The theory of complex dimensions describes the oscillations in the geometry (spectra and dynamics) of fractal strings. Such geometric oscillations can be seen most clearly in the explicit volume formula for the tubular neighborhoods of a p-adic fract...
In this article, a high-gain axisymmetric Minkowski fractal reflectarray is designed and fabricated for Ku-Band satellite internet communications. High gain is achieved here by carefully optimising the number of unit cells, their shape modifier, foca...
In this article, a second-order iterated Circular Minkowski fractal antenna (CMFA) tailored for ultra-wideband (UWB) applications is designed and developed. Leveraging the power of Minkowski fractal geometry, this antenna design achieves a high gain...
In this paper, the design, simulation, fabrication, and characterization study of a low-cost and directional hybrid four-element (2 × 2 configuration) Minkowski–Sierpinski fractal antenna array (MSFAA) for the high-efficiency IEEE 802.11a...
High-gain linear polarized antennas are widely used in wireless communications. However, the insertion loss of the feed network increases, limiting the potential for enhancing antenna gain. In this paper, a high-gain linear polarized Fabry–Pero...
In this study, we will discuss the engineering construction of a special sixth generation (6G) antenna, based on the fractal called Minkowski’s loop. The antenna has the shape of this known fractal, set at four iterations, to obtain maximum per...
In light of the predicament concerning the small gain and narrow frequency range of miniature antennas, this paper employs the implementation of a fractal repeating array structure and a double-layer folding antenna structure. Through these measures,...
Homogeneous random fractals form a probabilistic generalisation of self-similar sets with more dependencies than in random recursive constructions. Under the Uniform Strong Open Set Condition we show that the mean D-dimensional (average) Minkowski co...
A substrate-integrated waveguide (SIW) bandpass filter (BPF) with extraordinary selectivity and an adequate upper stopband for C-band Satellite Communication (SATCOM) applications is proposed in this paper. The design comprises comb-shaped slots engr...
The intersection of fractals, non-Euclidean geometry, spatial autocorrelation, and urban structure offers valuable theoretical and practical application insights, which echoes the overarching goal of this paper. Its research question asks about conne...
We propose the application of morphological, fractal and multifractal analysis to differentiate surface patterns on zirconia-based ceramics after laser treatments. Furthermore, we introduce two new approaches for ceramic surfaces: the Moran correlogr...
The direct wave between the transceiver antenna negatively affects the dynamic range and imaging quality of ground penetrating radar (GPR). Suppressing this direct wave is a vital problem in enhancing the performance of the whole GPR system. In this...
The paper presents microstrip patch antennas, which are based on the fractal antenna concept, and use planar periodic geometries, providing improved characteristics. The properties of the fractal structure were used in a single-fractal layer design a...
Fractal geometry has been proven to be useful in several disciplines. In the field of antenna engineering, fractal geometry is useful to design small and multiband antenna and arrays, and high-directive elements. A historic overview of the most signi...
A compact and wide-stop band half mode substrate integrated waveguide (HMSIW) filter, incorporated with a hybrid fractal on the upper plane and a complementary split ring resonator (CSRR), along with a defected ground structure (DGS) etched on the bo...
In the present work, Cu/Cr thin films were deposited on substrates of a different nature (Si, Glass, Bk7, and ITO) through a thermal evaporation deposition method. Non-contact atomic force microscopy (AFM) was used to obtain 3D AFM topographical maps...
This paper presents a circularly polarized hybrid cylindrical dielectric resonator antenna (HCDRA) over a modified Minkowski unit-cell-based metasurface for 5G n79 band (4.4–5 GHz) and IEEE 802.11n WLAN (5 GHz) applications. The location of the...
Fractal-like structures of varying complexity are common in nature, and measure-based dimensions (Minkowski, Hausdorff) supply their basic geometric characterization. However, at the level of fundamental dynamics, which is quantum, structure does not...
This paper deals with the hidden structure of prime numbers. Previous numerical studies have already indicated a fractal-like behavior of prime-indexed primes. The construction of binary images enables us to generalize this result. In fact, two-integ...
Modern expansion and three-dimensional growth are rapidly altering the morphological features of traditional cities. This morphological phenomenon fully reflects the internal organization mode and composition rules of modern cities. This study draws...
Julia and Mandelbrot sets, which characterize bounded orbits in dynamical systems over the complex numbers, are classic examples of fractal sets. We investigate the analogs of these sets for dynamical systems over the hyperbolic numbers. Hyperbolic n...
The specific advantage of fractal geometry to realize compact antenna features is exploited in this work for the design of a miniaturized Planar Inverted-F Antenna configuration with a large bandwidth. The conventional quadrilateral radiating element...
This paper presents a systematic methodology for identifying optimal scaling regions in segment-based box-counting fractal dimension calculations through a three-phase algorithmic framework combining grid offset optimization, boundary artifact detect...
A frequency-selective surface (FSS) optimization method combining a curve-fitting technique and an improved bacterial foraging optimization (IBFO) algorithm is proposed. In the method, novel Koch curve-like FSS and Minkowski fractal islands FSS were...
Dense 3D point clouds were generated from Structure-from-Motion Multiview Stereo (SFM-MVS) photogrammetry for five representative freshwater fish habitats in the Xingu river basin, Brazil. The models were constructed from Unmanned Aerial Vehicle (UAV...
The interaction mechanism between the cavitation bubble and a solid wall is a basic problem in bubble collapse prevention and application. In particular, when bubble collapse occurs near solid walls with arbitrarily complex geometries, it is difficul...
Pavement texture characteristics can reflect early performance decay, skid resistance, and other information. However, most statistical texture indicators cannot express this difference. This study adopts 3D image camera equipment to collect texture...