The incipient infinite cluster appearing at the bond percolation threshold can be decomposed into singly connected "links" and multiply connected "blobs." Here we decompose blobs into objects known in graph theory as 3-blocks. A 3-block is a graph that cannot be separated into disconnected subgraphs by cutting the graph at two or fewer vertices. Clusters, blobs, and 3-blocks are special cases o...

In order to understand characteristics common to distributions which have both fractal and non-fractal scale regions in a unified framework, we introduce a concept of typical scale. We employ a model of 2d gravity modified by the R term as a tool to understand such distributions through the typical scale. This model is obtained by adding an interaction term with a typical scale to a scale invar...

The concept of fractal geometry is useful for the analysis of irregular and complex structures often seen in nature. Here we apply this concept to investigate the structural mechanism of the development of pulmonary emphysema in the klotho mouse, which, after milk feeding, exhibits characteristics resembling aging and develops emphysema. We calculated the relationships between perimeter and siz...

Keywords: Fractal structure Fractal dimension Box-counting dimension Domain of words Language Regular expression Binary-coded decimal Search tree a b s t r a c t A fractal structure is a tool that is used to study the fractal behavior of a space. In this paper, we show how to apply a new concept of fractal dimension for fractal structures, extending the use of the box-counting dimension to new ...

In the previous article (Grujić 2001, to be referred to as I) we examined Anaxagoras’ worldview and compared his hierarchical cosmos with that of Democritus. We analyzed a number of possible interpretations of his cosmology and argued that his ideas could be put in terms of the modern concept of fractal structuring of the material objects. The idea of hierarchical structuring of the material wo...

Curvature measures are an important tool in geometric measure theory and other fields of mathematics for describing the geometry of sets in Euclidean space. But the ‘classical’ concepts of curvature are not directly applicable to fractal sets. We try to bridge this gap between geometric measure theory and fractal geometry by introducing a notion of curvature for fractals. For compact sets F ⊆ R...

In this paper, the notion of dimension preserving approximation for real-valued bivariate continuous functions, defined on a rectangular domain , has been introduced and several results, similar to well-known results constrained in terms approximants, have established. Further, some clue construction using concept fractal interpolation added. last part, multi-valued operators associated with $$...

introduction: soil hydraulic conductivity is considered as one of the most important hydraulic properties in water and solutionmovement in porous media. in recent years, variousmodels as pedo-transfer functions, fractal models and scaling technique are used to estimate the soil saturated hydraulic conductivity (ks). fractal models with two subset of two (solid and pore) and three phases (solid,...

The kinetics of the pressure induced hydration of modellipid membranes is studied in terms ofthe Avrami-Kolmogorov model and the fractal-like chemical reaction kinetics concept. As a general result, the stretched exponential relaxation function of the

In our recent papers we applied fractal methods to extract the earthquake precursory signatures from scaling characteristics of the ULF geomagnetic data, obtained in a seismic active region of Guam Island during the large earthquake of 8 August 1993. We found specific dynamics of their fractal characteristics (spectral exponents and fractal dimensions) before the earthquake: appearance of the f...