The fluctuations of the cardiac interbeat series contain rich information because they reflect variations of other functions on different time scales (e.g., respiration or blood pressure control). Nonlinear measures such as complexity and fractal scaling properties derived from 24 h heart rate dynamics of healthy subjects vary from childhood to old age. In this study, the age-related variations...

Using fractal in studying tribology is becoming more important. Although digitizing and processing the surface topography image of a friction surface and wear particle are the means for calculating of the respective fractal dimensions, they are extremely troublesome. To establish a method for calculating and analyzing the fractal phenomena of a surface, the use of computer software and hardware...

We study the scaling properties of the clusters grown by the Wolff algorithm on seven different Sierpinski-type fractals of Hausdorff dimension 1 < df ≤ 3 in the framework of the Ising model. The mean absolute value of the surface energy of Wolff cluster follows a power law with respect to the lattice size. Moreover, we investigate the probability density distribution of the surface energy of W...

A number of new methods have been recently developed to quantify complex heart rate (HR) dynamics based on nonlinear and fractal analysis, but their value in risk stratification has not been evaluated. This study was designed to determine whether selected new dynamic analysis methods of HR variability predict mortality in patients with depressed left ventricular (LV) function after acute myocar...

There is growing evidence that fluctuations in brain activity may exhibit scale-free ("fractal") dynamics. Scale-free signals follow a spectral-power curve of the form P(f ) ∝ f(-β), where spectral power decreases in a power-law fashion with increasing frequency. In this study, we demonstrated that fractal scaling of BOLD fMRI signal is consistently suppressed for different sources of cognitive...

Our purpose is to describe some recent progress in applying fractal concepts to systems of relevance to biology and medicine. We review several biological systems characterized by fractal geometry, with a particular focus on the long-range power-law correlations found recently in DNA sequences containing noncoding material. Furthermore, we discuss the finding that the exponent alpha quantifying...

Hack’s law is reviewed, emphasizing its implications for the elongation of river basins as well as its connections with their fractal characteristics. The relation between Hack’s law and the internal structure of river basins is investigated experimentally through digital elevation models. It is found that Hack’s exponent, elongation, and some relevant fractal characters are closely related. Th...

Electrocortical group neuron activity describe changes in neurotransmision cause by different factors. Such changes could by qualitative described by spectral analysis of electrocortical activity as a variation of relative spectral power in different frequency ranges. We used fractal dimension to compare treated animals with control to quantitativily describe degree of pathophysiological state....

We investigate numerically the power-law random matrix ensembles. Wave functions are fractal up to a characteristic length whose logarithm diverges asymmetrically with different exponents, 1 in the localized phase and 0.5 in the extended phase. The characteristic length is so anomalously large that for macroscopic samples there exists a finite critical region, in which this length is larger tha...