In addition to the striking beauty inherent in their complex nature, fractals have become a
fundamental ingredient of nonlinear dynamics and chaos theory since they were defined in …

The cosmic web structure is studied with the concepts and methods of fractal geometry,
employing the adhesion model of cosmological dynamics as a basic reference. The …

Galaxy structures form a complex irregular pattern, characterized by clusters of galaxies
which are organized in filaments around large voids. Recently the Sloan Digital Sky Survey …

After reviewing the basic relevant properties of stationary stochastic processes (SSP),
defining basic terms and quantities, we discuss the properties of the so-called Harrison …

The most fundamental premise to the standard model of the universe states that the large-
scale properties of the universe are the same in all directions and at all comoving positions …

Methods for the statistical characterization of the large-scale structure in the Universe will be
the main topic of the present text. The focus is on geometrical methods, mainly Minkowski …

In geostatistical applications, the terms correlation length and range are often used
interchangeably and refer to a characteristic covariance length ξ that normalizes the lag …

Aims. Our goal is to determine how the spatial correlation function of galaxies describes
biasing and fractal properties of the cosmic web. Methods. We calculated spatial correlation …

The fractal dimension of large scale galaxy clustering has been reported to be roughly DF∼
2 from a wide range of redshift surveys. If correct, this statistic is of interest for two main …

The study of galaxies and superclusters is a major field of interest of astrophysicists. With the
development of modern advanced telescopes and data acquisition systems, scientists could …