Polyominoes, shapes made up of squares connected edge-to-edge, provide a rich source of prototiles for edge-toedge fractal tilings. We give examples of fractal tilings with 2-fold and 4-fold rotational symmetry based on prototiles derived by dissecting polyominoes with 2-fold and 4-fold rotational symmetry, respectively. A systematic analysis is made of candidate prototiles based on lower-order...

Fractal antenna, as name concerns, uses fractal i.e. structure does not change and repeat it when large focus has created upon it. This repetition feature of this antenna provides a great flexibility that it can be designed and can used in different frequencies. Fractal geometry has shown its potential in many fields of engineering and technology. In antenna engineering fractal geometry is very...

Fractals are remarkable examples of self-similarity where a structure or dynamic pattern is repeated over multiple spatial or time scales. However, little is known about how fractal stimuli such as fractal surfaces interact with their local environment if it exhibits order. Here we show geometry-induced formation of fractal defect states in Koch nematic colloids, exhibiting fractal self-similar...

In this paper, sierpinski carpet fractal shape antenna for RFID applications is proposed. The proposed antenna has been designed with scaling factor of one-fourth with the aim of reducing antenna size and improved performance parameters. Fractal shaped has been developed to improve the characteristics and to miniaturize the size of proposed antenna. Usually, an antenna works at one or two frequ...

In this paper, we investigate the existence of extension operators fromW (Ω) toW (R) (1 < p < ∞) for a class of tree-shaped domains Ω with a self-similar fractal boundary previously studied by Mandelbrot and Frame. When the fractal boundary has no self-contact, the results of Jones imply that there exist such extension operators for all p ∈ [1,∞]. In the case when the fractal boundary self-inte...

We show that a metallic plate with periodic fractal-shaped slits can be homogenized as a plasmonic metamaterial with plasmon frequency dictated by the fractal geometry. Owing to the all-dimensional subwavelength nature of the fractal pattern, our system supports both transverse-electric and transverse-magnetic surface plasmons. As a result, this structure can be employed to focus light sources ...