Related papers: Fractal dimension analysis for automatic morpholog…
The fractal dimension provides a statistical index of object complexity by studying how the pattern changes with the measuring scale. Although useful in several classification tasks, the fractal dimension is under-explored in deep learning…
We suggest a new method for estimating the fractal dimension of the spatial distribution of galaxies, the method of selected cylinders. We show the capabilities of this method by constructing a two-point conditional column density for…
In this paper we study self-similar and fractal networks from the combinatorial perspective. We establish analogues of topological (Lebesgue) and fractal (Hausdorff) dimensions for graphs and demonstrate that they are naturally related to…
Several studies have investigated the fractal and multifractal nature of magnetic features in the solar photosphere and its variation with the solar magnetic activity cycle. Here we extend those studies by examining the fractal geometry of…
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…
Classifying the morphologies of galaxies is an important step in understanding their physical properties and evolutionary histories. The advent of large-scale surveys has hastened the need to develop techniques for automated morphological…
Homogeneity and isotropy of the universe at sufficiently large scales is a fundamental premise on which modern cosmology is based. Fractal dimensions of matter distribution is a parameter that can be used to test the hypothesis of…
The fractal or Hausdorff dimension is a measure of roughness (or smoothness) for time series and spatial data. The graph of a smooth, differentiable surface indexed in $\mathbb{R}^d$ has topological and fractal dimension $d$. If the surface…
The morphological classification of galaxies provides vital physical information about the orbital motions of stars in galaxies, and correlates in interesting ways with star formation history, and other physical properties. Galaxy…
In this work, decision tree learning algorithms and fuzzy inferencing systems are applied for galaxy morphology classification. In particular, the CART, the C4.5, the Random Forest and fuzzy logic algorithms are studied and reliable…
One of the most important properties of a galaxy is the total stellar mass, or equivalently the stellar mass-to-light ratio (M/L). It is not directly observable, but can be estimated from stellar population synthesis. Currently, a galaxy's…
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…
Perfect fractals are mathematical objects that, because they are generated by recursive processes, have self-similarity and infinite complexity. In particular, they also have a fractional dimension. Although several proposals for the study…
The morphology of a galaxy has been shown to encode the evolutionary history and correlates strongly with physical properties such as stellar mass, star formation rates and past merger events. While the majority of galaxies in the local…
Fractals are self-repeating patterns which have dimensions given by fractions rather than integers. While the dimension of a system unambiguously defines its properties, a fractional dimensional system can exhibit interesting properties.…
We describe application of the `shapelet' linear decomposition of galaxy images to morphological classification using images of $\sim$ 3000 galaxies from the Sloan Digital Sky Survey. After decomposing the galaxies we perform a principal…
We introduce fractional flat space, described by a continuous geometry with constant non-integer Hausdorff and spectral dimensions. This is the analogue of Euclidean space, but with anomalous scaling and diffusion properties. The basic tool…
We present an extended morphometric system to automatically classify galaxies from astronomical images. The new system includes the original and modified versions of the CASGM coefficients (Concentration $C_1$, Asymmetry $A_3$, and…
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…
Although geographic features, such as mountains and coastlines, are fractal, some studies have claimed that the fractal property is not universal. This claim, which is false, is mainly attributed to the strict definition of fractal…