We propose four fractal point processes (FPPs) as novel approaches to modeling and analyzing various types of self-similar traac: the fractal renewal process (FRP), the superposition of several fractal renewal processes (Sup-FRP), the fractal-shot-noise-driven Poisson process (FSNDP), and the fractal-binomial-noise-driven Poisson process (FBNDP). These models fall into two classes depending on ...

We investigate the influence of fractal structure on material properties. We calculate the statistical correlation functions of fractal media defined by level-cut Gaussian random fields. This allows the modeling of both surface fractal and mass fractal materials. Variational bounds on the conductivity, diffusivity and elastic moduli of the materials are evaluated. We find that a fractally rough...

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 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...

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 objective of this research is to model the mammographic parenchymal, ductal patterns and enhance microcalcifications using a fractal approach. According to the theory of deterministic fractal geometry, images can be modeled by deterministic fractal objects which are attractors of sets of two dimensional afflne transformations. In this paper, a methodology based on fractal image modeling is ...

The paper focuses on the use of the fractal paradigm in enterprise modeling. It investigates whether the properties of fractal organizations can be applied in business analysis and whether this results in useful outcomes and new insights. Based on an adaptation and operationalization of properties of fractal organizations, two real-world cases are analyzed using the adapted properties. The cont...

The problem of fractal modeling is very simple when we know the mathematical description of a fractal. We just apply one of the well-known algorithms. The inverse problem of finding the mathematical description for given fractal is not so trivial and we do not know any general method to solve this problem. So there are several approaches to this problem e.g. via Bézier curves, fractal compressi...

The objective of this research is to model the mammographic parenchymal, ductal patterns and enhance the microcalciications using deterministic fractal approach. According to the theory of deterministic fractal geometry, images can be modeled by deterministic fractal objects which are attractors of sets of two dimensional aane transformations. The Iterated Functions Systems and the Collage Theo...