Wireless applications, particularly with multiple resonances, put new demands on antennas pertaining to size, gain, efficiency, bandwidth, and more. One promising approach in this regard is to use fractal geometries to find the best distribution of currents within a volume to meet a particular design goal. In the miniaturization of wire antennas it has been found that the electromagnetic coupli...

Nature is lled with examples of phenomena that exhibit seemingly chaotic behavior, such as air turbulence, forest res and the like. However, under this behavior it is almost always possible to nd self-similarity, i.e. an invariance with respect to the scale used. The structures that appear as a consequence of self-similarity are known as fractals [12]. Fractals have been used in numerous discip...

Psychological and physiological benefits of viewing nature have been extensively studied for some time. More recently it has been suggested that some of these positive effects can be explained by nature's fractal properties. Virtually all studies on human responses to fractals have used stimuli that represent the specific form of fractal geometry found in nature, i.e. statistical fractals, as o...

Noncommutative geometry provides a framework, via the construction of spectral triples, for study certain classes fractals. Many fractals are constructed as natural limits sets with simpler structure: instance, Sierpiński gasket is limit finite graphs consisting various affine images an equilateral triangle. It thus to ask whether on class called piecewise C 1 -fractal curves, indeed limits, in...

With a view towards Riemannian or sub-Riemannian manifolds, RCD metric spaces and specially fractals, this paper proves Sobolev embedding theorems in the general framework of Dirichlet spaces. Under suitable assumptions that are verified variety settings, we obtain whole family Gagliardo-Nirenberg Trudinger-Moser inequalities with optimal exponents. These turn out to depend not only on Hausdorf...

The frequency of occurrence of prime numbers at unit number spacing intervals exhibits selfsimilar fractal fluctuations concomitant with inverse power law form for power spectrum generic to dynamical systems in nature such as fluid flows, stock market fluctuations, population dynamics, etc. The physics of long-range correlations exhibited by fractals is not yet identified. A recently developed ...

Fractals have experienced considerable success in quantifying the visual complexity exhibited by many natural patterns, and continue to capture the imagination of scientists and artists alike. Fractal patterns have also been noted for their aesthetic appeal, a suggestion further reinforced by the discovery that the poured patterns of the American abstract painter Jackson Pollock are also fracta...

Fractals are geometric shapes and patterns that can describe the roughness (or irregularity) present in almost every object nature. Many fractals may repeat their geometry at smaller or larger scales. This paper is second (and last) part of a series two papers dedicated to an eclectic survey describing infinite complexity amazing beauty from historical, theoretical, mathematical, aesthetical te...

Fractals have experienced considerable success in quantifying the complex structure exhibited by many natural patterns and have captured the imagination of scientists and artists alike. With ever widening appeal, they have been referred to both as "fingerprints of nature" and "the new aesthetics." Our research has shown that the drip patterns of the American abstract painter Jackson Pollock are...

We study the problem of adsorption of self-interacting linear polymers situated in fractal containers that belong to the three-dimensional (3d) Sierpinski gasket (SG) family of fractals. Each member of the 3d SG fractal family has a fractal impenetrable 2d adsorbing surface (which is, in fact, 2d SG fractal) and can be labelled by an integer b (2 ≤ b ≤ ∞). By applying the exact and Monte Carlo ...