Gosper Curve Research Articles

Acoustic materials based on the Gosper curve

In this work, slotted acoustic materials based on a space filling curve called the Peano-Gosper curve are proposed and investigated. The slits in such materials form a complex pattern because they are divided by walls built along lines generated by the Gosper curve algorithm. The pattern can be twisted around an axis normal to its surface to increase the tortuosity inside the material, and therefore, modify its acoustic properties, which can be controlled by the turning angle or pitch of the twist. A highly efficient semi-analytical model has been developed to accurately predict the acoustic properties, in particular the sound absorption of such materials. It only requires a representative part of the pattern, or better, scanning the surface of the fabricated material so that the actual geometry and dimensions (in particular slit widths) are well reproduced in a two-dimensional finite element mesh generated on a representative fluid domain. The mesh is used to solve a dedicated Poisson problem and determine a few key parameters, and the rest of the modelling is based on analytical formulas. Material samples with straight and twisted slit patterns were 3D printed and then measured in an impedance tube to confirm semi-analytical sound absorption predictions.

Improving the gas sensing performance of halide perovskite MAPbI3 film via fractal geometry electrode structure

The first successful fabrication of metal halide Perovskite MAPbI3 Film for NH3 gas sensing using fractal electrode structure is reported. High performance NH3 gas sensor was fabricated on ITO glass substrate by laser-patterning method. Gas sensors were fabricated using Hilbert, Peano, and Gosper curve structure electrodes, and their performance is compared to conventional interdigitated electrode. Gas sensing performance on Hilbert electrode design showed the highest response of 2.82 at 10 ppm NH3 gas, which is 145 % times higher compared to conventional interdigitated structures. Simulation study demonstrates that the electric field intensity and number of nodes of the fractal electrode are higher than those of the traditional interdigitated electrode. This study demonstrates that fractal electrode is a feasible strategy for optimizing the potential performance of MAPbI3-based Perovskite gas sensor with low-cost fabrication with no extra processing.

Multiband antenna design based on Gosper fractal for implantable biomedical devices

AbstractIn this paper, a novel multiband implantable planar inverted-F antenna (PIFA) antenna based on Gosper curve fractal geometry is designed for biomedical telemetry applications. The antenna has covered four dedicated frequency bands; medical implant communication system band (MICS 402–405 MHz), industrial, scientific, and medical bands (ISM 902–928 MHz and 2.4–2.5 GHz), and wireless medical telemetry services (WMTS 1395–1400 and 1429–1432 MHz). The proposed antenna is designed on Rogers RO 3010 substrate of thickness 25 mil and volume equal to 153.67 mm3. The reflection coefficient and the radiation pattern are measured inside muscle-mimicking liquid tissue phantom. The antenna has achieved the impedance bandwidth of 126, 406, 168, and 175 MHz at MICS (403 MHz), ISM (915 MHz), WMTS (1400 MHz), and ISM (2.45 GHz) with maximum gain value −33.6, −21.04, −15.48, and −10.25 dBi, respectively. The data link range between the implantable antenna and off body antenna has been performed with −16 dBm input power. Additionally, the obtained specific absorption rate with the input of 25 μW power has also been obtained within the safety limit and hence ensures the reliability of the proposed antenna.

Implantable Antenna Design Based on Gosper Curve Fractal Geometry

A Gosper curve fractal-based geometry novel Planar Inverted F-antenna (PIFA) antenna has been proposed for implantable biotelemetry applications. The antenna is designed to work inside the human muscle tissue at the MICS band (402–405 MHz). The antenna is composed of two layers of radiating patch stacked together on Rogers RO 3010 substrate with a thickness of 10 mil and a radius of 5 mm. The volumetric size of the proposed antenna is approximately 60 mm3. The initial antenna is designed inside the single layer human muscle tissue and optimized inside the multilayer tissue model. Furthermore, lumped equivalent circuit models, based on Bessel filter function, have been proposed and their results are analogized with the proposed antenna design with an error of 2.1%. The performance of fabricated antenna prototype inside human muscle, mimicking liquid phantom, is matched to a large extent closely to the proposed numerical antenna model that ensures its reliability.

Peano–Gosper, Koch and Minkowski fractal curves-based novel hybrid antenna using modified partial ground plane for multi-standard wireless applications

This paper presents the unique structure of a hybrid antenna with a blend of Peano–Gosper, Koch and Minkowski curves using a modified partial ground plane for multi-standard wireless applications. Initially, the Minkowski and Koch curves are amalgamated by using a versatile mathematical tool called Iterative Function System (IFS), and furthermore, their resultant structure is superimposed on each segment of Peano–Gosper curve to obtain the novel geometry of hybrid fractal antenna named Gosper–Koch–Minkowski Hybrid Fractal Antenna (GKMHFA). The partial ground plane with 50 Ω transmission line fed is used to analyse the performance of designed structure and found that it exhibits five different frequency bands above 9 GHz in the frequency range 1–20 GHz. Consequently, to attain the frequency bands below 9 GHz with enhanced bandwidth and reflection coefficient, the partial ground plane has been modified. The proposed antenna with the modified ground plane reveals seven distinct frequency points 1.5, 3.4, 8.6, 12.2, 14.1, 15.3 and 18.9 GHz with a maximum bandwidth 5.0 GHz along with improved reflection coefficient i.e. −45.65 dB at 1.5 GHz. The proposed antenna also reports positive gain and stable radiation patterns in the operational frequency bands, which make it a proficient candidate for the multi-standard wireless applications such as GPS, terrestrial communication, PCS, UMTS, advance wireless services, Bluetooth, WLAN, Wi-Fi, Wi-MAX, military satellite communication, television broadcasting, broadcasting satellite, FSS, Ku-band and K-band.

Broadband mid-infrared perfect absorber using fractal Gosper curve

Designing broadband metamaterial perfect absorbers is challenging due to the intrinsically narrow bandwidth of surface plasmon resonances. This paper reports an ultra-broadband metamaterial absorber by using space filling Gosper curve. The optimized result shows an average absorptivity of 95.78% from 2.64 to 9.79 µm across the entire mid-infrared region. Meanwhile, the absorber shows insensitivity to the polarization angle and the incident angle of the incident light. The underlying physical principles used in our broadband absorber involve a fractal geometry with multiple scales and a dissipative plasmonic crystal. The broadband perfect absorption can be attributed to multiple electric resonances at different wavelengths supported by a few segments in the defined Gosper curve.

Run length coding and efficient compression of hexagonal raster data based on Gosper curve

Abstract. Compared with regular quadrilateral grid, regular hexagonal grid is isotropy and has higher cell compactness and sampling density. This gives regular hexagonal grid advantages in visual display, spatial analysis, and many other aspects. However, the studies of raster data mainly focus on regular quadrilateral grid, and various encoding methods are also focused on it. The researches on hexagonal raster data are relatively insufficient.In this paper, encoding and compression for regular hexagonal grid are studied. By introducing Gosper curve which has good spatial aggregation and takes into account the morphological structure of regular hexagonal grid, the bidirectional correlation between Gosper curve and regular hexagonal grid is established. Then, a new encoding framework is built to determine the Gosper coding of each grid unit. The lossless compression is completed by performing run-length coding on adjacent coding sets in the target region.

Encoding and compressing hexagonal raster data by the Gosper curve

AbstractThis article mainly introduces a class of encoding and compression methods for hexagonal raster data. A new encoding mode is established with the introduction of the Gosper curve, which has good spatial aggregation. On this basis, straightforward encoding, lossless coding compression, and lossy coding compression can be carried out. First, the bidirectional correlation between the Gosper curve and the hexagonal grid data is established, and the Gosper coding value of each raster unit is determined. Then, the lossless compression of the data is completed by performing run‐length encoding on the coding set. Following the Gosper curve trend, partial grid units are semantically changed via adjacent fusion under certain threshold constraints. The run‐length encoding is carried out again to complete the lossy compression and further reduce the amount of encoding required. A break‐detection step is added during the process to avoid regional breaks. The experimental results show that the proposed method can efficiently compress data. Additionally, data compression of multi‐resolution and varying fusion thresholds is explored to summarize general patterns. Finally, the method proposed is compared with traditional row‐coding compression in hexagonal and quadrilateral grids to highlight its advantages for hexagonal raster data.

Metaphor Representation and Analysis of Non-Spatial Data in Map-Like Visualizations

Metaphors are rhetorical devices in linguistics that facilitate the understanding of an unfamiliar concept based on a familiar concept. Map representations are usually referred to as the second language of geo-science studies, and the metaphor method could be applied to maps to visualize non-spatial data via spatial element symbols. This study performs a cross-domain application of the map representation method through a map-like visualization. The procedure first designs the map layout with the aid of the Gosper curve. Under the guidance of the Gosper curve, the leaf data items without spatial attributes are arranged on the space plane. Through the bottom-up regional integration, one can complete the construction of the map framework. Then, the cartographic method is used to complete map-like renderings that reflect different data features through diverse visualizations. The map representation advantages, such as overview sensing and multi-scale representation, are also reflected in the map-like visualization and used to identify the characteristics of non-spatial data. Additionally, the electronic map provides a series of interactive convenience features for map observation and analysis. Using the help of map-like visualizations, one can perform a series of analyses of non-spatial data in a new form. To verify the proposed method, the authors conducted map-making experiments and data analyses using real data.

GosperMap: Using a Gosper Curve for Laying Out Hierarchical Data

The emergence of very large hierarchies that result from the increase in available data raises many problems of visualization and navigation. On data sets of such scale, classical graph drawing methods do not take advantage of certain human cognitive skills such as shape recognition. These cognitive skills could make it easier to remember the global structure of the data. In this paper, we propose a method that is based on the use of nested irregular shapes. We name it GosperMap as we rely on the use of a Gosper Curve to generate these shapes. By employing human perception mechanisms that were developed by handling, for example, cartographic maps, this technique facilitates the visualization and navigation of a hierarchy. An algorithm has been designed to preserve region containment according to the hierarchy and to set the leaves' sizes proportionally to a property, in such a way that the size of nonleaf regions corresponds to the sum of their children's sizes. Moreover, the input ordering of the hierarchy's nodes is preserved, i.e., the areas that represent two consecutive children of a node in the hierarchy are adjacent to one another. This property is especially useful because it guarantees some stability in our algorithm. We illustrate our technique by providing visualization examples of the repartition of tax money in the US over time. Furthermore, we validate the use of the GosperMap in a professional documentation context and show the stability and ease of memorization for this type of map.

Space-filling Patch Antennas with CPW Feed

In this paper, the performances of some space-filling monopole antennas with coplanar waveguide have been investigated. It may be contended that the bends and corners of these geometries would add to the radiation efficiency of the antenna, thereby improving its gain. Advantage of these configurations is that they lead to mutiband conformal antennas. A new version of Gosper curve patch antenna is introduced and its performance has been compared to conventional Gosper curve patch antenna.

Method for evaluating the fractal dimension of curves using convex hulls.

A local analysis for simple curves is performed using the geometric notions of size and deviation of an arc. For typical parametrized curves, the rate of decrease of these averaged measurements is related to the value of the fractal dimension. A method for calculating this dimension is derived, generalizing the variation method used for graphs of continuous functions to a large family of curves. Our method, the constant-deviation variable-step method, is tested on various types of curves (fractal Brownian motion, Gosper curve, and geographical coastline). A comparison is made with other methods such as the divider-step method, variation method, and diameter method. We show that our method offers the same level of performance while exhibiting much more general applications.