The fact that galaxy distribution exhibits fractal properties is well established since twenty years. Nowadays, the controversy concerns the range of the fractal regime, the value of the fractal dimension and the eventual presence of a cross-over to homogeneity. Fractal properties maybe studied with methods which do not assume homogeneity a priori as the standard statistical methods do. We show...

The colorimetric organization of RGB color images is investigated through the computation of the correlation integral of their three-dimensional histogram. For natural color images, as a common behavior, the correlation integral is found to follow a power law, with a noninteger exponent characteristic of a given image. This behavior identifies a fractal or multiscale self-similar distribution o...

Fractals are natural phenomena that exhibit a repeating pattern "exactly the same at every scale or nearly the same at different scales". Defect-free molecular fractals were assembled successfully in a recent work [Shang et al., Nature Chem., 2015, 7, 389-393]. Here, we adopted the feature of a repeating pattern in searching two-dimensional (2D) materials with intrinsic half-metallicity and hig...

in this work, sio2 –zro2 mixed oxides was prepared by the polymeric sol–gel route. the characterization of pore structure, which determines the permeation process of membrane, is of great importance. so far, most investigations have focused on such pore structure as specific surface area and pore size distribution, but the surface fractal, the important parameter reflecting the roughness of por...

In this letter, the possible dynamic scaling properties of protein molecules in folding are investigated theoretically by assuming that the protein molecules are percolated networks. It is shown that the fractal character and the fractal dimensionality may exist only for short sequences in large protein molecules and small protein molecules with homogeneous structure, the fractal dimensionality...

It is well known that some XML elements correspond to objects (in the sense of object-orientation) and others do not. The question we consider in this paper is what benefits we can derive from paying attention to such object semantics, particularly for the problem of keyword queries. Keyword queries against XML data have been studied extensively in recent years, with several lowest-common-ances...

This work introduces a novel tool for interactive, real-time affine transformations of two dimensional IFS fractals. The tool uses some of the nice properties of the barycentric coordinates that are assigned to the points that constitute the image of a fractal, and thus enables any affine transformation of the affine basis, done by click-and-drag, to be immediately followed by the same affine t...

Kolmogorov introduced a concept of ε-entropy to analyze information in classical continuous system. The fractal dimension of geometrical sets was introduced by Mandelbrot as a new criterion to analyze the complexity of these sets. The ε-entropy and the fractal dimension of a state in general quantum system were introduced by one of the present authors in order to characterize chaotic properties...