Fractals have been very successful in quantifying the visual complexity exhibited by many natural patterns, and have captured the imagination of scientists and artists alike. Our research has shown that the poured patterns of the American abstract painter Jackson Pollock are also fractal. This discovery raises an intriguing possibility - are the visual characteristics of fractals responsible fo...

This article reported patch antenna functioning at Wi- Fi and 5G bands. Wi-Fi band (2.4 GHz) is obtained by loading Epsilon Negative Transmission Line (ENGTL) metamaterials into the radiating (3.5 GHz). To acquire Circular Polarization (CP) band, conventional square embedded with poly fractals. The experimental simulated data are in close proximity. impedance bandwidth 4.01% 10.68% band. CP 2.4...

u1, . . . , ur are in kJx1, . . . , xsK with k and deg(u1, . . . , ur) finite. Intending applications to Hilbert-Kunz theory, we code the numbers deg(u1 1 , . . . , u ar r ) into a function φu, which empirically satisfies many functional equations related to “magnification by p”, where p = chark. p-fractals, introduced here, formalize these ideas. In the first interesting case (r = 3, s = 2), t...

Computers have led to the remarkable popularity of mathematically-generated fractal patterns. Fractals have also assumed a rapidly expanding role as an art form. Due to their growing impact on cultures around the world and their prevalence in nature, fractals constitute a central feature of our daily visual experiences throughout our lives. This intimate association raises a crucial question - ...

For the past two decades, fractals (e.g., the Hilbert and Peano space-filling curves) have been considered the natural method for providing a locality-preserving mapping. The idea behind a locality-preserving mapping is to map points that are nearby in the multi-dimensional space into points that are nearby in the one-dimensional space. In this paper, we argue against the use of fractals in loc...

Dealing with several structures of different complexities, we adopt various strategies to extract information. The general idea is to find appropriate tools to analyze the variation of the corresponding autocorrelation functions. First, for homogeneous media under different conditions, we recover, in a statistical way, a relationship between porosity and the autocorrelation function. Then, for ...

In this paper we show that the massive parallelism, the synchronous application of the rules, and the discrete nature of their computation, among other features, lead us to consider P systems as natural tools for dealing with fractals. Several examples of fractals encoded by P systems are presented and we wonder about using P systems as a new tool for representing and simulating the fractal nat...

We construct a theory of distributions in the setting of analysis on post-critically finite self-similar fractals, and on fractafolds and products based on such fractals. The results include basic properties of test functions and distributions, a structure theorem showing that distributions are locally-finite sums of powers of the Laplacian applied to continuous functions, and an analysis of th...

The use of fractals in computer graphics and vision in modeling unstructured images, and compressing images, is well known. However, the use of fractals for indexing images in content based retrieval of video and static images has not received as much attention. In this paper, we provide the theoretical arguments to justify their use in image retrieval. Our web-enabled implementation on the FER...

We use state-of-the-art public-domain Fortran codes based on the T-matrix method to calculate orientation and ensemble averaged scattering matrix elements for a variety of morphologically complex black carbon (BC) and BC-containing aerosol particles, with a special emphasis on the linear depolarization ratio (LDR). We explain theoretically the quasi-Rayleigh LDR peak at side-scattering angles t...