We find that the fractal scaling in a class of scale-free networks originates from the underlying tree structure called a skeleton, a special type of spanning tree based on the edge betweenness centrality. The fractal skeleton has the property of the critical branching tree. The original fractal networks are viewed as a fractal skeleton dressed with local shortcuts. An in silico model with both...

Fractal antennas have been shown to demonstrate repetitive multi-band or logperiodic behavior that has been attributed to the self-similar scale factor of the antenna’s geometry. This geometry, which has been used to model complex objects found in nature such as clouds and coastlines, has space filling properties that can be utilized to miniaturize antennas. These unique properties of fractals ...

Basic properties of 2D-nonlinear scale-space representations of images are considered. First, local-energy filters are used to estimate the Hausdorff dimension, , of images. A new fractal dimension, , defined as a property of 2D-curvature representations on multiple scales, is introduced as a natural extension of traditional fractal dimensions, and it is shown that the two types of fractal dime...

In this paper, we study the fractal characteristics of the futures market. We take the empirical study on London Gold Futures yield by Rescaled Range Analysis, analyzing the fractal characteristics of the futures market. We further determine fractal characteristics and the structure of the nonlinear time series through random disturb the original time series observation sequence. The result of ...

We describe two dimensional DNA walks, and analyze their fractal properties. We show results for the complete genome of S. cerevisiae. We find that the mean square deviation of the walks is superdifussive, corresponding to a fractal structure of dimension lower than two. Furthermore, the coding part of the genome seems to have smaller fractal dimension, and longer correlations, than noncoding p...

We have evaluated nine different methods for estimating the fractal dimension of intensity images based on their accuracy, spread and robustness to noise. For this purpose we have generated some 6000 digital images with varying size and known fractal properties. To observe the influence of noise we have distorted these images with Poisson noise, Gaussian noise of different strength and point sp...

The fractal and the small-world properties of complex networks are systematically studied both in the box-covering (BC) and the cluster-growing (CG) measurements. We elucidate that complex networks possessing the fractal (small-world) nature in the BC measurement are always fractal (small world) even in the CG measurement and vice versa, while the fractal dimensions d{B} by the BC measurement a...

The entropies of Shannon, Rényi and Kolmogorov are analyzed and compared together with their main properties. The entropy of some particular antennas with a pre-fractal shape, also called fractal antennas, is studied. In particular, their entropy is linked with the fractal geometrical shape and the physical performance.

– In this paper we show that the Internet web, from a user’s perspective, manifests robust scaling properties of the type P (n) ∝ n−τ , where n is the size of the basin connected to a given point, P represents the density of probability of finding n points downhill and τ = 1.9 ± 0.1 s a characteristic universal exponent. This scale-free structure is a result of the spontaneous growth of the web...