In this paper we address two issues in modeling natural terrain using fractal geometry: estimation of fractal dimension, and fractal surface reconstruction. For estimation of fractal dimension, we extend the fractal Brownian function approach to accommodate irregularly sampled data, and we develop methods for segmenting sets of points exhibiting self-similarity over only certain scales. For fra...

The recently introduced self-organizing height-arrow (HA) model is numerically investigated on the square lattice and analytically on the Bethe lattice. The concentration of occupied sites and critical exponents of distributions of avalanches are evaluated for two slightly different versions of the model. The obtained exponents for distributions of avalanches by mass, area, duration and appropr...

We start this article by rebuilding higher operads of weak higher transformations, and correct those in cite{Cambat}. As in cite{Cambat} we propose an operadic approach for weak higher $n$-transformations, for each $ninmathbb{N}$, where such weak higher $n$-transformations are seen as algebras for specific contractible higher operads. The last chapter of this article asserts that, up to precise...

The discovery of a fractal phenomenon in computer network and compressed packet video traac has added a new dimension to teletraac modeling and analysis. But some of the recent research eeort on the modeling and analysis of the fractal phenomena have generated results that are seemingly confusing or contradictory. The goal of this study is to correctly digest the recent contributions, examine t...

This paper applies a new traffic model, iterated function systems (IFS) for network traffic modelling, to explore computer network behaviour and analyse network performance. IFS model can generate various self-similar data flows according to a certain character. In the light of the experiments, we have discovered interesting phenomena. It is found that increasing the routers’ processing capacit...

introduction: water and soil retention curve is one of the most important properties of porous media to obtain in a laboratory retention curve and time associated with errors. for this reason, researchers have proposed techniques that help them to more easily acquired characteristic curve. one of these methods is the use of fractal geometry. determining the relationship between particle size di...

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 crossing number of Sierpiński graphs S(n, k) and their regularizations S(n, k) and S(n, k) is studied. Explicit drawings of these graphs are presented and proved to be optimal for S(n, k) and S(n, k) for every n ≥ 1 and k ≥ 1. These are the first nontrivial families of graphs of “fractal” type whose crossing number is known.

A number of recent papers have suggested that the series of time intervals produced in continuation tapping may have fractal properties. This proposition, nevertheless, was only based on the visual appraisal of graphical results, and was not statistically supported. In the present study, we applied the ARMA/ARFIMA modeling procedures proposed by Wagenmakers, Farrell, and Ratcliff (2005) to test...