dealing with fractal geometric modeling, the control on ffactal figures is not so easily achieved as with classical smooth ones. The difficult...

A new class of subgrid closures for large eddy simulation (LES) of turbulence is developed, based on the construction of synthetic, fractal subgrid-scale fields. The relevant mathematical tool, fractal interpolation, allows to interpolate the resolved velocity with fields that have fluctuations down to much smaller scales and to compute the required stresses explicitly. In one dimension, the ap...

Pulsed field gradient NMR self-diffusion studies of water were used to determine surface-to-volume ratios and specific surface areas of the grains forming a glacial sand deposit. Both quantities exhibit a noninteger power-law dependence as a function of the diameters of the grains. The associated fractal dimensions of the surface area ( D(s)) and of the pore volume ( D(v)) are found to be D(s)-...

Intensity variations in image texture can provide powerful quantitative information about physical properties of biological tissue. However, tissue patterns can vary according to the utilized imaging system and are intrinsically correlated to the scale of analysis. In the case of ultrasound, the Nakagami distribution is a general model of the ultrasonic backscattering envelope under various sca...