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: 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: 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: 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: 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: 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.
Abstract: In this paper, we introduce R Iterated Function System
and employ the Hutchinson Barnsley theory (HB) to construct a
fractal set as its unique fixed point by using Reich contractions in a
complete b metric space. We discuss about well posedness of fixed
point problem for b metric space.
Abstract: To develop a reliable and cost effective communication platform for the telemedicine applications, novel antenna design has been presented using bacterial foraging optimization (BFO) technique. The proposed antenna geometry is achieved by etching a modified Koch curve fractal shape at the edges and a square shape slot at the center of the radiating element of a patch antenna. It has been found that the new antenna has achieved 43.79% size reduction and better resonating characteristic than the original patch. Representative results for both simulations and numerical validations are reported in order to assess the effectiveness of the developed methodology.
Abstract: A new technique of topological multi-scale analysis is
introduced. By performing a clustering recursively to build a
hierarchy, and analyzing the co-scale and intra-scale similarities, an
Iterated Function System can be extracted from any data set. The study
of fractals shows that this method is efficient to extract
self-similarities, and can find elegant solutions the inverse problem of
building fractals. The theoretical aspects and practical
implementations are discussed, together with examples of analyses of
simple fractals.
Abstract: By utilizing the system of the recurrence equations, containing two parameters, the dynamics of two antagonistically interconnected populations is studied. The following areas of the system behavior are detected: the area of the stable solutions, the area of cyclic solutions occurrence, the area of the accidental change of trajectories of solutions, and the area of chaos and fractal phenomena. The new two-dimensional diagram of the dynamics of the solutions change (the fractal cabbage) has been obtained. In the cross-section of this diagram for one of the equations the well-known Feigenbaum tree of doubling has been noted.Keywordsbifurcation, chaos, dynamics of populations, fractals
Abstract: This paper investigates the fractals generated by the dynamical system of intuitionistic fuzzy contractions in the intuitionistic
fuzzy metric spaces by generalizing the Hutchinson-Barnsley theory. We prove some existence and uniqueness theorems of fractals in the
standard intuitionistic fuzzy metric spaces by using the intuitionistic fuzzy Banach contraction theorem. In addition to that, we analyze
some results on intuitionistic fuzzy fractals in the standard intuitionistic fuzzy metric spaces with respect to the Hausdorff intuitionistic
fuzzy metrics.
Abstract: The fractal-shaped orifices are assumed to have a
significant effect on the pressure drop downstream pipe flow due to
their edge self-similarity shape which enhances the mixing
properties. Here, we investigate the pressure drop after these fractals
using a digital micro-manometer at different stations downstream a
turbulent flow pipe then a direct comparison has been made with the
pressure drop measured from regular orifices with the same flow
area. Our results showed that the fractal-shaped orifices have a
significant effect on the pressure drop downstream the flow. Also
the pressure drop measured across the fractal-shaped orifices is
noticed to be lower that that from ordinary orifices of the same flow
areas. This result could be important in designing piping systems
from point of view of losses consideration with the same flow
control area. This is promising to use the fractal-shaped orifices as
flowmeters as they can sense the pressure drop across them
accurately with minimum losses than the regular ones.
Abstract: The overall objective of this paper is to retrieve soil
surfaces parameters namely, roughness and soil moisture related to
the dielectric constant by inverting the radar backscattered signal
from natural soil surfaces.
Because the classical description of roughness using statistical
parameters like the correlation length doesn't lead to satisfactory
results to predict radar backscattering, we used a multi-scale
roughness description using the wavelet transform and the Mallat
algorithm. In this description, the surface is considered as a
superposition of a finite number of one-dimensional Gaussian
processes each having a spatial scale. A second step in this study
consisted in adapting a direct model simulating radar backscattering
namely the small perturbation model to this multi-scale surface
description. We investigated the impact of this description on radar
backscattering through a sensitivity analysis of backscattering
coefficient to the multi-scale roughness parameters.
To perform the inversion of the small perturbation multi-scale
scattering model (MLS SPM) we used a multi-layer neural network
architecture trained by backpropagation learning rule. The inversion
leads to satisfactory results with a relative uncertainty of 8%.
Abstract: The IFS is a scheme for describing and manipulating complex fractal attractors using simple mathematical models. More precisely, the most popular “fractal –based" algorithms for both representation and compression of computer images have involved some implementation of the method of Iterated Function Systems (IFS) on complete metric spaces. In this paper a new generalized space called Multi-Fuzzy Fractal Space was constructed. On these spases a distance function is defined, and its completeness is proved. The completeness property of this space ensures the existence of a fixed-point theorem for the family of continuous mappings. This theorem is the fundamental result on which the IFS methods are based and the fractals are built. The defined mappings are proved to satisfy some generalizations of the contraction condition.
Abstract: The purpose of this paper is to present the fuzzy contraction
properties of the Hutchinson-Barnsley operator on the fuzzy
hyperspace with respect to the Hausdorff fuzzy metrics. Also we
discuss about the relationships between the Hausdorff fuzzy metrics
on the fuzzy hyperspaces. Our theorems generalize and extend some
recent results related with Hutchinson-Barnsley operator in the metric
spaces.
Abstract: We develop new nonlinear methods of
immunofluorescence analysis for a sensitive technology of
respiratory burst reaction of DNA fluorescence due to oxidative
activity in the peripheral blood neutrophils. Histograms in flow
cytometry experiments represent a fluorescence flashes frequency as
functions of fluorescence intensity. We used the Shannon-Weaver
index for definition of neutrophils- biodiversity and Hurst index for
definition of fractal-s correlations in immunofluorescence for
different donors, as the basic quantitative criteria for medical
diagnostics of health status. We analyze frequencies of flashes,
information, Shannon entropies and their fractals in
immunofluorescence networks due to reduction of histogram range.
We found the number of simplest universal correlations for
biodiversity, information and Hurst index in diagnostics and
classification of pathologies for wide spectra of diseases. In addition
is determined the clear criterion of a common immunity and human
health status in a form of yes/no answers type. These answers based
on peculiarities of information in immunofluorescence networks and
biodiversity of neutrophils. Experimental data analysis has shown the
existence of homeostasis for information entropy in oxidative activity
of DNA in neutrophil nuclei for all donors.
Abstract: Chaos and fractals are novel fields of physics and mathematics showing up a new way of universe viewpoint and creating many ideas to solve several present problems. In this paper, a novel algorithm based on the chaotic sequence generator with the highest ability to adapt and reach the global optima is proposed. The adaptive ability of proposal algorithm is flexible in 2 steps. The first one is a breadth-first search and the second one is a depth-first search. The proposal algorithm is examined by 2 functions, the Camel function and the Schaffer function. Furthermore, the proposal algorithm is applied to optimize training Multilayer Neural Networks.