Search results for: fractal method

Authors: Manish Kumar Thakur, Subrata Kumar Ghosh

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Various types of particles found in lubricant may be characterized by their fractal dimension. Some of the available methods are: yard-stick method or structured walk method, box-counting method. This paper presents a review of the developments and progress in fractal dimension computing methods as applied to characteristics the surface of wear particles. An overview of these methods, their implementation, their advantages and their limits is also present here. It has been accepted that wear particles contain major information about wear and friction of materials. Morphological analysis of wear particles from a lubricant is a very effective way for machine condition monitoring. Fractal dimension methods are used to characterize the morphology of the found particles. It is very useful in the analysis of complexity of irregular substance. The aim of this review is to bring together the fractal methods applicable for wear particles.

Keywords: fractal dimension, morphological analysis, wear, wear particles

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Authors: Zerroug Abdelhamid, Danielle Chassoux

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Various models are given to simulate homogeneous or heterogeneous cancerous tumors and extract in each case the boundary. The fractal dimension is then estimated by least squares method and compared to some previous methods.

Keywords: simulation, cancerous tumor, Markov fields, fractal dimension, extraction, recovering

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Authors: Khaled Harrar, Rachid Jennane

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The purpose of this study is the discrimination of 28 postmenopausal with osteoporotic femoral fractures from an age-matched control group of 28 women using texture analysis based on fractals. Two pre-processing approaches are applied on radiographic images; these techniques are compared to highlight the choice of the pre-processing method. Furthermore, the values of the fractal dimension are compared to those of the fractal signature in terms of the classification of the two populations. In a second analysis, the BMD measure at proximal femur was compared to the fractal analysis, the latter, which is a non-invasive technique, allowed a better discrimination; the results confirm that the fractal analysis of texture on calcaneus radiographs is able to discriminate osteoporotic patients with femoral fracture from controls. This discrimination was efficient compared to that obtained by BMD alone. It was also present in comparing subgroups with overlapping values of BMD.

Keywords: osteoporosis, fractal dimension, fractal signature, bone mineral density

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Authors: V. V. Reddy, N. V. Sarma

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A circularly polarized fractal boundary microstrip antenna is presented. The sides of a square patch along x-axis, y-axis are replaced with Minkowski and Koch curves correspondingly. By using the fractal curves as edges, asymmetry in the structure is created to excite two orthogonal modes for circular polarization (CP) operation. The indentation factors of the fractal curves are optimized for pure CP. The simulated results of the novel poly fractal antenna are demonstrated.

Keywords: fractal, circular polarization, Minkowski, Koch

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Authors: Saeedeh Shahbazkhany

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Cancer is a terrible disease that, if not diagnosed early, therapy can be difficult while it is easily medicable if it is diagnosed in early stages. So it is very important for cancer diagnosis that medical procedures are performed. In this paper we introduce a new method. In this method, we only need pictures of healthy cells and cancer cells. In fact, where we suspect cancer, we take a picture of cells or tissue in that area, and then take some pictures of the surrounding tissues. Then, fractal dimension of images are calculated and compared. Cancer can be easily detected by comparing the fractal dimension of images. In this method, we use Matlab software.

Keywords: Matlab software, fractal dimension, cancer, surrounding tissues, cells or tissue, new method

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Authors: O. Boussoufi, K. Lamrini Uahabi, M. Atounti

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The main purpose of this paper is to calculate the fractal dimension of some Julia Sets and Mandelbrot Set in the Misiurewicz Points. Using Matlab to generate the Julia Sets images that match the Misiurewicz points and using a Fractal software, we were able to find different measures that characterize those fractals in textures and other features. We are actually focusing on fractal dimension and the error calculated by the software. When executing the given equation of regression or the log-log slope of image a Box Counting method is applied to the entire image, and chosen settings are available in a FracLAc Program. Finally, a comparison is done for each image corresponding to the area (boundary) where Misiurewicz Point is located.

Keywords: box counting, FracLac, fractal dimension, Julia Sets, Mandelbrot Set, Misiurewicz Points

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Authors: S. Sushma, S. Balasubramanian, K. C. Latha, R. Sridhar

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Structural texture measures are used to address the aspect of breast cancer risk assessment in screening mammograms. The current study investigates whether texture properties characterized by local Fractal Dimension (FD) and lacunarity contribute to assess breast cancer risk. Fractal Dimension represents the complexity while the lacunarity characterize the gap of a fractal dimension. In this paper, we present our result confirming that the lacunarity value resulted in algorithm using mammogram images states that level of lacunarity will be low when the Fractal Dimension value will be high.

Keywords: breast cancer, fractal dimension, image analysis, lacunarity, mammogram

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Authors: Hamidreza Namazi

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Fractal analysis is assessing fractal characteristics of data. It consists of several methods to assign fractal characteristics to a dataset which may be a theoretical dataset or a pattern or signal extracted from phenomena including natural geometric objects, sound, market fluctuations, heart rates, digital images, molecular motion, networks, etc. Fractal analysis is now widely used in all areas of science. An important limitation of fractal analysis is that arriving at an empirically determined fractal dimension does not necessarily prove that a pattern is fractal; rather, other essential characteristics have to be considered. For this purpose a Visual C++ based software called FRATSAN (FRActal Time Series ANalyser) was developed which extract information from signals through three measures. These measures are Fractal Dimensions, Jeffrey’s Measure and Hurst Exponent. After computing these measures, the software plots the graphs for each measure. Besides computing three measures the software can classify whether the signal is fractal or no. In fact, the software uses a dynamic method of analysis for all the measures. A sliding window is selected with a value equal to 10% of the total number of data entries. This sliding window is moved one data entry at a time to obtain all the measures. This makes the computation very sensitive to slight changes in data, thereby giving the user an acute analysis of the data. In order to test the performance of this software a set of EEG signals was given as input and the results were computed and plotted. This software is useful not only for fundamental fractal analysis of signals but can be used for other purposes. For instance by analyzing the Hurst exponent plot of a given EEG signal in patients with epilepsy the onset of seizure can be predicted by noticing the sudden changes in the plot.

Keywords: EEG signals, fractal analysis, fractal dimension, hurst exponent, Jeffrey’s measure

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Authors: A. El Hamdouni, J. Zbitou, A. Tajmouati, L. El Abdellaoui, A. Errkik, A. Tribak, M. Latrach

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This paper presents a novel fractal antenna structure proposed for UWB (Ultra – Wideband) applications. The frequency band 3.1-10.6 GHz released by FCC (Federal Communication Commission) as the commercial operation of UWB has been chosen as frequency range for this antenna based on coplanar waveguide (CPW) feed and circular shapes fulfilled according to fractal geometry. The proposed antenna is validated and designed by using an FR4 substrate with overall area of 34 x 43 mm2. The simulated results performed by CST-Microwave Studio and compared by ADS (Advanced Design System) show good matching input impedance with return loss less than -10 dB between 2.9 GHz and 11 GHz.

Keywords: Fractal antenna, Fractal Geometry, CPW Feed, UWB, FCC

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Authors: Mitra Saberi, Saeideh Fakhari, Amir Karam, Ali Ahmadabadi

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Geomorphology is the scientific study of the characteristics of form and shape of the Earth's surface. The existence of types of landforms and their variation is mainly controlled by changes in the shape and position of land and topography. In fact, the interest and application of fractal issues in geomorphology is due to the fact that many geomorphic landforms have fractal structures and their formation and transformation can be explained by mathematical relations. The purpose of this study is to identify and analyze the fractal behavior of landforms of macro geomorphologic regions of Iran, as well as studying and analyzing topographic and landform characteristics based on fractal relationships. In this study, using the Iranian digital elevation model in the form of slopes, coefficients of deposition and alluvial fan, the fractal dimensions of the curves were calculated through the box counting method. The morphometric characteristics of the landforms and their fractal dimension were then calculated for 4criteria (height, slope, profile curvature and planimetric curvature) and indices (maximum, Average, standard deviation) using ArcMap software separately. After investigating their correlation with fractal dimension, two-way regression analysis was performed and the relationship between fractal dimension and morphometric characteristics of landforms was investigated. The results show that the fractal dimension in different pixels size of 30, 90 and 200m, topographic curves of different landform units of Iran including mountain, hill, plateau, plain of Iran, from1.06in alluvial fans to1.17in The mountains are different. Generally, for all pixels of different sizes, the fractal dimension is reduced from mountain to plain. The fractal dimension with the slope criterion and the standard deviation index has the highest correlation coefficient, with the curvature of the profile and the mean index has the lowest correlation coefficient, and as the pixels become larger, the correlation coefficient between the indices and the fractal dimension decreases.

Keywords: box counting method, fractal dimension, geomorphology, Iran, landform

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Authors: Fuad M. Alkoot

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The main component of a machine learning system is the classifier. Classifiers are mathematical models that can perform classification tasks for a specific application area. Additionally, many classifiers are combined using any of the available methods to reduce the classifier error rate. The benefits gained from the combination of multiple classifier designs has motivated the development of diverse approaches to multiple classifiers. We aim to investigate using fractal geometry to develop an improved classifier combiner. Initially we experiment with measuring the fractal dimension of data and use the results in the development of a combiner strategy.

Keywords: fractal geometry, machine learning, classifier, fractal dimension

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Authors: Md. Enamul Haque, Abdullah Al Kaisan, Mahmudur R. Saniat, Aminur Rahman

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In this paper, we have implemented both sequential and parallel version of fractal image compression algorithms using CUDA (Compute Unified Device Architecture) programming model for parallelizing the program in Graphics Processing Unit for medical images, as they are highly similar within the image itself. There is several improvements in the implementation of the algorithm as well. Fractal image compression is based on the self similarity of an image, meaning an image having similarity in majority of the regions. We take this opportunity to implement the compression algorithm and monitor the effect of it using both parallel and sequential implementation. Fractal compression has the property of high compression rate and the dimensionless scheme. Compression scheme for fractal image is of two kinds, one is encoding and another is decoding. Encoding is very much computational expensive. On the other hand decoding is less computational. The application of fractal compression to medical images would allow obtaining much higher compression ratios. While the fractal magnification an inseparable feature of the fractal compression would be very useful in presenting the reconstructed image in a highly readable form. However, like all irreversible methods, the fractal compression is connected with the problem of information loss, which is especially troublesome in the medical imaging. A very time consuming encoding process, which can last even several hours, is another bothersome drawback of the fractal compression.

Keywords: accelerated GPU, CUDA, parallel computing, fractal image compression

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Authors: Abraham Terán Salcedo, Didier Samayoa Ochoa

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This work presents a numerical implementation of a method for estimating the box-counting dimension of self-avoiding curves on a planar space, fractal objects captured on digital images; this method is named fractioning estimator. Classical methods of digital image processing, such as noise filtering, contrast manipulation, and thresholding, among others, are used in order to obtain binary images that are suitable for performing the necessary computations of the fractioning estimator. A user interface is developed for performing the image processing operations and testing the fractioning estimator on different captured images of real-life fractal objects. To analyze the results, the estimations obtained through the fractioning estimator are compared to the results obtained through other methods that are already implemented on different available software for computing and estimating the box-counting dimension.

Keywords: box-counting, digital image processing, fractal dimension, numerical method

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Authors: Adnan H. M. Al-Helali, Hamza A. Ali

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The growth of censorship and pervasive monitoring on the Internet, Steganography arises as a new means of achieving secret communication. Steganography is the art and science of embedding information within electronic media used by common applications and systems. Generally, hiding information of multimedia within images will change some of their properties that may introduce few degradation or unusual characteristics. This paper presents a new image steganography approach for hiding information of multimedia (images, text, and audio) using generated Mandelbrot Fractal image as a cover. The proposed technique has been extensively tested with different images. The results show that the method is a very secure means of hiding and retrieving steganographic information. Experimental results demonstrate that an effective improvement in the values of the Peak Signal to Noise Ratio (PSNR), Mean Square Error (MSE), Normalized Cross Correlation (NCC), and Image Fidelity (IF) over the pervious techniques.

Keywords: fractal image, information hiding, Mandelbrot set fractal, steganography

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Authors: I. Slim, H. Akkari, A. Ben Abdallah, I. Bhouri, M. Hedi Bedoui

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Osteoporosis is a common disease characterized by low bone mass and deterioration of micro-architectural bone tissue, which provokes an increased risk of fracture. This work treats the texture characterization of trabecular bone radiographs. The aim was to analyze according to clinical research a group of 174 subjects: 87 osteoporotic patients (OP) with various bone fracture types and 87 control cases (CC). To characterize osteoporosis, Fractal and MultiFractal (MF) methods were applied to images for features (attributes) extraction. In order to improve the results, a new method of MF spectrum based on the q-stucture function calculation was proposed and a combination of Fractal and MF attributes was used. The Support Vector Machines (SVM) was applied as a classifier to distinguish between OP patients and CC subjects. The features fusion (fractal and MF) allowed a good discrimination between the two groups with an accuracy rate of 96.22%.

Keywords: fractal, micro-architecture analysis, multifractal, osteoporosis, SVM

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Authors: T. Benyetho, L. El Abdellaoui, J. Terhzaz, H. Bennis, N. Ababssi, A. Tajmouati, A. Tribak, M. Latrach

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This work presents a new planar multiband antenna based on fractal geometry. This structure is optimized and validated into simulation by using CST-MW Studio. To feed this antenna we have used a CPW line which makes it easy to be incorporated with integrated circuits. The simulation results presents a good matching input impedance and radiation pattern in the GSM band at 900 MHz and ISM band at 2.4 GHz. The final structure is a dual band fractal antenna with 70 x 70 mm² as a total area by using an FR4 substrate.

Keywords: Antenna, CPW, fractal, GSM, multiband

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Authors: Kamal, Adil Ahmad

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Earthquakes are among the most versatile natural and dynamic processes, and hence a fractal model is considered to be the best representative of the same. We present a novel method to process and analyse information hidden in earthquake sequences using Fractal Dimensions and Iterative Function Systems (IFS). Spatial and temporal variations in the fractal dimensions of seismicity observed around the Indian peninsula in last 30 years are studied. This was used as a possible precursor before large earthquakes in the region. IFS images for observed seismicity in the Himalayan belt were also obtained. We scan the whole data set and coarse grain of a selected window to reduce it to four bins. A critical analysis of four-cornered chaos-game clearly shows that the spatial variation in earthquake occurrences in Himalayan range is not random. Two subzones of Himalaya have a tendency to follow each other in time.

Keywords: earthquakes, fractals, Himalaya, iterated function systems

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Authors: Gülşen Akın Evingür, Önder Pekcan

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The fractal analysis is a bridge between the microstructure and macroscopic properties of gels. Fractal structure is usually provided to define the complexity of crosslinked molecules. The complexity in gel systems is described by the fractal dimension (Df). In this study, polyacrylamide- graphene oxide (GO) composite gels were prepared by free radical crosslinking copolymerization. The fractal analysis of polyacrylamide- graphene oxide (GO) composite gels were analyzed in various GO contents during gelation and were investigated by using Fluorescence Technique. The analysis was applied to estimate Df s of the composite gels. Fractal dimension of the polymer composite gels were estimated based on the power law exponent values using scaling models. In addition, here we aimed to present the geometrical distribution of GO during gelation. And we observed that as gelation proceeded GO plates first organized themselves into 3D percolation cluster with Df=2.52, then goes to diffusion limited clusters with Df =1.4 and then lines up to Von Koch curve with random interval with Df=1.14. Here, our goal is to try to interpret the low conductivity and/or broad forbidden gap of GO doped PAAm gels, by the distribution of GO in the final form of the produced gel.

Keywords: composite gels, fluorescence, fractal, scaling

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Authors: Narek Margaryan, Zhozef Panosyan

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Due to their unique properties, carbon nanofilms have become the object of general attention and intensive research. In this case it plays a very important role to study surface properties of these films. It is also important to study processes of forming of this films, which is accompanied by a process of self-organization at the nano and micro levels. For more detailed investigation, we examined diamond-like carbon (DLC) layers deposited by chemical vapor deposition (CVD) method on Ge substrate and hydro-generated grapheme layers obtained on surface of colloidal solution using grouping method. In this report surface transformation of these CVD nanolayers is studied by atomic force microscopy (AFM) upon deposition time. Also, it can be successfully used to study surface properties of self-assembled grapheme layers. In turn, it is possible to sketch out their boundary line, which enables one to draw an idea of peculiarities of formation of these layers. Images obtained by AFM are investigated as a mathematical set of numbers and fractal and roughness analysis were done. Fractal dimension, Regne’s fractal coefficient, histogram, Fast Fourier transformation, etc. were obtained. The dependence of fractal parameters on the deposition duration for CVD films and on temperature of solution tribolayers was revealed. As an important surface parameter for our carbon films, surface energy was calculated as function of Regne’s fractal coefficient. Surface potential was also measured with Kelvin probe method using semi-contacting AFM. The dependence of surface potential on the deposition duration for CVD films and on temperature of solution for hydro-generated graphene was found as well. Results obtained by fractal analysis method was related with purly esperimental results for number of samples.

Keywords: nanostructured films, self-assembled grapheme, diamond-like carbon, surface potential, Kelvin probe method, fractal analysis

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Authors: Mohammadsadegh Zanganehfar

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Since the introduction of fractal geometry in 1970, numerous efforts have been made by architects and researchers to transfer this area of mathematical knowledge in the discipline of architecture and postmodernist discourse. The discourse of complexity and architecture is one of the most significant ongoing discourses in the discipline of architecture from the '70s until today and has generated significant styles such as deconstructivism and parametrism in architecture. During these years, several projects were designed and presented by designers and architects using fractal geometry, but due to the lack of sufficient knowledge and appropriate comprehension of the features and characteristics of this nonlinear geometry, none of the fractal-based designs have been successful and satisfying. Fractal geometry as a geometric technology has a long presence in the history of architecture. The current research attempts to identify and discover the characteristics, features, potentials, and functionality of fractals despite their aesthetic aspect by examining case studies of pre-modern architecture in Asia and investigating the function of fractals.

Keywords: Asian architecture, fractal geometry, fractal technique, geometric properties

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Authors: T. K. Dutta, K. K. Das, N. Dutta

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The salient feature of this paper is primarily concerned with Ricker’s population model: f(x)=x e^(r(1-x/k)), where r is the control parameter and k is the carrying capacity, and some fruitful results are obtained with the following objectives: 1) Determination of bifurcation values leading to a chaotic region, 2) Development of Statistical Methods and Analysis required for the measure of Fractal dimensions, 3) Calculation of various fractal dimensions. These results also help that the invariant probability distribution on the attractor, when it exists, provides detailed information about the long-term behavior of a dynamical system. At the end, some open problems are posed for further research.

Keywords: Feigenbaum universality, chaos, Lyapunov exponent, fractal dimensions

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Authors: Darsh N. Patel, Eric Olson

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Fractals can be found everywhere, whether it be the shape of a leaf or a system of blood vessels. Fractals are used to help study and understand different physical and mathematical processes; however, their artistic nature is also beautiful to simply explore. This project explores fractals generated by a cubically convergent extension to Newton's method. With this iteration as a starting point, a complex plane spanning from -2 to 2 is created with a color wheel mapped onto it. Next, the polynomial whose roots the fractal will generate from is established. From the Fundamental Theorem of Algebra, it is known that any polynomial has as many roots (counted by multiplicity) as its degree. When generating the fractals, each root will receive its own color. The complex plane can then be colored to indicate the basins of attraction that converge to each root. From a computational point of view, this project’s code identifies which points converge to which roots and then obtains fractal images. A zoom path into the fractal was implemented to easily visualize the self-similar structure. This path was obtained by selecting keyframes at different magnifications through which a path is then interpolated. Using parallel processing, many images were generated and condensed into a video. This project illustrates how practical techniques used for scientific visualization can also have an artistic side.

Keywords: fractals, cubic method, Julia programming language, basin of attraction

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Authors: Rhea Kapoor

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Fractal dimension provides a way to characterize non-geometric shapes like those found in nature. The purpose of this research is to estimate Minkowski fractal dimension of human lung images for early detection of lung cancer. Lung cancer is the leading cause of death among all types of cancer and an early histopathological analysis will help reduce deaths primarily due to late diagnosis. A Python application program, PathoPy2.0, was developed for analyzing medical images in pixelated format and estimating Minkowski fractal dimension using a new box-counting algorithm that allows windowing of images for more accurate calculation in the suspected areas of cancerous growth. Benchmark geometric fractals were used to validate the accuracy of the program and changes in fractal dimension of lung images to indicate the presence of issues in the lung. The accuracy of the program for the benchmark examples was between 93-99% of known values of the fractal dimensions. Fractal dimension values were then calculated for lung images, from National Cancer Institute, taken over time to correctly detect the presence of cancerous growth. For example, as the fractal dimension for a given lung increased from 1.19 to 1.27 due to cancerous growth, it represents a significant change in fractal dimension which lies between 1 and 2 for 2-D images. Based on the results obtained on many lung test cases, it was concluded that fractal dimension of human lungs can be used to diagnose lung cancer early. The ideas behind PathoPy2.0 can also be applied to study patterns in the electrical activity of the human brain and DNA matching.

Keywords: fractals, histopathological analysis, image processing, lung cancer, Minkowski dimension

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Authors: Adnan H. M. Al-Helali, Hamza A. Ali

Abstract:

Growth of censorship and pervasive monitoring on the Internet, Steganography arises as a new means of achieving secret communication. Steganography is the art and science of embedding information within electronic media used by common applications and systems. Generally, hiding information of multimedia within images will change some of their properties that may introduce few degradation or unusual characteristics. This paper presents a new image steganography approach for hiding information of multimedia (images, text, and audio) using generated Mandelbrot Fractal image as a cover. The proposed technique has been extensively tested with different images. The results show that the method is a very secure means of hiding and retrieving steganographic information. Experimental results demonstrate that an effective improvement in the values of the Peak Signal to Noise Ratio (PSNR), Mean Square Error (MSE), Normalized Cross Correlation (NCC) and Image Fidelity (IF) over the previous techniques.

Keywords: fractal image, information hiding, Mandelbrot et fractal, steganography

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Authors: Fatima Achouri, Kaddour Chouicha, Abdelwahab Khatir

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It is clear that concrete of quality must be made with selected materials chosen in optimum proportions that remain after implementation, a minimum of voids in the material produced. The different methods of formulations what we use, are based for the most part on a granular curve which describes an ‘optimal granularity’. Many authors have engaged in fundamental research on granular arrangements. A comparison of mathematical models reproducing these granular arrangements with experimental measurements of compactness have to verify that the minimum porosity P according to the following extent granular exactly a power law. So the best compactness in the finite medium are obtained with power laws, such as Furnas, Fuller or Talbot, each preferring a particular setting between 0.20 and 0.50. These considerations converge on the assumption that the optimal granularity Caquot approximates by a power law. By analogy, it can then be analyzed as a granular structure of fractal-type since the properties that characterize the internal similarity fractal objects are reflected also by a power law. Optimized mixtures may be described as a series of installments falling granular stuff to better the tank on a regular hierarchical distribution which would give at different scales, by cascading effects, the same structure to the mix. Likely this model may be appropriate for the entire extent of the size distribution of the components, since the cement particles (and silica fume) correctly deflocculated, micrometric dimensions, to chippings sometimes several tens of millimeters. As part of this research, the aim is to give an illustration of the application of fractal analysis to characterize the granular concrete mixtures optimized for a so-called fractal dimension where different concretes were studying that we proved a fractal structure of their granular mixtures regardless of the method of formulation or the type of concrete.

Keywords: concrete formulation, fractal character, granular packing, method of formulation

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Authors: Youness Laaroussi, Zine Elabidine Guennoun, Amine Amar

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Modeling and forecasting dynamics of rainfall occurrences constitute one of the major topics, which have been largely treated by statisticians, hydrologists, climatologists and many other groups of scientists. In the same issue, we propose in the present paper a new hybrid method, which combines Extreme Values and fractal theories. We illustrate the use of our methodology for transformed Emberger Index series, constructed basing on data recorded in Oujda (Morocco). The index is treated at first by Peaks Over Threshold (POT) approach, to identify excess observations over an optimal threshold u. In the second step, we consider the resulting excess as a fractal object included in one dimensional space of time. We identify fractal dimension by the box counting. We discuss the prospect descriptions of rainfall data sets under Generalized Pareto Distribution, assured by Extreme Values Theory (EVT). We show that, despite of the appropriateness of return periods given by POT approach, the introduction of fractal dimension provides accurate interpretation results, which can ameliorate apprehension of rainfall occurrences.

Keywords: extreme values theory, fractals dimensions, peaks Over threshold, rainfall occurrences

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Authors: Beibit Karibayev, Akmaral Imanbayeva, Timur Namazbayev

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Currently, the small spacecraft (SSC) industry is experiencing a big boom in popularity. This is primarily due to ease of use, low cost and mobility. In addition, these programs can be implemented not only at the state level but also at the level of companies, universities and other organizations. For remote sensing of the Earth (ERS), small spacecraft with an orientation system is used. It is important to take into account here that a remote sensing device, for example, a camera for photographing the Earth's surface, must be directed at the Earth's surface. But this, at first glance, the limitation can be turned into an advantage using a patch antenna. This work proposed to use a patch antenna based on a unidirectional fractal in the SSC. The CST Microwave Studio software package was used for simulation and research. Copper (ε = 1.0) was chosen as the emitting element and reflector. The height of the substrate was 1.6 mm, the type of substrate material was FR-4 (ε = 4.3). The simulation was performed in the frequency range of 0 – 6 GHz. As a result of the research, a patch antenna based on fractal geometry was developed for ERS nanosatellites. The capabilities of these antennas are modeled and investigated. A method for calculating and modeling fractal geometry for patch antennas has been developed.

Keywords: antenna, earth remote sensing, fractal, small spacecraft

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Authors: Lingge Tan, Hongpeng Xu, Jieun Yang, Maarten Hornikx

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Acoustic diffusers are important components in enhancing the quality of room acoustics. This paper provides a type of modular diffuser based on the Sierpinski Triangle of the plane and combines it with fractal theory to expand the effective frequency range. In numerical calculations and full-scale model experiments, the effect of fractal design elements on normal-incidence diffusion coefficients is examined. It is demonstrated the reasonable times of iteration of modules is three, and the coverage density is 58.4% in the design frequency from 125Hz to 4kHz.

Keywords: acoustic diffuser, fractal, Sierpinski-triangle, diffusion coefficient

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Authors: Hamed Khezrzadeh

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Many investigations on the micromechanical structure of materials indicate that there exist fractal patterns at the micro scale in some of the main construction and industrial materials. A recently presented micro-fractal theory brings together the well-known periodic homogenization and the fractal geometry to construct an appropriate model for determination of the mechanical properties of particle reinforced composite materials. The proposed multi-step homogenization scheme considers the mechanical properties of different constituent phases in the composite together with the interaction between these phases throughout a step-by-step homogenization technique. In the proposed model the interaction of different phases is also investigated. By using this method the effect of fibers grading on the mechanical properties also could be studied. The theory outcomes are compared to the experimental data for different types of particle-reinforced composites which very good agreement with the experimental data is observed.

Keywords: fractal geometry, homogenization, micromehcanics, particulate composites

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Authors: I. Zahraoui, J. Terhzaz, A. Errkik, El. H. Abdelmounim, A. Tajmouati, L. Abdellaoui, N. Ababssi, M. Latrach

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This paper presents a novel design of a microstrip fractal antenna based on the use of Sierpinski triangle shape, it’s designed and simulated by using FR4 substrate in the operating frequency bands (GPS, WiMAX), the design is a fractal antenna with a modified ground structure. The proposed antenna is simulated and validated by using CST Microwave Studio Software, the simulated results presents good performances in term of radiation pattern and matching input impedance.

Keywords: dual-band antenna, fractal antenna, GPS band, modified ground structure, sierpinski triangle, WiMAX band

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