Academic literature on the topic 'Fractal de Gosper'

The boundaries of central place models proved to be fractal lines, which compose fractal texture of central place networks. However, the fractal texture cannot be verified by empirical analyses based on observed data. On the other hand, fractal structure of central place systems in the real world can be empirically confirmed by positive studies, but there are no corresponding models. The spatial structure of classic central place models bears Euclidean dimension [Formula: see text] rather than fractal dimensions [Formula: see text]. This paper is devoted to deriving structural fractals of central place models from the textural fractals. The method is theoretical deduction based on the dimension rules of fractal sets. The main results and findings are as follows. First, the central place fractals were formulated by the [Formula: see text] numbers and [Formula: see text] numbers. Second, three structural fractal models were constructed for central place systems according to the corresponding fractal dimensions. Third, the classic central place models proved to comprise Koch snowflake curve, Sierpinski space filling curve, and Gosper snowflake curve. Moreover, the traffic principle plays a leading role in urban and rural settlements evolution. A conclusion was reached that the textural fractal dimensions of central place models can be converted into the structural fractal dimensions and vice versa, and the structural dimensions can be directly used to appraise human settlement distributions in reality. Thus, the textural fractals can be indirectly employed to characterize the systems of human settlements.

In this contribution, fractal antenna arrays are analyzed for their applicability in multiple-input multiple-output (MIMO) radars. Array geometries based on the Fudgeflake fractal and the Gosper island fractal are investigated. In addition, a concept for the combination of both fractals is shown in order to increase the flexibility concerning the number of transmitting and receiving antennas. The presented fractal MIMO concepts can be utilized in order to improve the angular resolution and to reduce the sidelobe level for a given number of transmitting and receiving antennas. It is shown that a fractal MIMO concept with 21 transmitting antennas and 21 receiving antennas improves the angular resolution to 4.6 degrees and reduces side lobe level by 3.1 dB compared to a MIMO configuration based on two linear arrays with the same number of antenna elements. In addition, the results are experimentally validated by broadband radar measurements.

Fractal geometry is a subject that studies non-integer dimensional figures. Most of the fractal geometry figures have a nested or recursive structure. This paper attempts to apply the nested or recursive structure characteristics of fractal geometry to wireless sensor networks. We selected two filling curves, Node-Gosper and Moore, as our research subjects. Node-Gosper Curve is a curve based on node-replacement with a fractal dimension of two. Its first-order graph consists of seven basic line segments. When the hierarchy becomes larger, it can be filled with a hexagonal-like shape. To allow the mobile anchor node of wireless sensor networks to walk along this curve, the number of levels of the Node-Gosper Curve can be adjusted according to parameters such as the sensing area and transmission range. Many space-filling curves have the common shortcoming that they cannot loop on their own, that is, the starting point and the end point are not close, which will cause the mobile anchor node to use extra paths from the end point back to the starting point. The Moore curve has a self-loop, i.e., the starting point and the ending point are almost at the same position. This paper applies Moore curve to the path planning of the mobile anchor node. We can use this path to traverse the entire sensing area and stay in the central point of each square cluster to collect the information of the nodes where the events occurred. The self-loop characteristic of the Moore curve is expected to reach each sensor to collect data faster than other space filling curves, that is, the transmission latency of the sensor traversal will be reduced

Space-filling curves (SFCs) represent an efficient and straightforward method for sparse-space indexing to transform an n-dimensional space into a one-dimensional representation. This is often applied for multidimensional point indexing which brings a better perspective for data analysis, visualization and queries. SFCs are involved in many areas such as big data analysis and visualization, image decomposition, computer graphics and geographic information systems (GISs). The indexing methods subdivide the space into logic clusters of close points and they differ in various parameters including the cluster order, the distance metrics, and the pattern shape. Beside the simple and highly preferred triangular and square uniform grids, the hexagonal uniform grids have gained high interest especially in areas such as GISs, image processing and data visualization for the uniform distance between cells and high effectiveness of circle coverage. While the linearization of hexagons is an obvious approach for memory representation, it seems there is no hexagonal SFC indexing method generally used in practice. The main limitation of hexagons lies in lacking infinite decomposition into sub-hexagons and similarity of tiles on different levels of hierarchy. Our research aims at defining a fast and robust hexagonal SFC method. The Gosper fractal is utilized to preserve the benefits of hexagonal grids and to efficiently and hierarchically linearize points in a hexagonal grid while solving the non-convex shape and recursive transformation issues of the fractal. A comparison to other SFCs and grids is conducted to verify the robustness and effectiveness of our hexagonal method.

Abstract This study aims at prospecting copper and gold promising areas in Saveh 1:100,000 sheet, situated in Urumieh-Dokhtar magmatic belt (Central Iran). Geographic information system (GIS) is effective in recognition of probable mineral resources by collecting, processing, exploration layer weighting and integrating thematic maps. As there is no certainty in different geological phenomena, modeling and integrating information layers are used to obtain suitable results for determining potential areas. In this study, index overlay method, which is a combination of software processing and expertise knowledge, was used. The survey layers consist of the lithologic units, geophysical data, mineralization, faults and structures and alteration. For more exact survey, concentration-area (C-A) fractal modeling was applied to the map of results obtained from integration. Applying fractal model to this map, the results of the original map were prioritized and became more limited. In the end for assessing the validity of determined promising areas, the results were compared with geochemical anomaly maps of stream sediments and also field observation was performed. Areas with high exploration priority with limited extend exist in center, west and some parts of NW, conformed to granodiorite intrusives and also next priority exists in center, west, NE and NW conformed to granite, diorite, and also subvolcanic rocks respectively. These prioroties are related to fault systems. In order to perform X-ray Diffraction (XRD), Inductively Coupled Plasma – Mass Sepctrometry (ICP-MS) analyses and microscopic studies, lithogeochemical samplings were done. All investigations indicate the possibility of pyrite, chalcopyrite and galena epithermal mineralizations resulted from post magmatic fluids, and also secondary products like hematite, goethite, and malachite as a result of oxidation processes in these areas.

Submitted by Automa??o e Estat?stica (sst@bczm.ufrn.br) on 2015-12-14T21:36:46Z No. of bitstreams: 1 AlbanisaFelipeDosSantos_DISSERT.pdf: 4703287 bytes, checksum: e882be5f3bf32915ca0f8f6710487c3d (MD5)<br>Approved for entry into archive by Arlan Eloi Leite Silva (eloihistoriador@yahoo.com.br) on 2015-12-16T17:33:34Z (GMT) No. of bitstreams: 1 AlbanisaFelipeDosSantos_DISSERT.pdf: 4703287 bytes, checksum: e882be5f3bf32915ca0f8f6710487c3d (MD5)<br>Made available in DSpace on 2015-12-16T17:33:34Z (GMT). No. of bitstreams: 1 AlbanisaFelipeDosSantos_DISSERT.pdf: 4703287 bytes, checksum: e882be5f3bf32915ca0f8f6710487c3d (MD5) Previous issue date: 2013-07-25<br>Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico - CNPq<br>Neste trabalho, as propriedades de auto-similaridade dos fractais s?o exploradas para o desenvolvimento de superf?cies seletivas de frequ?ncia (Frequency Selectives Surfaces - FSS) com v?rias bandas de rejei??o. Em particular, s?o considerados fractais de Gosper, na defini??o dos formatos dos elementos das FSS. Por conta da dificuldade de impress?o de detalhes dos elementos das FSS, s?o considerados apenas elementos pr?-fractais, com at? tr?s itera??es fractais. As simula??es foram realizadas com o uso do programa comercial Ansoft Designer. Para fins de valida??o de resultados, foram constru?dos v?rios prot?tipos de FSS com elementos pr?-fractais. No processo de fabrica??o, os formatos dos elementos pr?-fractais foram desenhados com aux?lio do programa Corel Draw. Os prot?tipos constru?dos foram medidos atrav?s de um analisador de redes vetorial (modelo N3250A, da Agilent Technologies). A utiliza??o de elementos pr?-fractais nas estruturas de FSS consideradas, permitiu verificar que o aumento do n?vel fractal possibilita a redu??o do tamanho dos elementos, por?m reduz a largura de banda das mesmas. Neste sentido, ? tamb?m investigado o efeito produzido pelo cascateamento de estruturas de FSS na largura de banda. Foi observado que o uso de estruturas cascateadas, al?m de aumentar a largura de banda, permitiu, em alguns casos, a obten??o de at? respostas em frequ?ncia com tr?s bandas de opera??o entre 6 GHz e 15 GHz.<br>The fractal self-similarity property is studied to develop frequency selective surfaces (FSS) with several rejection bands. Particularly, Gosper fractal curves are used to define the shapes of the FSS elements. Due to the difficulty of making the FSS element details, the analysis is developed for elements with up to three fractal levels. The simulation was carried out using Ansoft Designer software. For results validation, several FSS prototypes with fractal elements were fabricated. In the fabrication process, fractals elements were designed using computer aided design (CAD) tools. The prototypes were measured using a network analyzer (N3250A model, Agilent Technologies). Matlab software was used to generate compare measured and simulated results. The use of fractal elements in the FSS structures showed that the use of high fractal levels can reduce the size of the elements, at the same time as decreases the bandwidth. We also investigated the effect produced by cascading FSS structures. The considered cascaded structures are composed of two FSSs separated by a dielectric layer, which distance is varied to determine the effect produced on the bandwidth of the coupled geometry. Particularly, two FSS structures were coupled through dielectric layers of air and fiberglass. For comparison of results, we designed, fabricated and measured several prototypes of FSS on isolated and coupled structures. Agreement was observed between simulated and measured results. It was also observed that the use of cascaded FSS structures increases the FSSs bandwidths and, in particular cases, the number of resonant frequencies, in the considered frequency range. In future works, we will investigate the effects of using different types of fractal elements, in isolated, multilayer and coupled FSS structures for applications on planar filters, high-gain microstrip antennas and microwave absorbers