Terrain morphology has been on the radar of Computer Graphics for more than twenty years and various techniques for its modeling have been presented. These approaches range from fractal and multifractal surface generation to physically-based models of erosion and weathering. From all the weathering phenomena that can be observed in Nature, the hydraulic erosion has the major visual importance. ...

This study makes the first attempt to use the 2/3-order fractional Laplacian modeling of enhanced diffusing movements of random turbulent particle resulting from nonlinear inertial interactions. A combined effect of the inertial interactions and the molecule Brownian diffusivities is found to be the bi-fractal mechanism behind multifractal scaling in the inertial range of scales of moderate Rey...

Wireless applications, protocols and simulators can significantly benefit from thorough understanding and accurate modeling of the medium access control (MAC) layer residual bit-errors at high bitrates. In this paper, we analyze and model the biterrors encountered at the highest achievable 11 Mbps data rate of an 802.11b wireless local area network. We employ autocorrelation, aggregation and va...

The multifractal dimension of chaotic attractors has been studied in a weakly coupled superlattice driven by an incommensurate sinusoidal voltage as a function of the driving voltage amplitude. The derived multifractal dimension for the observed bifurcation sequence shows different characteristics for chaotic, quasiperiodic, and frequency-locked attractors. In the chaotic regime, strange attrac...

During 2002, the Voyager 1 spacecraft was in the heliosphere between 83.4 and 85.9 AU (1 AU is the mean distance from the Sun to Earth) at 34 N heliographic latitude. The magnetic field strength profile observed in this region had a multifractal structure in the range of scales from 2 to 16 days. The multifractal spectrum observed near 85 AU is similar to that observed near 40 AU, indicating re...

One-dimensional detrended fluctuation analysis (DFA) and multifractal detrended fluctuation analysis (MFDFA) are widely used in the scaling analysis of fractal and multifractal time series because they are accurate and easy to implement. In this paper we generalize the one-dimensional DFA and MFDFA to higher-dimensional versions. The generalization works well when tested with synthetic surfaces...

We demonstrate analytically and numerically the possibility that the fractal property of a scale-free network cannot be characterized by a unique fractal dimension and the network takes a multifractal structure. It is found that the mass exponents τ(q) for several deterministic, stochastic, and real-world fractal scale-free networks are nonlinear functions of q, which implies that structural me...

We consider the self-similar phase space with reduced fractal dimension d being distributed within domain 0 < d < 1 with spectrum f(d). Related thermostatistics is shown to be governed by the Tsallis’ formalism of the non-extensive statistics, where role of the non-additivity parameter plays inverted value τ̄(q) ≡ 1/τ(q) > 1 of the multifractal function τ(q) = qd(q)− f(d(q)), being the specific ...

The properties of several multifractal formalisms based on wavelet coefficients are compared from both mathematical and numerical points of view. When it is based directly on wavelet coefficients, the multifractal formalism is shown to yield, at best, the increasing part of the weak scaling exponent spectrum. The formalism has to be based on new multiresolution quantities, the wavelet leaders, ...

Nonlinear phenomena in animal vocalizations fundamentally includes known features, namely, frequency jump, subharmonics, biphonation, and deterministic chaos. In the present study, the multifractal detrended fluctuation analysis (MFDFA) has been employed to characterize the phase couplings revealed in the feeding clicks of Hippocampus kuda yellow seahorse. The fluctuation function Fq(s), genera...