Related papers: The fractal dimension of the Appalachian Trail
Even though many objects and phenomena of importance in geophysics have been shown to have fractal character, there are still many of them which show self-similar character and yet to be studied. The objective of the present work is to…
Fractal surfaces are ubiquitous in nature as well as in the sciences. The examples range from the cloud boundaries to the corroded surfaces. Fractal dimension gives a measure of the irregularity in the object under study. We present a…
We relate the fractal dimension of the backbone, and the spectral dimension of Eden trees to the dynamical exponent z. In two dimensions, it gives fractal dimension of backbone equal to 4/3 and spectral dimension of trees equal to 5/4. In…
Transport in complex systems is characterized by a fractal dimension -- the walk dimension -- that indicates the diffusive or anomalous nature of the underlying random walk process. Here we report on the experimental retrieval of this key…
A fractal can be simply understood as a set or pattern in which there are far more small things than large ones, e.g., far more small geographic features than large ones on the earth surface, or far more large-scale maps than small-scale…
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…
Using a sample of 133 991 galaxies distributed in the sky region $100^{\circ} <\alpha<270^{\circ}$ and $7^{\circ}<\delta<65^{\circ}$, extracted from the SDSS NASA/AMES Value Added Galaxy Catalog (AMES-VAGC), we estimate the fractal…
Investigating a model of scale-invariant random spatial network suggested by Aldous, Kendall constructed a random metric $T$ on $\mathbb{R}^d$, for which the distance between points is given by the optimal connection time, when travelling…
Several two-dimensional studies in spiral galaxies show that HII star formation regions have a fractal distribution, with a fractal dimension of approximately 2.3. In this work, the fractal dimension is calculated through the box-counting…
Little is known about the portion of the Milky Way lying beyond the Galactic center at distances of more than 9 kilo-parsec from the Sun. These regions are opaque at optical wavelengths due to absorption by interstellar dust, and distances…
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…
The geometric characteristics of dust clouds provide important information on the physical processes that structure such clouds. One of such characteristics is the $2D$ fractal dimension $D$ of a cloud projected onto the sky plane. In…
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…
We calculate the spectral dimension of a wide class of tree-like fractals by solving the random walk problem through a new analytical technique, based on invariance under generalized cutting-decimation transformations. These fractals are…
Motivated by recent claims of a proof that the length scale exponent for the end-to-end distance scaling of self-avoiding walks is precisely $7/12=0.5833...$, we present results of large-scale simulations of self-avoiding walks and…
Fractals are fascinating structures, not only for their aesthetic appeal, but also because they allow for the investigation of physical properties in non-integer dimensions. In these unconventional systems, a myriad of intrinsic features…
Accurately measuring street dimensions is essential to evaluating how their design influences both travel behavior and safety. However, gathering street-level information at city scale with precision is difficult given the quantity and…
We report on the numerical measures on different spin interfaces and FK cluster boundaries in the Askhin-Teller (AT) model. For a general point on the AT critical line, we find that the fractal dimension of a generic spin cluster interface…
We have measured the distance to the massive star-forming region W3OH in the Perseus spiral arm of the Milky Way to be 1.95 $\pm$ 0.04 kilo-parsecs ($5.86\times10^{16}$ km). This distance was determined by triangulation, with the Earth's…
The soft condensed matter of biological organisms exhibits atomic motions whose properties depend strongly on temperature and hydration conditions. Due to the superposition of rapidly fluctuating alternative motions at both very low…