Plant Leaf Identification Using Gabor Wavelets

This article presents a novel method of plant classification using Gabor wavelet filters to extract texture filters in a foliar surface. The aim of this promising method is to add to the results obtained by other leaf attributes (such as shape, contour, color, among others), increasing, therefore, the percentage of classification of plant species. To corroborate the efficiency of the technique, an experiment using 20 species from Brazilian flora was done and discussed. The results are also compared with texture Fourier descriptors and cooccurrence matrices. (C) 2009 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 19, 236-243, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.20201

Reator Gerador de Flocos - RGF : concepção e desenvolvimento básico

O objetivo geral do presente trabalho foi a concepção e o desenvolvimento de um sistema compacto de floculação em linha, em escala semipiloto, com o aproveitamento da energia cinética do fluxo hidráulico para promover a agitação necessária à dispersão de um polímero floculante e a geração dos flocos ao longo de um reator tubular helicoidal. O sistema denominado de Reator Gerador de Flocos (RGF), foi desenvolvido para a geração de flocos aerados ou não (com o uso de um colóide de Fe(OH)3, como modelo) e uma poliacrilamida catiônica de alto peso molecular (Mafloc 490C). Foram testados 5 modelos diferentes de RGFs (variação no comprimento/volume) para a geração dos flocos em diferentes vazões de alimentação e foi selecionado o reator mais eficiente em termos de separação sólido/líquido. Os estudos de avaliação da eficiência de floculação do RGF foram realizados comparativamente através da caracterização dos flocos formados e do comportamento dos flocos numa etapa posterior de separação sólido/líquido. Nos ensaios de geração de flocos não aerados foram medidos o tempo de sedimentação, a turbidez do sobrenadante e o volume sedimentado em cone Imhoff. Ainda, análise fotográfica possibilitou a medição do tamanho dos flocos não aerados e através da correlação logarítmica com a massa dos mesmos, foi possível determinar a dimensão fractal (dF) destes flocos de Fe(OH)3. A eficiência na geração de flocos aerados no RGF com o emprego de microbolhas (diâmetros inferiores a 70 mm) foi avaliada através da velocidade de ascensão dos flocos em uma célula cilíndrica fixa à uma coluna de flotação posterior ao RGF. Estudos de caracterização do regime hidráulico do reator com o emprego de traçadores (azul de metileno) e a determinação do gradiente de velocidade (G) e do número de Reynolds (Re) foram realizados. A curva de resposta do traçador apresentou um pico intenso e estreito, no perfil de velocidade investigado (3L.min-1), caracterizando um fluxo do tipo pistão para o RGF. Ainda, um regime turbulento (Re > 5000) e um G de 1420 s-1 foram determinados. O RGF 3 (modelo 3, com 12m/1,2 L) apresentou a melhor eficiência na geração dos flocos, com e sem o emprego de microbolhas. Nos ensaios de sedimentação, os melhores resultados em termos de velocidade de separação foram obtidos nas seguintes condições experimentais: 4 L.min-1 de vazão de alimentação, 5 mg.L-1 de Mafloc 490C, atingindo velocidade da ordem de 19 m.h-1, turbidez residual de 1 NTU, e volume de sólidos sedimentáveis de 7 mL.L-1. As análises fotográficas permitiram estimar flocos com diâmetros num intervalo entre 400 e 2000 mm. A partir do emprego da equação de sedimentação para fluxo laminar de Stokes, foi constatado o decréscimo da densidade flocos de Fe(OH)3 com o aumento do tamanho dos mesmos, atingindo um valor médio de 1019 kg.m-3. Um dF de 2,98 foi obtido, caracterizando um floco esférico, de baixa porosidade e com estrutura densa. Os melhores resultados na velocidade de ascensão dos flocos aerados foram obtidos com os seguintes parâmetros: vazão de alimentação de 2 L.min-1, concentração de 5 mg.L-1 de Mafloc 490C, sendo obtidas velocidades na ordem de 112 m.h-1. Esses flocos aerados ascendem com velocidades equivalentes à bolhas com diâmetros entre 185 e 240 mm (D50 entre 30-70 mm para as microbolhas individuais e isoladas). A alta velocidade de separação sólido/líquido obtida nos estudos com flocos aerados comparativamente com os flocos não aerados mostram claramente a viabilidade de emprego das microbolhas na separação por floculação- flotação (flutuação). Os resultados obtidos permitem prever um elevado potencial de aplicação em nível industrial do RGF, principalmente por apresentar um baixo tempo de residência, ausência de partes móveis (agitadores), pequena área ocupada, uma mistura do tipo pistão (ideal para floculação), ausência de curto-circuitos ou zonas mortas e um crescimento uniforme com elevada cinética na geração dos flocos.

O desdobramento de uma atitude teórica em relação à linguagem - contriuições empíricas e teóricas para a educação lingüística fundamentadas na Teoria Dialética da Atividade

Este trabalho tem como objetivo investigar a existência de uma atitude teórica com relação à língua em estudantes das Ciências da Linguagem, com o propósito de dar-lhes orientação para que desdobrem sua relação empírica em uma relação teórica com as línguas e com as Ciências da Linguagem. O referencial teórico utilizado tem como base: a Teoria Histórico-Cultural da Atividade (VYGOTSKY, LEONTJEV, LURIA, DAVYDOV, COLE, ERGESTRÖM), a Teoria Bildung – Teoria do Auto-Desenvolvimento Humano (HUMBOLDT, PESTALOZZI, FRÖBEL, KLAFKI) – e a Teoria de Sistemas Evolucionários (mais conhecida através de subteorias como a Teoria do Caos, Geometria Fractal ou Sistema Dinâmico Não-linear – JANTSCH, JUDIN, PRIGOGINE, HAREN, MANDELBOT, FEIGENBAUM, entre outros). O primeiro resultado desta pesquisa é a construção de instrumentos de investigação fundamentados em: (1) uma metodologia baseada na Lógica Dialética para operações heurísticas com conceitos pares; (2) uma Heurística Intradisciplinar para formação de sistemas em Ciências da Linguagem; (3) um projeto de um Experimento Educacional com participantes “ideais”. O segundo resultado expõe as conseqüências da concretização do Experimento Educacional com sete estudantes de Letras da Fundação Universidade Federal de Rio Grande (FURG), num período intermitente de dois anos. Os principais resultados verificados foram que: (1) esses estudantes de Letras possuem um conhecimento tácito sobre teorias lingüísticas; (2) a Heurística Intradisciplinar é um meio produtivo para aprimorar o conhecimento e a habilidade para formação de sistemas auto-refletidos nas Ciências da Linguagem; (3) o uso de Multimídia é uma ferramenta produtiva para criar sistemas complexos interativos; (4) a utilização do Experimento Educacional proporcionou o desencadeamento da iniciação científica dos estudantes do projeto.

Verificação da memória longa persistente no mercado de bitcoins : uma análise do expoente de Hurst ao longo do tempo

Um dos principais fatores de estudo do mercado de capitais é a discussão a respeito da teoria de eficiência de mercado, que no caso diverge em relação ao comportamento do preço da maioria dos ativos. Este trabalho tem o intuito de analisar o comportamento do principal índice de preços do mercado de bitcoins (BPI) durante o período de julho de 2010 a setembro de 2014. Inicialmente será testada a hipótese do passeio aleatório para o BPI. Em seguida serão verificadas as correlações de longa data nas séries financeiras temporais utilizando como instrumento de análise o expoente de Hurst (H), que inicialmente foi usado para calcular correlações em fenômenos naturais e posteriormente sua abrangência alcançou a área financeira. O estudo avalia o expoente H através de métodos distintos destacando-se a análise R/S e a DFA. Para o cálculo do expoente ao longo do tempo, utiliza-se uma janela móvel de 90 dias deslocando-se de 10 em 10 dias. Já para o cálculo em diferentes escalas verifica-se, para cada dia, o valor do expoente H nos últimos 360, 180 e 90 dias respectivamente. Os resultados evidenciaram que o índice BPI apresenta memória longa persistente em praticamente todo o período analisado. Além disso, a análise em diferentes escalas indica a possibilidade de previsão de eventos turbulentos no índice neste mesmo período. Finalmente foi possível comprovar a hipótese de mercados fractais para a série histórica de retornos do BPI.

Simulação de fluxo de fluidos em meios porosos desordenados uma análise de efeito de escala na estimativa da permeabilidade e do coeficiente de arrasto

The present study provides a methodology that gives a predictive character the computer simulations based on detailed models of the geometry of a porous medium. We using the software FLUENT to investigate the flow of a viscous Newtonian fluid through a random fractal medium which simplifies a two-dimensional disordered porous medium representing a petroleum reservoir. This fractal model is formed by obstacles of various sizes, whose size distribution function follows a power law where exponent is defined as the fractal dimension of fractionation Dff of the model characterizing the process of fragmentation these obstacles. They are randomly disposed in a rectangular channel. The modeling process incorporates modern concepts, scaling laws, to analyze the influence of heterogeneity found in the fields of the porosity and of the permeability in such a way as to characterize the medium in terms of their fractal properties. This procedure allows numerically analyze the measurements of permeability k and the drag coefficient Cd proposed relationships, like power law, for these properties on various modeling schemes. The purpose of this research is to study the variability provided by these heterogeneities where the velocity field and other details of viscous fluid dynamics are obtained by solving numerically the continuity and Navier-Stokes equations at pore level and observe how the fractal dimension of fractionation of the model can affect their hydrodynamic properties. This study were considered two classes of models, models with constant porosity, MPC, and models with varying porosity, MPV. The results have allowed us to find numerical relationship between the permeability, drag coefficient and the fractal dimension of fractionation of the medium. Based on these numerical results we have proposed scaling relations and algebraic expressions involving the relevant parameters of the phenomenon. In this study analytical equations were determined for Dff depending on the geometrical parameters of the models. We also found a relation between the permeability and the drag coefficient which is inversely proportional to one another. As for the difference in behavior it is most striking in the classes of models MPV. That is, the fact that the porosity vary in these models is an additional factor that plays a significant role in flow analysis. Finally, the results proved satisfactory and consistent, which demonstrates the effectiveness of the referred methodology for all applications analyzed in this study.

Compositional analysis for an unbiased measure of soil aggregation

Soil aggregation is an index of soil structure measured by mean weight diameter (MWD) or scaling factors often interpreted as fragmentation fractal dimensions (D-f). However, the MWD provides a biased estimate of soil aggregation due to spurious correlations among aggregate-size fractions and scale-dependency. The scale-invariant D-f is based on weak assumptions to allow particle counts and sensitive to the selection of the fractal domain, and may frequently exceed a value of 3, implying that D-f is a biased estimate of aggregation. Aggregation indices based on mass may be computed without bias using compositional analysis techniques. Our objective was to elaborate compositional indices of soil aggregation and to compare them to MWD and D-f using a published dataset describing the effect of 7 cropping systems on aggregation. Six aggregate-size fractions were arranged into a sequence of D-1 balances of building blocks that portray the process of soil aggregation. Isometric log-ratios (ilrs) are scale-invariant and orthogonal log contrasts or balances that possess the Euclidean geometry necessary to compute a distance between any two aggregation states, known as the Aitchison distance (A(x,y)). Close correlations (r>0.98) were observed between MWD, D-f, and the ilr when contrasting large and small aggregate sizes. Several unbiased embedded ilrs can characterize the heterogeneous nature of soil aggregates and be related to soil properties or functions. Soil bulk density and penetrater resistance were closely related to A(x,y) with reference to bare fallow. The A(x,y) is easy to implement as unbiased index of soil aggregation using standard sieving methods and may allow comparisons between studies. (C) 2012 Elsevier B.V. All rights reserved.

Análise e otimização de superfícies seletivas de Frequência utilizando redes neurais artificiais e algoritmos de otimização natural

The bidimensional periodic structures called frequency selective surfaces have been well investigated because of their filtering properties. Similar to the filters that work at the traditional radiofrequency band, such structures can behave as band-stop or pass-band filters, depending on the elements of the array (patch or aperture, respectively) and can be used for a variety of applications, such as: radomes, dichroic reflectors, waveguide filters, artificial magnetic conductors, microwave absorbers etc. To provide high-performance filtering properties at microwave bands, electromagnetic engineers have investigated various types of periodic structures: reconfigurable frequency selective screens, multilayered selective filters, as well as periodic arrays printed on anisotropic dielectric substrates and composed by fractal elements. In general, there is no closed form solution directly from a given desired frequency response to a corresponding device; thus, the analysis of its scattering characteristics requires the application of rigorous full-wave techniques. Besides that, due to the computational complexity of using a full-wave simulator to evaluate the frequency selective surface scattering variables, many electromagnetic engineers still use trial-and-error process until to achieve a given design criterion. As this procedure is very laborious and human dependent, optimization techniques are required to design practical periodic structures with desired filter specifications. Some authors have been employed neural networks and natural optimization algorithms, such as the genetic algorithms and the particle swarm optimization for the frequency selective surface design and optimization. This work has as objective the accomplishment of a rigorous study about the electromagnetic behavior of the periodic structures, enabling the design of efficient devices applied to microwave band. For this, artificial neural networks are used together with natural optimization techniques, allowing the accurate and efficient investigation of various types of frequency selective surfaces, in a simple and fast manner, becoming a powerful tool for the design and optimization of such structures

Estudo do acoplamento entre superfícies seletivas de frequência assimétricas em estruturas de multicamadas

This work presents the development of new microwaves structures, filters and high gain antenna, through the cascading of frequency selective surfaces, which uses fractals Dürer and Minkowski patches as elements, addition of an element obtained from the combination of the other two simple the cross dipole and the square spiral. Frequency selective surfaces (FSS) includes a large area of Telecommunications and have been widely used due to its low cost, low weight and ability to integrate with others microwaves circuits. They re especially important in several applications, such as airplane, antennas systems, radomes, rockets, missiles, etc. FSS applications in high frequency ranges have been investigated, as well as applications of cascading structures or multi-layer, and active FSS. In this work, we present results for simulated and measured transmission characteristics of cascaded structures (multilayer), aiming to investigate the behavior of the operation in terms of bandwidth, one of the major problems presented by frequency selective surfaces. Comparisons are made with simulated results, obtained using commercial software such as Ansoft DesignerTM v3 and measured results in the laboratory. Finally, some suggestions are presented for future works on this subject

Análise e síntese de antenas e superfícies seletivas de frequência utilizando computação evolucionária e inteligência de enxames

The frequency selective surfaces, or FSS (Frequency Selective Surfaces), are structures consisting of periodic arrays of conductive elements, called patches, which are usually very thin and they are printed on dielectric layers, or by openings perforated on very thin metallic surfaces, for applications in bands of microwave and millimeter waves. These structures are often used in aircraft, missiles, satellites, radomes, antennae reflector, high gain antennas and microwave ovens, for example. The use of these structures has as main objective filter frequency bands that can be broadcast or rejection, depending on the specificity of the required application. In turn, the modern communication systems such as GSM (Global System for Mobile Communications), RFID (Radio Frequency Identification), Bluetooth, Wi-Fi and WiMAX, whose services are highly demanded by society, have required the development of antennas having, as its main features, and low cost profile, and reduced dimensions and weight. In this context, the microstrip antenna is presented as an excellent choice for communications systems today, because (in addition to meeting the requirements mentioned intrinsically) planar structures are easy to manufacture and integration with other components in microwave circuits. Consequently, the analysis and synthesis of these devices mainly, due to the high possibility of shapes, size and frequency of its elements has been carried out by full-wave models, such as the finite element method, the method of moments and finite difference time domain. However, these methods require an accurate despite great computational effort. In this context, computational intelligence (CI) has been used successfully in the design and optimization of microwave planar structures, as an auxiliary tool and very appropriate, given the complexity of the geometry of the antennas and the FSS considered. The computational intelligence is inspired by natural phenomena such as learning, perception and decision, using techniques such as artificial neural networks, fuzzy logic, fractal geometry and evolutionary computation. This work makes a study of application of computational intelligence using meta-heuristics such as genetic algorithms and swarm intelligence optimization of antennas and frequency selective surfaces. Genetic algorithms are computational search methods based on the theory of natural selection proposed by Darwin and genetics used to solve complex problems, eg, problems where the search space grows with the size of the problem. The particle swarm optimization characteristics including the use of intelligence collectively being applied to optimization problems in many areas of research. The main objective of this work is the use of computational intelligence, the analysis and synthesis of antennas and FSS. We considered the structures of a microstrip planar monopole, ring type, and a cross-dipole FSS. We developed algorithms and optimization results obtained for optimized geometries of antennas and FSS considered. To validate results were designed, constructed and measured several prototypes. The measured results showed excellent agreement with the simulated. Moreover, the results obtained in this study were compared to those simulated using a commercial software has been also observed an excellent agreement. Specifically, the efficiency of techniques used were CI evidenced by simulated and measured, aiming at optimizing the bandwidth of an antenna for wideband operation or UWB (Ultra Wideband), using a genetic algorithm and optimizing the bandwidth, by specifying the length of the air gap between two frequency selective surfaces, using an optimization algorithm particle swarm

Novas configurações de monopólios planares quase-fractais para sistemas de comunicações móveis

The characteristic properties of the fractal geometry have shown to be very useful for the construction of filters, frequency selective surfaces, synchronized circuits and antennas, enabling optimized solutions in many different commercial uses at microwaves frequency band. The fractal geometry is included in the technology of the microwave communication systems due to some interesting properties to the fabrication of compact devices, with higher performance in terms of bandwidth, as well as multiband behavior. This work describes the design, fabrication and measurement procedures for the Koch quasi-fractal monopoles, with 1 and 2 iteration levels, in order to investigate the bandwidth behavior of planar antennas, from the use of quasi-fractal elements printed on their rectangular patches. The electromagnetic effect produced by the variation of the fractal iterations and the miniaturization of the structures is analyzed. Moreover, a parametric study is performed to verify the bandwidth behavior, not only at the return loss but also in terms of SWR. Experimental results were obtained through the accomplishment of measurements with the aid of a vetorial network analyzer and compared to simulations performed using the Ansoft HFSS software. Finally, some proposals for future works are presented

Análise e projeto de superfícies seletivas de frequência com elementos pré-fractais para aplicações em comunicações indoor

In this thesis, a frequency selective surface (FSS) consists of a two-dimensional periodic structure mounted on a dielectric substrate, which is capable of selecting signals in one or more frequency bands of interest. In search of better performance, more compact dimensions, low cost manufacturing, among other characteristics, these periodic structures have been continually optimized over time. Due to its spectral characteristics, which are similar to band-stop or band-pass filters, the FSSs have been studied and used in several applications for more than four decades. The design of an FSS with a periodic structure composed by pre-fractal elements facilitates the tuning of these spatial filters and the adjustment of its electromagnetic parameters, enabling a compact design which generally has a stable frequency response and superior performance relative to its euclidean counterpart. The unique properties of geometric fractals have shown to be useful, mainly in the production of antennas and frequency selective surfaces, enabling innovative solutions and commercial applications in microwave range. In recent applications, the FSSs modify the indoor propagation environments (emerging concept called wireless building ). In this context, the use of pre-fractal elements has also shown promising results, allowing a more effective filtering of more than one frequency band with a single-layer structure. This thesis approaches the design of FSSs using pre-fractal elements based on Vicsek, Peano and teragons geometries, which act as band-stop spatial filters. The transmission properties of the periodic surfaces are analyzed to design compact and efficient devices with stable frequency responses, applicable to microwave frequency range and suitable for use in indoor communications. The results are discussed in terms of the electromagnetic effect resulting from the variation of parameters such as: fractal iteration number (or fractal level), scale factor, fractal dimension and periodicity of FSS, according the pre-fractal element applied on the surface. The analysis of the fractal dimension s influence on the resonant properties of a FSS is a new contribution in relation to researches about microwave devices that use fractal geometry. Due to its own characteristics and the geometric shape of the Peano pre-fractal elements, the reconfiguration possibility of these structures is also investigated and discussed. This thesis also approaches, the construction of efficient selective filters with new configurations of teragons pre-fractal patches, proposed to control the WLAN coverage in indoor environments by rejecting the signals in the bands of 2.4~2.5 GHz (IEEE 802.11 b) and 5.0~6.0 GHz (IEEE 802.11a). The FSSs are initially analyzed through simulations performed by commercial software s: Ansoft DesignerTM and HFSSTM. The fractal design methodology is validated by experimental characterization of the built prototypes, using alternatively, different measurement setups, with commercial horn antennas and microstrip monopoles fabricated for low cost measurements

Otimização de superfícies seletivas de frequência com elementos pré-fractais utilizando rede neural MLP e algoritmos de busca populacional

This thesis describes design methodologies for frequency selective surfaces (FSSs) composed of periodic arrays of pre-fractals metallic patches on single-layer dielectrics (FR4, RT/duroid). Shapes presented by Sierpinski island and T fractal geometries are exploited to the simple design of efficient band-stop spatial filters with applications in the range of microwaves. Initial results are discussed in terms of the electromagnetic effect resulting from the variation of parameters such as, fractal iteration number (or fractal level), fractal iteration factor, and periodicity of FSS, depending on the used pre-fractal element (Sierpinski island or T fractal). The transmission properties of these proposed periodic arrays are investigated through simulations performed by Ansoft DesignerTM and Ansoft HFSSTM commercial softwares that run full-wave methods. To validate the employed methodology, FSS prototypes are selected for fabrication and measurement. The obtained results point to interesting features for FSS spatial filters: compactness, with high values of frequency compression factor; as well as stable frequency responses at oblique incidence of plane waves. This thesis also approaches, as it main focus, the application of an alternative electromagnetic (EM) optimization technique for analysis and synthesis of FSSs with fractal motifs. In application examples of this technique, Vicsek and Sierpinski pre-fractal elements are used in the optimal design of FSS structures. Based on computational intelligence tools, the proposed technique overcomes the high computational cost associated to the full-wave parametric analyzes. To this end, fast and accurate multilayer perceptron (MLP) neural network models are developed using different parameters as design input variables. These neural network models aim to calculate the cost function in the iterations of population-based search algorithms. Continuous genetic algorithm (GA), particle swarm optimization (PSO), and bees algorithm (BA) are used for FSSs optimization with specific resonant frequency and bandwidth. The performance of these algorithms is compared in terms of computational cost and numerical convergence. Consistent results can be verified by the excellent agreement obtained between simulations and measurements related to FSS prototypes built with a given fractal iteration

Arranjos Log-Periódicos Compactos em Microfita com Elementos Fractais de Koch

This work aims to present how the application of fractal geometry to the elements of a log-periodic array can become a good alternative when one wants to reduce the size of the array. Two types of log-periodic arrays were proposed: one with fed by microstrip line and other fed by electromagnetic coupling. To the elements of these arrays were applied fractal Koch contours, at two levels. In order to validate the results obtained some prototypes were built, which were measured on a vector network analyzer and simulated in a software, for comparison. The results presented reductions of 60% in the total area of the arrays, for both types. By analyzing the graphs of return loss, it was observed that the application of fractal contours made different resonant frequencies appear in the arrays. Furthermore, a good agreement was observed between simulated and measured results. The array with feeding by electromagnetic coupling presented, after application of fractal contours, radiation pattern with more smooth forms than the array with feeding by microstrip line

Efeito da inclinação do plano de terra para antenas de microfita multicamadas com elementos parasitas fractais

This work presents the analysis of an antenna of fractal microstrip of Koch with dielectric multilayers and inclinations in the ground plane, whose values of the angles are zero degree (without inclinations), three, seven and twelve degrees. This antenna consists of three dielectric layers arranged vertically on each other, using feeding microstrip line in patch 1, of the first layer, which will feed the remaining patches of the upper layers by electromagnetic coupling. The objective of this work is to analyze the effects caused by increase of the angle of inclination of the ground plane in some antenna parameters such as return loss, resonant frequency, bandwidth and radiation pattern. The presented results demonstrate that with the increase of the inclination angle it is possible to get antennas with characteristics multiband, with bigger bandwidth, and improving the impedance matching for each case analyzed, especially the larger angle

Estudo do efeito de substratos metamateriais em parâmetros de antenas de microfita

Microstrip antennas are subject matter in several research fields due to its numerous advantages. The discovery, at 1999, of a new class of materials called metamaterials - usually composed of metallic elements immersed in a dielectric medium, have attracted the attention of the scientific community, due to its electromagnetic properties, especially the ability to use in planar structures, such as microstrip, without interfering with their traditional geometry. The aim of this paper is to analyze the effects of one and bidimensional metamaterial substrates in microstrip antennas, with different configurations of resonance rings, SRR, in the dielectric layer. Fractal geometry is applied to these rings, in seeking to verify a multiband behavior and to reduce the resonance frequency of the antennas. The results are then given by commercial software Ansoft HFSS, used for precise analysis of the electromagnetic behavior of antennas by Finite Element Method (FEM). To reach it, this essay will first perform a literature study on fractal geometry and its generative process. This paper also presents an analysis of microstrip antennas, with emphasis on addressing different types of substrates as part of its electric and magnetic anisotropic behavior. It s performed too an approach on metamaterials and their unique properties