Related papers: Fractal dimension in star formation regions
The distribution of visible matter in the universe, such as galaxies and galaxy clusters, has its origin in the week fluctuations of density that existed at the epoch of recombination. The hierarchical distribution of the universe, with its…
The properties of spatial distribution of luminous matter are investigated analysing all the available three dimensional catalogues of galaxies. In standard view, galaxies are believed to have a fractal distribution at small scale with a…
There are many research available on the study of real-valued fractal interpolation function and fractal dimension of its graph. In this paper, our main focus is to study the dimensional results for vector-valued fractal interpolation…
We present newly obtained three-dimensional gaseous maps of the Milky Way Galaxy; HI, H$_2$ and total-gas (HI plus H$_2$) maps, which were derived from the HI and $^{12}$CO($J=1$--0) survey data and rotation curves based on the kinematic…
The local structure of a fractal set is described by its dimension $D$, which is the exponent of a power-law relating the mass ${\cal N}$ in a ball to its radius $\epsilon$: ${\cal N}\sim \epsilon^D$. It is desirable to characterise the…
In this study, we present a method to measure changes over time of fractal dimension. We confirmed that our method can calculate the fractal dimension with the same precision as conventional methods, and tracking performance of our method…
The small-angle scattering curves of deterministic mass fractals are studied and analyzed in the momentum space. In the fractal region, the curve I(q)q^D is found to be log-periodic with a good accuracy, and the period is equal to the…
Our goal is to identify bipolar HII regions and to understand their morphology, their evolution, and the role they play in the formation of new generations of stars. We use the Spitzer and Herschel Hi-GAL surveys to identify bipolar HII…
While the numerical methods which utilizes partitions of equal-size, including the box-counting method, remain the most popular choice for computing the generalized dimension of multifractal sets, two mass- oriented methods are investigated…
Irregular boundary lines can be characterized by fractal dimension, which provides important information for spatial analysis of complex geographical phenomena such as cities. However, it is difficult to calculate fractal dimension of…
To any spectral triple (A,D,H) a dimension d is associated, in analogy with the Hausdorff dimension for metric spaces. Indeed d is the unique number, if any, such that |D|^-d has non trivial logarithmic Dixmier trace. Moreover, when d is…
We show that when the standard techniques for calculating fractal dimensions in empirical data (such as the box counting) are applied on uniformly random structures, apparent fractal behavior is observed in a range between physically…
The image fractal analysis is actively used in all science branches. In particular in materials science the fractal analysis is applied to study microstructure of deformed metals because its structure can be interpreted as the fractal…
Due to the fractal nature of retinal blood vessels, the retinal fractal dimension is a natural parameter for researchers to explore and has garnered interest as a potential diagnostic tool. This review aims to summarize the current…
When suitably rescaled, the distribution of the angular gaps between branches of off-lattice radial DLA is shown to approach a size-independent limit. The power-law expected from an asymptotic fractal dimension D=1.71 arises only for very…
Fractals represent one of the fundamental manifestations of complexity, and fractal networks serve as tools for characterizing and investigating the fractal structures and properties of large-scale systems. Higher-order networks have…
A fractal bears a complex structure that is reflected in a scaling hierarchy, indicating that there are far more small things than large ones. This scaling hierarchy can be effectively derived using head/tail breaks - a clustering and…
The presence of radial truncations in stellar disks is reviewed. There is ample evidence that many disk galaxies have relatively shaprt truncations in their disks. These often are symmetric and independent of the wavelength band of the…
We discuss the definition and measurability questions of random fractals and find under certain conditions a formula for upper and lower Minkowski dimensions. For the case of a random self-similar set we obtain the packing dimension.
Exact Tolman solutions are used to analyse the implications if the galactic number has a fractal form out to a distance of about 150 Mpc in a universe which is homogeneous on the large scale. It is concluded that such a model requires…