Related papers: Cut-out sets, fractal voids and cosmic structure
The boundaries of central place models proved to be fractal lines, which compose fractal texture of central place networks. A textural fractal can be employed to explain the scale-free property of regional boundaries such as border lines,…
A random sequential box-covering algorithm recently introduced to measure the fractal dimension in scale-free networks is investigated. The algorithm contains Monte Carlo sequential steps of choosing the position of the center of each box,…
We present results from a detailed numerical study of the small-scale and loop production properties of cosmic string networks, based on the largest and highest resolution string simulations to date. We investigate the non-trivial fractal…
This paper seeks to build on the extensive connections that have arisen between automata theory, combinatorics on words, fractal geometry, and model theory. Results in this paper establish a characterization for the behavior of the fractal…
The fractal dimension $D$ is used to map the large-scale galaxy distribution in the Universe by color types: blue, green and red. Using a $NUVrK$-complete COSMOS2020 subsample of 618,952 galaxies observed up to $z=4$, number densities were…
The thesis deals with recognizing diffeomorphisms from fractal properties of discrete orbits, generated by iterations of such diffeomorphisms. The notion of fractal properties of a set refers to the box dimension, the Minkowski content and…
These are the lecture notes for a course at the Summer School on "Applied Analysis" at the Technical University Chemnitz in September 2011. We start with the definition of a fractal algebra and show that the fractal property is enormously…
A way to add an extra dimension is briefly discussed.
We show a relation between fractional calculus and fractals, based only on physical and geometrical considerations. The link has been found in the physical origins of the power-laws, ruling the evolution of many natural phenomena, whose…
We derive a sharp scaling law for deviations of edge-isoperimetric sets in the lattice $\mathbb Z^d$ from the limiting Wulff shape in arbitrary dimensions. As the number $n$ of elements diverges, we prove that the symmetric difference to…
Using cosmological dressing rules, we uplift flat-space unitarity cuts to discontinuity relations for dS/EAdS observables. In this representation, Cutkosky delta functions map directly to "Disc" operations in the exchanged energy variable.…
Necessary and sufficient conditions allowing a previously unknown space to be explored through scanning operators are reexamined with respect to measure theory. Generalized conceptions of distances and dimensionality evaluation are…
The fractal properties of four-dimensional Euclidean simplicial manifold generated by the dynamical triangulation are analyzed on the geodesic distance D between two vertices instead of the usual scale between two simplices. In order to…
We consider the fragmentation process with mass loss and discuss self-similar properties of the arising structure both in time and space focusing on dimensional analysis. This exhibits a spectrum of mass exponents $\theta$, whose exact…
Recently, we pointed out that on a class on non exactly decimable fractals two different parameters are required to describe diffusive and vibrational dynamics. This phenomenon we call dynamical dimension splitting is related to the lack of…
The interstellar medium seems to have an underlying fractal structure which can be characterized through its fractal dimension. However, interstellar clouds are observed as projected two-dimensional images, and the projection of a…
In fractal geometry, the main objects of study have been geometric objects with a global dimension that need not be integer valued. More recently, locally fractal objects, ones in which the dimension is a local property rather than a global…
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and…
Atomization stretches and folds the liquid-gas interface before fragmenting it into ligaments and droplets, making fractal measures a natural descriptor of the breakup state. We examine this idea in two-dimensional volume-of-fluid direct…
We study the kinetics of random sequential adsorption of a mixture of particles with continuous distribution of sizes for different deposition rules. It appears in the long time limit the resulting system can be described using the fractal…