Related papers: Fractal light from lasers
We numerically study light scattering and absorption in self-similar aggregates of dielectric nanoparticles, as generated by simulated ballistic deposition upon a surface starting from a single seed particle. The resulting structure…
This paper presents an analysis of the smoothness problem in cosmology by focussing on the ambiguities originated in the simplifying hypotheses aimed at observationally verifying if the large-scale distribution of galaxies is homogeneous,…
Many biological processes and objects can be described by fractals. The paper uses a new type of objects - blinking fractals - that are not covered by traditional theories considering dynamics of self-similarity processes. It is shown that…
In many problems of classical analysis extremal configurations appear to exhibit complicated fractal structure. This makes it much harder to describe extremals and to attack such problems. Many of these problems are related to the…
The array of micro-prisms was described by model of multi-period blazed gratings consisting of triangular apertures. The origins of hexagram-shaped diffraction patterns were interpreted based on multiple-beam interference and diffraction…
Photonic crystals with a sufficiently high refractive index contrast display partial or full band gaps. However, imperfections in the metamaterial cause light scattering and extinction of the interfering propagating waves. Positive as well…
We exhibit a characteristic structure of the class of all regular graphs of degree d that stems from the spectra of their adjacency matrices. The structure has a fractal threadlike appearance. Points with coordinates given by the mean and…
Fractal structures appear in a vast range of physical systems. A literature survey including all experimental papers on fractals which appeared in the six Physical Review journals (A-E and Letters) during the 1990's shows that experimental…
In this article, we considered a fractal image as a fractal curve, that is, as a walk on a grid in Euclidean space $\R^d$. We placed integers on the generating vectors of a grid, such that opposite directions have opposite numbers. This…
To help understand the underlying mechanisms of neural networks (NNs), several groups have, in recent years, studied the number of linear regions $\ell$ of piecewise linear functions generated by deep neural networks (DNN). In particular,…
Two-point correlation function of galaxy distribution shows that the structure in the present Universe is scale-free up to a certain scale (at least several tens Mpc), which suggests that a fractal structure may exist. If small primordial…
Self-similarity is the essence of fractal images and, as such, characterizes natural stochastic textures. This paper is concerned with the property of self-similarity in the statistical sense in the case of fully-textured images that…
When information is spatially repeated in self-similar fractal beam patterns, only a portion of the diffracted beam is needed to reconstruct the kernel data. What is unique to a fractal-encoding scheme is that the image demultiplexing…
This paper presents a review of the fractal approach for describing the large scale distribution of galaxies. We start by presenting a brief, but general, introduction to fractals, which emphasizes their empirical side and applications…
Grating spectra exhibit sharp variations of the scattered light, known as grating anomalies. The latter are due to resonances that have fascinated specialists of optics and physics for decades and are nowadays used in many applications. We…
Despite rapidly growing disk observations, it remains a mystery what primordial dust aggregates look like and what the physical and chemical properties of their constituent grains (monomers) are in young planet-forming disks. Confrontation…
The formation of a new type of laser-induced periodic surface structures using a femtosecond pulsed laser is studied on the basis of the Sipe-Drude theory solved with a FDTD scheme. Our numerical results indicate the possibility of…
Fractals emerge everywhere in nature, exhibiting intricate geometric complexities through the self-organizing patterns that span across multiple scales. Here, we investigate beyond steady-states the interplay between this geometry and the…
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…
The visible problem is related to the arithmetic on the fractals. The visibility of self-similar set has been studied in the past. In this work, we investigate the visibility of non-self-similar sets. We begin by analyzing the structure of…