Abstract: Through the emergence of modern architecture, an aggressive desire for new design theories appeared through the works of architects and critics. The discourse of complexity and volumetric composition happened to be an important and controversial issue in the discipline of architecture which was discussed through a general point of view in Robert Venturi and Denise Scott Brown's book “Complexity and contradiction in architecture” in 1966, this paper attempts to identify chaos theory as a scientific model of complexity and its relation to architecture design theory by conducting a qualitative analysis and multidisciplinary critical approach through architecture and basic sciences resources. Accordingly, we identify chaotic architecture as the correlation between chaos theory and the discipline of architecture, and as an independent nonlinear design theory with specific characteristics and properties.
Abstract: 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 70's until today and has generated significant styles such as deconstructivism and parametricism 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.
Abstract: In the mining environment, tailings dam embankment is among the hazards and risk areas. The tailings dam embankment could fail and result to damages to facilities, human injuries or even fatalities. Periodic monitoring of the dam embankment is needed to help assess the safety of the tailings dam embankment. Artificial intelligence techniques such as fractals can be used to analyse the stability of the monitored dataset from survey measurement techniques. In this paper, the fractal dimension (D) was determined using D = 2-H. The Hurst parameters (H) of each monitored prism were determined by using a time domain of rescaled range programming in MATLAB software. The fractal dimensions of each monitored prism were determined based on the values of H. The results reveal that the values of the determined H were all within the threshold of 0 ≤ H ≤ 1 m. The smaller the H, the bigger the fractal dimension is. Fractal dimension values ranging from 1.359 x 10-4 m to 1.8843 x 10-3 m were obtained from the monitored prisms on the based on the tailing dam embankment dataset used. The ranges of values obtained indicate that the tailings dam embankment is stable.
Abstract: In the present work, we consider one category of curves
denoted by L(p, k, r, n). These curves are continuous arcs which are
trajectories of roots of the trinomial equation zn = αzk + (1 − α),
where z is a complex number, n and k are two integers such that
1 ≤ k ≤ n − 1 and α is a real parameter greater than 1. Denoting
by L the union of all trinomial curves L(p, k, r, n) and using the
box counting dimension as fractal dimension, we will prove that the
dimension of L is equal to 3/2.
Abstract: This paper presents an overview of the methodologies
and algorithms for statistical texture analysis of 2D images. Methods
for digital-image texture analysis are reviewed based on available
literature and research work either carried out or supervised by the
authors.
Abstract: Soil moisture content is a key variable in many environmental sciences. Even though it represents a small proportion of the liquid freshwater on Earth, it modulates interactions between the land surface and the atmosphere, thereby influencing climate and weather. Accurate modeling of the above processes depends on the ability to provide a proper spatial characterization of soil moisture. The measurement of soil moisture content allows assessment of soil water resources in the field of hydrology and agronomy. The second parameter in interaction with the radar signal is the geometric structure of the soil. Most traditional electromagnetic models consider natural surfaces as single scale zero mean stationary Gaussian random processes. Roughness behavior is characterized by statistical parameters like the Root Mean Square (RMS) height and the correlation length. Then, the main problem is that the agreement between experimental measurements and theoretical values is usually poor due to the large variability of the correlation function, and as a consequence, backscattering models have often failed to predict correctly backscattering. In this study, surfaces are considered as band-limited fractal random processes corresponding to a superposition of a finite number of one-dimensional Gaussian process each one having a spatial scale. Multiscale roughness is characterized by two parameters, the first one is proportional to the RMS height, and the other one is related to the fractal dimension. Soil moisture is related to the complex dielectric constant. This multiscale description has been adapted to two-dimensional profiles using the bi-dimensional wavelet transform and the Mallat algorithm to describe more correctly natural surfaces. We characterize the soil surfaces and sub-surfaces by a three layers geo-electrical model. The upper layer is described by its dielectric constant, thickness, a multiscale bi-dimensional surface roughness model by using the wavelet transform and the Mallat algorithm, and volume scattering parameters. The lower layer is divided into three fictive layers separated by an assumed plane interface. These three layers were modeled by an effective medium characterized by an apparent effective dielectric constant taking into account the presence of air pockets in the soil. We have adopted the 2D multiscale three layers small perturbations model including, firstly air pockets in the soil sub-structure, and then a vegetable canopy in the soil surface structure, that is to simulate the radar backscattering. A sensitivity analysis of backscattering coefficient dependence on multiscale roughness and new soil moisture has been performed. Later, we proposed to change the dielectric constant of the multilayer medium because it takes into account the different moisture values of each layer in the soil. A sensitivity analysis of the backscattering coefficient, including the air pockets in the volume structure with respect to the multiscale roughness parameters and the apparent dielectric constant, was carried out. Finally, we proposed to study the behavior of the backscattering coefficient of the radar on a soil having a vegetable layer in its surface structure.
Abstract: Zone Plates (ZPs) are used in many areas of physics where planar fabrication is advantageous in comparison with conventional curved lenses. There are several types of ZPs, such as the well-known Fresnel ZPs or the more recent Fractal ZPs and Fibonacci ZPs. The material selection of the lens plays a very important role in the beam modulation control. This work presents a comparison between two Fresnel ZP made from different materials in the ultrasound domain: Polylactic Acid (PLA) and brass. PLA is the most common material used in commercial 3D-printers due to its high design flexibility and low cost. Numerical simulations based on Finite Element Method (FEM) and experimental results are shown, and they prove that the focusing capabilities of brass ZPs and PLA ZPs are similar. For this reason, PLA is proposed as a Magnetic Resonance Imaging (MRI) compatible material with great potential for therapeutic ultrasound focusing applications.
Abstract: 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%.
Abstract: The wide range of industrial applications involved with boiling flows promotes the necessity of establishing fundamental knowledge in boiling flow phenomena. For this purpose, a number of experimental and numerical researches have been performed to elucidate the underlying physics of this flow. In this paper, the improved wall boiling models, implemented on ANSYS CFX 14.5, were introduced to study subcooled boiling flow at elevated pressure. At the heated wall boundary, the Fractal model, Force balance approach and Mechanistic frequency model are given for predicting the nucleation site density, bubble departure diameter, and bubble departure frequency. The presented wall heat flux partitioning closures were modified to consider the influence of bubble sliding along the wall before the lift-off, which usually happens in the flow boiling. The simulation was performed based on the Two-fluid model, where the standard k-ω SST model was selected for turbulence modelling. Existing experimental data at around 5 bars were chosen to evaluate the accuracy of the presented mechanistic approach. The void fraction and Interfacial Area Concentration (IAC) are in good agreement with the experimental data. However, the predicted bubble velocity and Sauter Mean Diameter (SMD) are over-predicted. This over-prediction may be caused by consideration of only dispersed and spherical bubbles in the simulations. In the future work, the important physical mechanisms of bubbles, such as merging and shrinking during sliding on the heated wall will be incorporated into this mechanistic model to enhance its capability for a wider range of flow prediction.
Abstract: This paper investigates the nature of the fluctuation of the daily average Solar wind speed time series collected over a period of 2492 days, from 1st January, 1997 to 28th October, 2003. The degree of self-similarity and scalability of the Solar Wind Speed signal has been explored to characterise the signal fluctuation. Multi-fractal Detrended Fluctuation Analysis (MFDFA) method has been implemented on the signal which is under investigation to perform this task. Furthermore, the singularity spectra of the signals have been also obtained to gauge the extent of the multifractality of the time series signal.
Abstract: In this paper, we present a neural approach for
unsupervised natural color-texture image segmentation, which is
based on both Kohonen maps and mathematical morphology, using
a combination of the texture and the image color information of the
image, namely, the fractal features based on fractal dimension are
selected to present the information texture, and the color features
presented in RGB color space. These features are then used to train
the network Kohonen, which will be represented by the underlying
probability density function, the segmentation of this map is made
by morphological watershed transformation. The performance of our
color-texture segmentation approach is compared first, to color-based
methods or texture-based methods only, and then to k-means method.
Abstract: A coplanar waveguide (CPW) feed is presented, and comprising a split ring resonator (SRR) loaded fractal with water lily shape is used for multi band applications. The impedance matching of the antenna is determined by the number of Koch curve fractal unit cells. The antenna is designed on a FR4 substrate with a permittivity of εr = 4.4 and size of 14 x 16 x 1.6 mm3 to generate multi resonant mode at 3.8 GHz covering S band, 8.68 GHz at X band, 13.96 GHz at Ku band, and 19.74 GHz at K band with reflection coefficient better than -10 dB. Simulation results show that the antenna exhibits the desired voltage standing wave ratio (VSWR) level and radiation patterns across the wide frequency range. The fundamental parameters of the antenna such as return loss, VSWR, good radiation pattern with reasonable gain across the operating bands are obtained.
Abstract: The effect of directional search using iterated functional system has been studied on four images taken from databases. The images are portioned successively towards smaller dimension. Presented method provides the faster rate of convergence with respect to processing time in the flat region, but the same has been found to be slower at the border of the images and edges. It has also been revealed that the PSNR is lower at the edges and border portions of the image, and it is found to be higher in the uniform gray region, under the same external illumination and external noise environment.
Abstract: Fractal based digital image compression is a specific
technique in the field of color image. The method is best suited for
irregular shape of image like snow bobs, clouds, flame of fire; tree
leaves images, depending on the fact that parts of an image often
resemble with other parts of the same image. This technique has
drawn much attention in recent years because of very high
compression ratio that can be achieved. Hybrid scheme incorporating
fractal compression and speedup techniques have achieved high
compression ratio compared to pure fractal compression. Fractal
image compression is a lossy compression method in which selfsimilarity
nature of an image is used. This technique provides high
compression ratio, less encoding time and fart decoding process. In
this paper, fractal compression with quad tree and DCT is proposed
to compress the color image. The proposed hybrid schemes require
four phases to compress the color image. First: the image is
segmented and Discrete Cosine Transform is applied to each block of
the segmented image. Second: the block values are scanned in a
zigzag manner to prevent zero co-efficient. Third: the resulting image
is partitioned as fractals by quadtree approach. Fourth: the image is
compressed using Run length encoding technique.
Abstract: Computer aided diagnosis systems provide vital
opinion to radiologists in the detection of early signs of breast cancer
from mammogram images. Architectural distortions, masses and
microcalcifications are the major abnormalities. In this paper, a
computer aided diagnosis system has been proposed for
distinguishing abnormal mammograms with architectural distortion
from normal mammogram. Four types of texture features GLCM
texture, GLRLM texture, fractal texture and spectral texture features
for the regions of suspicion are extracted. Support vector machine
has been used as classifier in this study. The proposed system yielded
an overall sensitivity of 96.47% and an accuracy of 96% for
mammogram images collected from digital database for screening
mammography database.
Abstract: The purpose of this study is the discrimination of 28
postmenopausal with osteoporotic femoral fractures from an agematched
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.
Abstract: The main parameters affecting the workability are the
water content, particle size, and the total surface of the grains, as long
as the mixing water begins by wetting the surface of the grains and
then fills the voids between the grains to form entrapped water, the
quantity of water remaining is called free water. The aim of this study is to undertake a fractal approach through
the relationship between the concrete formulation parameters and
workability. To develop this approach a series of concrete taken from
the literature was investigated by varying formulation parameters
such as G/S, the quantity of cement C and the quantity of water W. We also call another model as the model of water layer thickness
and model of paste layer thickness to judge their relevance, hence the
following results: the relevance of the water layer thickness model is
considered as a relevant when there is a variation in the water
quantity. The model of the paste layer thickness is only applicable if
we considered that the paste is made with the grain value Dmax =
2.85: value from which we see a stability of the model.
Abstract: Optic disk segmentation plays a key role in the mass
screening of individuals with diabetic retinopathy and glaucoma
ailments. An efficient hardware-based algorithm for optic disk
localization and segmentation would aid for developing an automated
retinal image analysis system for real time applications. Herein,
TMS320C6416DSK DSP board pixel intensity based fractal analysis
algorithm for an automatic localization and segmentation of the optic
disk is reported. The experiment has been performed on color and
fluorescent angiography retinal fundus images. Initially, the images
were pre-processed to reduce the noise and enhance the quality. The
retinal vascular tree of the image was then extracted using canny
edge detection technique. Finally, a pixel intensity based fractal
analysis is performed to segment the optic disk by tracing the origin
of the vascular tree. The proposed method is examined on three
publicly available data sets of the retinal image and also with the data
set obtained from an eye clinic. The average accuracy achieved is
96.2%. To the best of the knowledge, this is the first work reporting
the use of TMS320C6416DSK DSP board and pixel intensity based
fractal analysis algorithm for an automatic localization and
segmentation of the optic disk. This will pave the way for developing
devices for detection of retinal diseases in the future.
Abstract: This paper is aimed at proposing a rhombus shaped
wearable fractal antenna for wireless communication systems. The
geometrical descriptors of the antenna have been obtained using
bacterial foraging optimization (BFO) for wide band operation. The
method of moment based IE3D software has been used to simulate
the antenna and observed that miniaturization of 13.08% has been
achieved without degrading the resonating properties of the proposed
antenna. An analysis with different substrates has also been done in
order to evaluate the effectiveness of electrical permittivity on the
presented structure. The proposed antenna has low profile, light
weight and has successfully demonstrated wideband and multiband
characteristics for wearable electronic applications.
Abstract: Image compression based on fractal coding is a lossy
compression method and normally used for gray level images range
and domain blocks in rectangular shape. Fractal based digital image
compression technique provide a large compression ratio and in this
paper, it is proposed using YUV colour space and the fractal theory
which is based on iterated transformation. Fractal geometry is mainly
applied in the current study towards colour image compression
coding. These colour images possesses correlations among the colour
components and hence high compression ratio can be achieved by
exploiting all these redundancies. The proposed method utilises the
self-similarity in the colour image as well as the cross-correlations
between them. Experimental results show that the greater
compression ratio can be achieved with large domain blocks but more
trade off in image quality is good to acceptable at less than 1 bit per
pixel.