...Chaos and Fractals What is a Fractal A fractal is a never ending pattern. Fractals are never ending complex patterns that are self-similar across different scales. They are created by by being repeated over and over in a feedback loop. Fractals are everywhere. They can be found in nature, algebra, and math. Nature Algebra Geometry Mandelbrot Set This was created in 1980 shortly after the first personal computer in order to calculate numbers thousands and sometimes millions of times. Equation (old)Z=(new)Z2+C We start by plugging a value for the variable C into the simple equation below. Each complex number is actually a point in a 2-dimensional plane. The equation gives an answer, Znew . We plug this back into the equation, as Zold and calculate it again. We are interested in what happens for different starting values of C. When you square a number it gets bigger. Then you square the answer and it get even bigger.. Eventually, it goes to infinity. This is the fate of most starting values of C. Some values of C do not get bigger, but get smaller, or alternate between a set of fixed values. These are the points inside the Mandelbrot Set, which we color black. Outside the Set, all the values of C cause the equation to go to infinity, and the colors are proportional to the speed at which they expand. Ju Fractals in Nature Natural fractals can be found anywhere in nature. Even in our body. It can be the blood vessels in our arms, or...
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... 2008 Fractal Geometry A fractal is generally “a rough or fragmented geometric shape that can be subdivided into parts.” One of the ways that fractal geometry is used is in the area of medicine. In the past few years fractal analysis techniques have gained increasing attention in signal and image processing, especially in medical sciences such as Pathology. Fractal analysis has found applications in the detection of coding regions in DNA and measurement of the space-filling properties of tumors, blood vessels and neurons. Fractal concepts have also been usefully incorporated into models of biological processes, including cell growth, blood vessel growth, periodontal disease and viral infections. Other very interesting applications are founded in medical imaging Fractal analysis is widely used in image processing, both in characterizing shapes of objects and in assessing texture. Breast masses present shape and texture characteristics that vary between benign masses and malignant tumors in mammograms. Limited studies have been conducted on the application of fractal analysis specifically for classifying breast masses. The fractal dimension of the contour of a mass may be computed either directly from the two dimensional contour or from one-dimensional signatures derived from the contour. Other ways that fractal geometry is use is in biology with different applications and techniques use to classify and distinguish various types of cells. The use of fractal dimension...
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...CHAOS THEORY It is a field of study in mathematics, with applications in several disciplines including, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions—a response popularly referred to as the butterfly effect. Chaotic behavior can be observed in many natural systems, such as weather and climate. This behavior can be studied through analysis of a chaotic mathematical model, or through analytical techniques such as recurrence plots and Poincare maps. This latter idea is known as sensitive dependence on initial conditions , a circumstance discovered by Edward Lorenz (who is generally credited as the first experimenter in the area of chaos) in the early 1960s. DEFINITION: It is the study of non linear dynamics, in which seemingly random events are actually predictable from simple deterministic equation. Chaos theory concerns deterministic systems whose behavior can in principle be predicted. Chaotic systems are predictable for a while and then appear to become random. The amount of time for which the behavior of a chaotic system can be effectively predicted depends on three things: * How much uncertainty we are willing to tolerate in the forecast? * How accurately we are able to measure its current state? * Which time scale is depending on the dynamics of the system? The two main components of chaos theory are the ideas that systems - no matter how complex they may be - rely upon an underlying...
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...Chaotic Growth with the Logistic Model of P.-F. Verhulst Hugo Pastijn Department of Mathematics, Royal Military Academy B-1000 Brussels, Belgium Hugo.Pastijn@rma.ac.be Summary. Pierre-Fran¸ois Verhulst was born 200 years ago. After a short biograc phy of P.-F. Verhulst in which the link with the Royal Military Academy in Brussels is emphasized, the early history of the so-called “Logistic Model” is described. The relationship with older growth models is discussed, and the motivation of Verhulst to introduce different kinds of limited growth models is presented. The (re-)discovery of the chaotic behaviour of the discrete version of this logistic model in the late previous century is reminded. We conclude by referring to some generalizations of the logistic model, which were used to describe growth and diffusion processes in the context of technological innovation, and for which the author studied the chaotic behaviour by means of a series of computer experiments, performed in the eighties of last century by means of the then emerging “micro-computer” technology. 1 P.-F. Verhulst and the Royal Military Academy in Brussels In the year 1844, at the age of 40, when Pierre-Fran¸ois Verhulst on November c 30 presented his contribution to the “M´moires de l’Acad´mie” of the young e e Belgian nation, a paper which was published the next year in “tome XVIII” with the title: “Recherches math´matiques sur la loi d’accroissement de la e population” (mathematical investigations of the law of...
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...Before answering this question I think it is important to start with the chaos theory and its principles. Chaos is a science of surprises, nonlinear systems and unpredictability. Chaos teaches people to expect unexpected, to deal with impossible. In everyday language chaos means dynamic and random behavior. From the science perspective, chaos theory deals with nonlinear things that are effectively impossible to predict or control, like turbulence, weather, the stock market, our brain states, and so on. Chaos theory relies on basic principles: butterfly effect, unpredictability, order and disorder, mixing feedback and fractals. The answer on the question about shareholder’s focus on a single issue and its effect on a corporation lies deep in the roots of butterfly effect theory. Butterfly effect theory is often associated with Edward Lorenz, mathematician and meteorologist, who has proved from the theoretical example that formation of hurricane in one place depends on whether or not a distant butterfly had flapped its wings several weeks earlier. Thus, a butterfly that flaps its wings in Hong Kong can result in tornado in Texas. Small change at one place in nonlinear systems can result in large differences in a later state. The same scenario is related to a shareholder who can make a big change in the company just by focusing on a single issue. The answer is based on a scientific theory that a single occurrence, no matter how small, can change the course of the universe...
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...Henon attractor application in real life The Henon map is one of the many 2-Dimensional maps. There are at least two maps known as Henon map. One of which is the 2-D dissipative quadratic map, given by the following X and Y equations that produce a fractal made up of strands [3] : xn+1 = 1 - axn2 + byn yn+1 = xn The Henon map can also be written in terms of a single variable with two time delays, Since the second equation above can be written as yn = xn-1: xn+1 = 1 - axn2 + bxn-1 It’s a simple invertible iterated map that showed a chaotic attractor and it’s a simplified version of the Poincare map for the Lorenz model. It was named after its discoverer, the French mathematician and astronomer Michele Henon.[2] [5] [pic] Fig. 1 Henon map with parameters a = 1.4 and b = 0.3. The chaotic behavior of the attractor has many physical applications. Such as: ▪ Application to the transverse betatron motion in cyclic accelerators ▪ Application of the Henon Chaotic Model on to design of low density parity ▪ Application to Financial Markets ▪ Application on area-conserving ▪ Deterministic chaos in financial time series by recurrence plots ▪ Application to the motion of stars Application in air bubble formation Introduction Below the explanation of how the Henon attractor effects a real life application is presented, which is based on the bubble formation. This experiment took place in order to detect the chaotic dynamics...
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...HURST EXPONENT AND FINANCIAL MARKET PREDICTABILITY Bo Qian Khaled Rasheed Department of Computer Science University of Georgia Athens, GA 30601 USA [qian, khaled]@cs.uga.edu ABSTRACT The Hurst exponent (H) is a statistical measure used to classify time series. H=0.5 indicates a random series while H>0.5 indicates a trend reinforcing series. The larger the H value is, the stronger trend. In this paper we investigate the use of the Hurst exponent to classify series of financial data representing different periods of time. Experiments with backpropagation Neural Networks show that series with large Hurst exponent can be predicted more accurately than those series with H value close to 0.50. Thus Hurst exponent provides a measure for predictability. KEY WORDS Hurst exponent, time series analysis, neural networks, Monte Carlo simulation, forecasting In time series forecasting, the first question we want to answer is whether the time series under study is predictable. If the time series is random, all methods are expected to fail. We want to identify and study those time series having at least some degree of predictability. We know that a time series with a large Hurst exponent has strong trend, thus it’s natural to believe that such time series are more predictable than those having a Hurst exponent close to 0.5. In this paper we use neural networks to test this hypothesis. Neural networks are nonparametric universal function approximators [9] that can learn from data without...
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...important to know the vocabulary of art in order to understand it. 3 Art is all around us and it has touched everyone. Art, like science, is a human activity. It is inspired by creativity and is the ability to make things of beauty. It is, indeed, very difficult to define art. It can also be difficult to understand art. You should be aware that your experience to any work of art is unique. Rather than asking what art is, it might better to ask what art does. 4 • Art creates beauty: Art has always added beauty to our lives. At times, the artist has looked to nature as the standard of beauty, and thus imitated it. At other times the artist has improved upon nature to give an idealized form. 5 Rose garden: a painting using fractals 6 • Art enhances our environment: Works of art have been used to create pleasing environments for centuries. Paintings hang on walls; sculptures find their way into rooms and courtyards; photographs are found in books and so on. • Art reveals truth: Many cultures have tries to reveal truth through art; truth about the way the world works; truth about the way the world is....
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...MN 325-final test 1. The Vroom-Yetton Leadership Model—indentify and explain the five decision-making styles. Explain how three of the situational factors affect the degree of involvement by subordinates. The question will indicate which factors to explain and a general response is expected. ∙ Autocratic I (AI)—a manger solves a problem using the information that is already available ∙ Autocratic II (AII)—a manager obtains additional information from subordinates and then solves the problem ∙ Consultative I (CI)—a manager shares the problem with subordinate on an individual basis and obtain their ideas and suggestions. Again, the manager chooses a solution to the problem at hand ∙ Consultative II (CII)—a manger shares the problem with subordinates as a group. The final decision may or may not reflect subordinate input ∙ Group (G)—a manager meets with subordinates as a group. However, the manager acts as a chairperson who focuses on directs discussions, but does not impose his or her will on the group. True subordinates’ participation, in a democratic sense, is sought. ∙ Situational factors: o (A)—does the problem posses a quality requirement? o (B)—Do I have sufficient information to make a high-quality decision? o (C) –Is the problem structured? o (D)—Is acceptance of the decision by subordinates important for effective implementation? o (E)—If I were to make the decision by myself, am I reasonably certain that it would be...
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...App. Math. and Comp. Intel., Vol. 2 (1) (2013) 137–148 http://amci.unimap.edu.my © 2013 Institute of Engineering Mathematics, UniMAP Modeling of prediction system: An application of the nearest neighbor approach to chaotic data N. Z. A. Hamida,b,*and M. S. M. Nooranib a Department of Mathematics, Faculty of Science and Mathematics, Universiti Pendidikan Sultan Idris 35900, Tanjung Malim, Perak, Malaysia b School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600, Bangi, Selangor, Malaysia Received: 20 February 2012; Revised: 12 February 2013, Accepted: 25 February 2013 Abstract: This paper is about modeling of chaotic systems via nearest neighbor approach. This approach holds the principle that future data can be predicted using past data information. Here, all the past data known as neighbors. There are various prediction models that have been developed through this approach. In this paper, the zeroth-order approximation method (ZOAM) and improved ZOAM, namely the k-nearest neighbor approximation (KNNAM) and weighted distance approximation method (WDAM) were used. In ZOAM, only one nearest neighbor is used to predict future data while KNNAM uses more than one nearest neighbor and WDAM add the distance element for prediction process. These models were used to predict one of the chaotic data, Logistic map. 3008 Logistic map data has been produced, in which the first 3000 data were used to train the model while...
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...most people chances are slim to none, in fact many may not even consider the fact that there might even be any kind of relationship between nature and themselves. As far as anyone might be concerned in today’s society, nature could just mean their backyard, or neighborhood park. In reality there is much more to you and I and this wilderness we refer to as nature. In this paper I argue that there exists a higher connection between man and nature that serves to unify all living things. Today, man and nature are commonly referred to in opposition of one another. Man destroys nature in order to expand and urbanize while nature destroys all man creates over time. People tend to see nature as some uncontrollable wild factor full of danger and chaos. Many think like Thomas Hobbes who would say that the very state of nature is chaotic; that if man were without society he would be inherently evil selfish with only self interest in mind and life would be lonely, difficult and short. However, if taken from a Rousseauian stand point, nature and man share an interest for self-preservation giving them a natural sense of compassion and the state of nature is calm and peaceful. I would have to say that the Rousseauian perspective makes more sense and ties into reality better than Hobbes’s state of nature. The main reason being that all nature moves towards a state of homeostasis or equilibrium, in other words, peace. For example, the human body constantly adjusts to the surrounding environment...
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...Losing Your Place Sue Clifford and Angela King The main players fall silent, the filming is over, the recording is finished, but the sound technician has hushed everyone to get some 'atmos'. Coughs, car noise echoing off the warehouses, birdsong, boards creaking, trees breathing in the wind, these are the sounds of the everyday, so particular to this place, that to cut the film and add studio voiceovers needs an underlay of this local atmosphere in order to ensure continuity and authenticity. That elusive particularity, so often undervalued as 'background noise', is as important as the stars. It is the richness we take for granted. How do we know where we are in time and space? How do we understand ourselves in the world? Common Ground has been exploring and developing a new concept, that of local distinctiveness. It is characterised by elusiveness, it is instantly recognizable yet difficult to describe; It is simple yet may have profound meaning to us. It demands a poetic quest and points up the shortcomings in all those attempts to understand the things around us by compartmentalising them, fragmenting, quantifying, reducing. Local distinctiveness is essentially about places and our relationship with them. It is as much about the commonplace as about the rare, about the everyday as much as the endangered, and about the ordinary as much as the spectacular. In other cultures it might be about people's deep relationship with the land. Here discontinuities have...
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...Virtual Management - a New Business Organization Paradigm JJ Murphy Negotiation Newsletter Calum Coburn Co Ltd ( private paper). This article discusses how traditional organizational management methods and structures are failing to adequately accommodate a complexity-based world view, which is characterized by discontinuous change, hyper competition and the exponential explosion of information science. Virtual organizational management is the needed change in the management paradigm. -------------------------------------------------------------------------------- This article argues that traditional management methods and structures are failing to adequately accommodate a complexity-based world view, which is characterized by discontinuous change, hyper competition and the exponential explosion of information science and shows how the management paradigm has been updated by the new era of the virtual structures. While the management structures and systems developed by such researchers as Weber, Fayol, Taylor and Drucker in the 19th and 20th centuries established a management paradigm which has endured up to the millennium, these "simple" structures and systems were more suited to a time when competition was slower, less aggressive, and characterized by long periods of stability, and when information science was in its embryonic or primordial stage. It is abundantly clear, however, that the arrival of the 21st Century demands a fundamental rethink, and the development of...
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...Part IV Emerging and Integrating Perspectives January-2007 MAC/ADSM Page-213 1403_985928_17_cha14 January-2007 MAC/ADSM Page-214 1403_985928_17_cha14 CHAPTER 14 Complexity Perspective Jean Boulton and Peter Allen Basic principles The notion that the world is complex and uncertain and potentially fast-changing is much more readily acceptable as a statement of the obvious than it might have been 30 years ago when complexity science was born. This emerging worldview sits in contradistinction to the view of the world as predictable, linear, measurable and controllable, indeed mechanical; it is the so-called mechanical worldview which underpins many traditional approaches to strategy development and general management theory (see Mintzberg, 2002 for an overview). The complexity worldview presents a new, integrated picture of the behaviour of organisations, marketplaces, economies and political infrastructures; these are indeed complex systems as we will explain below. Some of these behaviours are recognised in other theories and other empirical work. Complexity theory is unique in deriving these concepts through the lens of a coherent, self-consistent scientific perspective whilst nevertheless applying it to everyday, practical problems. These key principles can be summarised here: There is more than one possible future This is a very profound point. We are willing to accept the future may be too complicated to know, but the notion...
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...UNVERSITY OF GUYANA social science department of business & management studies Group Assignment Names: Alexis Parris-14/0312/1864 Narotam Bisnauth- Sherry Wilson-Fraser- Willana Cameron- Jenelle Richards- Kester Bowen- Course: ACT 2101 Semester 1 for the Academic Year: 2015-2016 Presented to: Ms. Elizabeth Persaud 2015 lucky 10/1/2015 Table of Content Introduction………………………………………………………………………………..2-3 Description………………………………………………………………………………..4-16 Analysis………………………………………………………………………………………17- Conclusion…………………………………………………………………………………… Bibliography…………………………………………………………………………………. Introduction Management theories have evolved over a number of centuries. According to (Koontz and Weihrich 1990, p 4), management is the process of designing and maintaining an environment in which individuals, working together in groups, efficiently accomplish selected aims. Theories are perspectives with which people make sense of their world experiences (Stoner et.al 1995, p 31-32). Theory is a systematic grouping of interdependent concepts and principles that give a significant area of knowledge. Theory is in its lowest form a classification, a set of pigeon holes, a filing cabinet in which fact can accumulate. Nothing is more lost than a loose fact, (Homans 1958, p 5). Management theories are the set of general rules that guide the managers to manage an organization. Management theories...
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