Many fractal curves can be produced as the limit of a sequence of polygonal curves, where the curves are generated via an iterative process, for example an L-system. One can visualise such a sequences of curves as an animation that steps through the sequence. A small part of the curve at one step of the iteration is close to a corresponding part of the curve at the previous step, and so it is n...

In this paper an innovative model that describes the SAR imaging process of natural scenes is presented. It is completely fractal-based. In the hypothesis of small slope regime of the surface, we evaluate here, in closed form, the Power Spectrum Density of the SAR image. The proposed model effectively accounts for the effect of finite sensor resolutions and for the peculiarity of SAR acquisitio...

In this paper an innovative, completely fractal-based model describing the SAR imaging process of natural scenes is presented. In the hypothesis that a small slope regime can be assumed for the surface, we evaluate here, in closed form, the Power Spectral Densities of the SAR image. The proposed model effectively accounts for the effect of finite sensor resolutions and for the peculiarity of SA...

BACKGROUND AND AIMS Fractal analysis allows calculation of fractal dimension, fractal abundance and lacunarity. Fractal analysis of plant roots has revealed correlations of fractal dimension with age, topology or genotypic variation, while fractal abundance has been associated with root length. Lacunarity is associated with heterogeneity of distribution, and has yet to be utilized in analysis o...

The fractal features including fractal dimension (FD) and lacunarity measures are often used as indicators of texture. Several FD and lacunarity estimation methods leading to different results have been proposed in the literature. This paper is devoted mainly to show the need to combine the lacunarity with fractal dimension for the discrimination between different textures and especially to che...

Fractal geometry provides a powerful tool for scale-free spatial analysis of cities, but the fractal dimension calculation results always depend on methods and scopes of study area. This phenomenon has been puzzling many researchers. This paper is devoted to discussing the problem of uncertainty of fractal dimension estimation and the potential solutions to it. Using regular fractals as archety...

Digital photography is a promised method for estimating the fractal characteristics of leaf veins. In this study, the effects of different threshold levels and image processing methods using Adobe Photoshop software on the fractal dimension values were examined from a digital photo of nectarine leaf. The results showed that the nectarine leaf vein has typical fractal characteristics and its fra...

A contact problem is considered in which an elastic half-plane is pressed against a rigid fractally rough surface, whose pro­ le is de­ ned by a Weierstrass series. It is shown that no applied mean pressure is su ̄ ciently large to ensure full contact and indeed there are not even any contact areas of ­ nite dimension|the contact area consists of a set of fractal character for all values of the ...

Fractal behavior is scale-invariant and widely characterized by fractal dimension. However, the cor-respondence between them is that fractal behavior uniquely determines a fractal dimension while a fractal dimension can be related to many possible fractal behaviors. Therefore, fractal behavior is independent of the fractal generator and its geometries, spatial pattern, and statistical propertie...

Protein surface roughness is a structural property associated with ligand-protein and protein-protein binding interfaces. In this work we apply for the first time the concept of surface roughness, expressed as the fractal dimension, to address structure and function of G protein-coupled receptors (GPCRs) which are an important group of drug targets. We calculate the exposure ratio and the fract...