The colonic tissue is a complicated dynamic system and the colonic activities it generates are composed of irregular segmental waves, which are referred to as erratic fluctuations or spikes. They are also highly irregular with subunit fractal structure. The traditional time-frequency domain statistics like the averaged amplitude, the motility index and the power spectrum, etc. are insufficient ...

This paper introduces a method for modification of the formula of the fractal box counting dimension. The method is based on the utilization of the probability distribution formula in the fractal box count. The purpose of this method is to use it for the discrimination of oil spill areas from the surrounding features e.g., sea surface and look-alikes in RADARSAT-1 SAR data. The result shows tha...

The large-scale images and videos are one kind of the main source of big data. Dynamic texture (DT) is essential for understanding the video sequences with spatio-temporal similarities. This paper presents a powerful tool called dynamic fractal analysis to DT description and classification, which integrates rich description of DT with strong robustness to environmental changes. The proposed dyn...

-We have re-examined the inertial range behavior of a passive scalar which is advected by a large-scale velocity field causing a cascade of tracer variance to small scales, where it is dissipated by diffusion. This has been done within the context of an idealized model based on mixing by a 2D area-preserving map alternating with a weak diffusion step; the model is a special case of the general ...

We reply here to the comment by Maddux (2004, in this issue), which discusses a fractal probability rule (PR) for the spatial distribution of species proposed by Harte and Kinzig (1997) and Harte et al. (1999b) as a means of deriving the characteristics of species distributions that exhibit power law species-area relationships. In his comment, Maddux derives certain properties of spatial distri...

The Lévy stability analysis is carried out for ee collisions at Z mass using Monte Carlo method. The Lévy index μ is found to be μ = 1.701± 0.043. The self-similar generalized dimensions D(q) and multi-fractal spectrum f(α) are presented. The Rényi dimension D(q) decreases with increasing q. The self-similar multi-fractal spectrum is a convex curve with a maximum at q = 0, α = 1.169 ± 0.011. Th...

Frequency-magnitude statistics for natural hazards can greatly help in probabilistic hazard assessments. An example is the case of earthquakes, where the generality of a power-law (fractal) frequency-rupture area correlation is a major feature in seismic risk mapping. Other examples of this power-law frequency-size behaviour are landslides and wildfires. In previous studies, authors have made t...

Studies over the past decade have reported power-law distributions for the areas of terrestrial lakes and Arctic melt ponds, as well as fractal relationships between their areas and coastlines. Here we report similar fractal structure of ponds in a tidal flat, thereby extending the spatial and temporal scales on which such phenomena have been observed in geophysical systems. Images taken during...

The fractal distribution is the best statistical model for the size-frequency distributions that result from some lithic reduction processes. Fractals are a large class of complex, self-similar sets that can be described using power-law relations. Fractal statistical distributions are characterized by an exponent, D, called the fractal dimension. I show how to determine whether the size-frequen...