Search results for: Mandelbrot set fractal

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

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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: 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: Anca Radulescu, Danae Evans

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The relationship between a network’s hardwiring and its emergent dynamics are central to neuroscience. We study the principles of this correspondence in a canonical setup (in which network nodes exhibit well-studied complex quadratic dynamics), then test their universality in biological networks. By extending methods from discrete dynamics, we study the effects of network connectivity on temporal patterns, encapsulating long-term behavior into the rich topology of network Mandelbrot sets. Then elements of fractal geometry can be used to predict and classify network behavior.

Keywords: canonical model, complex dynamics, dynamic networks, fractals, Mandelbrot set, network connectivity

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Authors: Ana Barbir, S. Ivelic Bradanovic, D. Pecaric, J. Pecaric

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We proved a converse to Sherman's inequality. Using the concept of f-divergence we obtained some inequalities for the well-known entropies, such as Shannon entropies that have many applications in many applied sciences, for example, in information theory, biology and economics Zipf-Mandelbrot law gave improvement in account for the low-rankwords in corpus. Applications of Zipf-Mandelbrot law can be found in linguistics, information sciences and also mostly applicable in ecological eld studies. We also introduced an entropy by applying the Zipf-Mandelbrot law and derived some related inequalities.

Keywords: f-divergence, majorization inequality, Sherman inequality, Zipf-Mandelbrot entropy

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Authors: Neda Lovričević, Đilda Pečarić, Josip Pečarić

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The Jensen functional in its discrete form is brought in relation to the Csiszar divergence functional, this time via its monotonicity property. This approach presents a generalization of the previously obtained results that made use of interpolating Jensen-type inequalities. Thus the monotonicity property is integrated with the Zipf-Mandelbrot law and applied to f-divergences for probability distributions that originate from the Csiszar divergence functional: Kullback-Leibler divergence, Hellinger distance, Bhattacharyya distance, chi-square divergence, total variation distance. The Zipf-Mandelbrot and the Zipf law are widely used in various scientific fields and interdisciplinary and here the focus is on the aspect of the mathematical inequalities.

Keywords: Jensen functional, monotonicity, Csiszar divergence functional, f-divergences, Zipf-Mandelbrot law

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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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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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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: Blair D. Macdonald

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After nearly one hundred years of its origin, foundational quantum mechanics remains one of the greatest unexplained mysteries in physicists today. Within this time, chaos theory and its geometry, the fractal, has developed. In this paper, the propagation behaviour with an iteration of a simple fractal, the Koch Snowflake, was described and analysed. From an arbitrary observation point within the fractal set, the fractal propagates forward by oscillation—the focus of this study and retrospectively behind by exponential growth from a point beginning. It propagates a potentially infinite exponential oscillating sinusoidal wave of discrete triangle bits sharing many characteristics of light and quantum entities. The model's wave speed is potentially constant, offering insights into the perception and a direction of time where, to an observer, when travelling at the frontier of propagation, time may slow to a stop. In isolation, the fractal is a superposition of component bits where position and scale present a problem of location. In reality, this problem is experienced within fractal landscapes or fields where 'position' is only 'known' by the addition of information or markers. The quantum' measurement problem', 'uncertainty principle,' 'entanglement,' and the classical-quantum interface are addressed; these are a problem of scale invariance associated with isolated fractality. Dual forward and retrospective perspectives of the fractal model offer the opportunity for unification between quantum mechanics and cosmological mathematics, observations, and conjectures. Quantum and cosmological problems may be different aspects of the one fractal geometry.

Keywords: measurement problem, observer, entanglement, unification

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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: Nkiru I. Ibeakuzie, Paul D. J. Watson, John F. Pescatore

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In roadway construction, the cost of soil-cement stabilization per unit area is significantly influenced by the binder content, hence the need to optimise cement usage. This research work will characterize the influence of soil fractal geometry on properties of cement-stabilized soil, and strive to determine a correlation between mechanical proprieties of cement-stabilized soil and the mass fractal dimension Dₘ indicated by particle size distribution (PSD) of aggregate mixtures. Since strength development in cemented soil relies not only on cement content but also on soil PSD, this study will investigate the possibility of reducing cement content by changing the PSD of soil, without compromising on strength, reduced permeability, and compressibility. A series of soil aggregate mixes will be prepared in the laboratory. The mass fractal dimension Dₘ of each mix will be determined from sieve analysis data prior to stabilization with cement. Stabilized soil samples will be tested for strength, permeability, and compressibility.

Keywords: fractal dimension, particle size distribution, cement stabilization, cement content

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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: Reza Bazargan lari, Mohammad H. Fattahi

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Natural resources management including water resources requires reliable estimations of time variant environmental parameters. Small improvements in the estimation of environmental parameters would result in grate effects on managing decisions. Noise reduction using wavelet techniques is an effective approach for pre-processing of practical data sets. Predictability enhancement of the river flow time series are assessed using fractal approaches before and after applying wavelet based pre-processing. Time series correlation and persistency, the minimum sufficient length for training the predicting model and the maximum valid length of predictions were also investigated through a fractal assessment.

Keywords: wavelet, de-noising, predictability, time series fractal analysis, valid length, ANN

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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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