Related papers: Fractal dimension in star formation regions
The distribution of metals in the Galaxy provides important information about galaxy formation and evolution. HII regions are the most luminous objects in the Milky Way at mid-infrared to radio wavelengths and can be seen across the entire…
Clouds in observations are fractals: they show self-similarity across scales ranging from one to 1000 km. This includes individual storms and large-scale cloud structures typical of organised convection. It is not known whether global…
The spiral structure of the Milky Way is not conclusive, even for the disc regions in the solar neighbourhood. Especially, the arm-like structures uncovered from the over-density maps of evolved stars are inconsistent with the commonly…
Context. Gas within a galaxy is forced to establish pressure balance against gravitational forces. The shape of an unperturbed gaseous disk can be used to constrain dark matter models. Aims. We derive the 3-D HI volume density distribution…
We provide a rigorous study on dimensions of fractal interpolation function defined on a closed and bounded interval of $\mathbb{R}$ which is associated to a continuous function with respect to a base function, scaling functions and a…
An alternate definition of the box-counting dimension is proposed, to provide a better approximation for fractals involving rotation such as the 'Bradley Spiral' structure. A curve fitting comparison of this definition with the box-counting…
Fractal plays an important role in nonlinear science. The most important parameter to model fractal is fractal dimension. Existing information dimension can calculate the dimension of probability distribution. However, given a mass function…
The analysis of the distribution of stars in open clusters may yield important information on the star formation process and early dynamical evolution of stellar clusters. Here we address this issue by systematically characterizing the…
This work is an analytical and numerical study of the composition of several fractals into one and of the relation between the composite dimension and the dimensions of the component fractals. In the case of composition of standard IFS with…
This work tests if the large-scale galaxy distribution can be characterized as a fractal system. The $\Lambda$CDM cosmology with $H_0=(70\pm 5)$ km/s/Mpc is adopted to study the UltraVISTA DR1, COSMOS2015 and SPLASH surveys, alongside the…
Fractal exponents ($d$) for human cranial sutures are calculated using the box counting method. The results were found around $d = 1.5$ (within the range $1.3\div 1.7$), supporting the random walk model for the suture formation process.…
We study algorithmic problems on subsets of Euclidean space of low fractal dimension. These spaces are the subject of intensive study in various branches of mathematics, including geometry, topology, and measure theory. There are several…
Aims: We derive the 3-D HI volume density distribution for the Galactic disk out to R = 60 kpc. Methods: Our analysis is based on parameters for the warp and rotation curve derived previously. The data are taken from the…
An algorithm for calculating generalized fractal dimension of a time series using the general information function is presented. The algorithm is based on a strings sort technique and requires $O(N \log_2 N)$ computations. A rough estimate…
This paper studies the effect of the distance choice in radial (non-average) statistical tools used for fractal characterization of galaxy distribution. After reviewing the basics of measuring distances of cosmological sources, various…
We explore the fractal nature of particle showers using Monte-Carlo simulation. We define the fractal dimension of showers measured in a high granularity calorimeter designed for a future lepton collider. The shower fractal dimension…
Two fundamental empirical laws have been established in the analysis of galaxy space distribution. First, recent analyses have revealed that the three dimensional distribution of galaxies and clusters is characterized by large scale…
The fact that galaxy distribution exhibits fractal properties is well established since twenty years. Nowadays, the controversy concerns the range of the fractal regime, the value of the fractal dimension and the eventual presence of a…
Fractal geometry proved to be an effective mathematical tool for exploring real geographical space based on digital maps and remote sensing images. Whether the fractal theory tool can be applied to abstract geographical space has not been…
Multiple resolution analysis of two dimensional structures composed of randomly adsorbed penetrable rods, for densities below the percolation threshold, has been carried out using box-counting functions. It is found that at relevant…