Related papers: Sphractal: Estimating the Fractal Dimension of Sur…
A novel algorithm is proposed for quantitative comparisons between compact surfaces embedded in the three-dimensional Euclidian space. The key idea is to identify those objects with the associated surface measures and compute a weak…
We describe the fractal solid by a special continuous medium model. We propose to describe the fractal solid by a fractional continuous model, where all characteristics and fields are defined everywhere in the volume but they follow some…
Macroporous silicon is widely employed in sensing and optoelectronic applications due to its large internal surface area and adjustable pore structure. However, quantitative correlations between morphology and functionality require…
This paper introduces the concept of Fractal Frenet equations, a set of differential equations used to describe the behavior of vectors along fractal curves. The study explores the analogue of arc length for fractal curves, providing a…
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 structural evolution of a nano-powder by repeated dispersion and settling can lead to characteristic fractal substructures. This is shown by numerical simulations of a two-dimensional model agglomerate of adhesive rigid particles. The…
The light scattering experiment establishes a relationship between refractive index fluctuations and fractal dimension in weakly scattering tissue-like media. Based on the box-counting approach, an analytical model is developed and shows…
Fourier decay of fractal measures on surfaces plays an important role in geometric measure theory and partial differential equations. In this paper, we study the quadratic surfaces of high co-dimensions. Unlike the case of co-dimension 1,…
This work proposes the application of fractal descriptors to the analysis of nanoscale materials under different experimental conditions. We obtain descriptors for images from the sample applying a multiscale transform to the calculation of…
Traditional laws of friction believe that the friction coefficient of two specific solids takes constant value. However, molecular simulations revealed that the friction coefficient of nanosized asperity depends strongly on contact size and…
We introduce fractal liquids by generalizing classical liquids of integer dimensions $d = 1, 2, 3$ to a fractal dimension $d_f$. The particles composing the liquid are fractal objects and their configuration space is also fractal, with the…
A simple method of calculating the Hausdorff-Besicovitch dimension of the Kronecker Product based fractals is presented together with a compact R script realizing it. The proposed new formula is based on traditionally used values of the…
We study numerically the fractal structure of the intrinsic geometry of random surfaces coupled to matter fields with $c=1$. Using baby universe surgery it was possible to simulate randomly triangulated surfaces made of 260.000 triangles.…
Digital analysis of mammographic images is a complementary tool to clinical evaluation, commonly used to identify tumors and/or microcalcifications in mammograms. Recent mammographic equipment, can automatically classify them using this…
X-ray diffraction with high spatial resolution is a prerequisite for the characterization of (poly)-crystalline materials on micro- or nanoscopic scales. This can be achieved by utilizing a focused X-ray beam and scanning of the sample.…
If our aesthetic preferences are affected by fractal geometry of nature, scaling regularities would be expected to appear in all art forms, including music. While a variety of statistical tools have been proposed to analyze time series in…
Small-angle scattering (SAS) of X-rays, neutrons or light from ensembles of randomly oriented and placed deterministic fractal structures are studied theoretically. In the standard analysis, a very few parameters can be determined from SAS…
Any space-filling packing of spheres can be cut by a plane to obtain a space-filling packing of disks. Here, we deal with space-filling packings generated using inversive geometry leading to exactly self-similar fractal packings. First, we…
Algorithmic fractal dimensions -- constructs of computability theory -- have recently been used to answer open questions in classical geometric measure theory, questions of mathematical analysis whose statements do not involve computability…
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…