1. Complexity, Self Adaptive Complex Systems, And Chaos Theory Co., have been applying the concepts of chaos theory and complex adaptive systems in developing 'selforganizing' http://www.brint.com/Systems.htm

Register For Free Access Now!! Get FREE Latest In-Depth Articles in Newsletter, e-mail subscribe@brint.com About BRINT News About BRINT Contact Us ... Advertise Channels General Business Business Technology E-Business Knowledge Management Resources News World Information! Conferences ... Books Community Join the Network! Online Community Sponsored Events Executive Jobs SEARCH HELP Organizations as Self-Adaptive Complex Systems Subject Portals Complex Systems Systems Thinking Chaos Theory Systems Dynamics ... Tools for Complex Systems Research "Where chaos begins, classical science stops. For as long as the world has had physicists inquiring into the laws of nature, it has suffered a special ignorance about disorder in the atmosphere, in the fluctuations of the wildlife populations, in the oscillations of the heart and the brain. The irregular side of nature, the discontinuous and erratic side these have been puzzles to science, or worse, monstrosities." Jame Gleick in Chaos: Making A New Science What is Chaos? A working definition from The Qualitative Study of Unstable Aperiodic Behavior in Deterministic Nonlinear Dynamical Systems (Kellert). A more complete defintion of Chaos is offered on Santa Fe Institute's server at:

2. Chaos Theory An Introduction to Mathematical chaos theory and Fractal Geometry, by Manus J. Donahue III.Category Science Math Chaos and Fractals Chaos......The chaos theory. Home Email An Introduction to Mathematical chaos theory and FractalGeometry. For a printable version of this document, please click here. http://www.duke.edu/~mjd/chaos/chaos.html

The Chaos Theory Home E-mail An Introduction to Mathematical Chaos Theory and Fractal Geometry For a printable version of this document, please click here ATTENTION: I wrote this explanatory paper on chaos theory about five years ago. The number of interested visitors I get constantly amazes me, some 100,000 in just the last two years alone! In the wake of an economic as well as a technological revolution, it's comforting to see the number of intelligent people out there interested in understanding (at some basic level) a pure science such as chaos theory. Due to the incredible success of this essay (numerous online awards as well as a citation in the New York Times ), I have taken it upon myself to write a book that deals with what I feel to be some of the most interesting breakthroughs in theoretical physics to date. In addition to a chapter on chaos theory (approximately four times as long as this introductory essay and with more interesting examples), I have also included chapters on relativity, quantum mechanics, string theory and the universe, and even a section on the applications of such theories and how they're shaping the future of both science and society. The book is a combination of philosophy and theoretical physics (as I believe the two to be related), skipping over the burdensome mathematics of the theories (as most people have better things to do :) in favor of raw explanatory emphasis, interesting anecdotes and helpful examples. The book, entitled

3. SCTPLS News, tutorials, data library, and information on conferences. http://www.societyforchaostheory.org/

Welcome to www.societyforchaostheory.org Our th Annual International Conference will take place in Boston Aug 8-10 This year’s focus is Big Questions, Tough Problems Our keynote speakers will be physicist Dr. Eugene Stanley and anthropologist Dr. Clifford T. Brown. Stanley, who is listed by the Science Citation Index as one of the 100 Most-Cited Physicists, studies nonlinear dynamics in such phenomena as the economy, heartbeats, protein folding, Alzheimer disease, and liquid water critical points. Brown, who studies the social and economic organization of the Maya Culture, will be speaking on “Dynamics and Patterns in the Rise and Fall of States: Problems and Data." Three all-new workshops will be offered on Friday: Drawing Conclusions from Time Series,” by Drs. Mary Ann Metzger and Dick Bird, “Introduction to Fractals and Chaos,” by Dr. Larry Liebovitch, and “Agent-Based Computational Laboratories,” by Dr. Catherine Dibble. Rates are $125 per workshop for regular attendees, $75 for students. To encourage members to take full advantage of this opportunity, there is a special rate of $200 if you take two of the three workshops. In addition, Dr. Steve Guastello will be offering a free extended session on Accident Analysis and Prevention during the regular conference schedule. A call for papers and symposia may be found here A registration form may be found here WANTED : CORRAL IN SOME NEW MEMBERS, AND WE’LL GIVE YOU A HEFTY REWARD!

4. CHAOS WITHOUT THE MATH Introduction to chaos theory and complexity describes the concepts without using equations or higher mathematics. Browse footnotes and a collection of links. INTRODUCTION TO chaos theory AND FRACTALS. BEST RESOURCE TO COMPLEXITY http://www.wfu.edu/~petrejh4/chaosind.htm

CHAOS WITHOUT THE MATH BY JUDY PETREE'S HOMEPAGE PART 1: HISTORY OF CHAOS WHO FOUND IT, WHAT ARE THEY DOING WITH IT, AND WHAT'S NEXT? PART 2: INSTABILITY WHAT CAUSES IT? PART 3: THE STRANGE ATTRACTOR WHAT TAKES OVER? PART 4: PHASE TRANSITION WHAT HAPPENS AT DECISION TIME? PART 5: DEEP CHAOS TO BE OR NOT TO BE? PART 6: SELF-ORGANIZATION WHAT IS THIS NEW COMPLEXITY? PART 7: CONCLUSION HOW CAN WE FIND IT AND USE IT? Look for the best links below ANDREW HO HAS A COMPLETE INDEX OF LINKS TO CHAOS. THE NON-LINEARITY AND COMPLEXITY HOMEPAGE. THE SANTA FE INSTITUTE STUDIES THE SCIENCE OF COMPLEXITY. THEOLOGICAL IMPLICATIONS OF CHAOS. CHAOS FROM ILYA PRIGOGINE CENTER STRANGE ATTRACTORS LORE COMPLEX SYSTEMS SEARCH INDEX CHAOTIC BEHAVIOR LIST OTHER SITES OF INTEREST INTRODUCTION TO CHAOS THEORY AND FRACTALS BEST RESOURCE TO COMPLEXITY AN ONLINE COURSE IN CHAOS THEORY AND COMPLEXITY. EXCELLENT MANCHESTER'S FRACTALS IN ACTION. RAE'S STORY OF HOW LORENZ DISCOVERED CHAOS. RAE ALSO PRESENTS THE MATHEMATICS OF CHAOS THE INSTITUTE OF NON-LINEAR SCIENCE.

5. Chaos Theory And Fractals History of chaos as well as extensive information on chaos theory and fractals. Contains several pictures of fractals and links to other chaos theory and fractals pages. http://www.mathjmendl.org/chaos/

Chaos Theory and Fractals By Jonathan Mendelson and Elana Blumenthal Outline Introduction to Chaos Determinism Early Chaos Edward Lorenz ... Works Cited Introduction to Chaos The dictionary definition of chaos is turmoil, turbulence, primordial abyss, and undesired randomness, but scientists will tell you that chaos is something extremely sensitive to initial conditions. Chaos also refers to the question of whether or not it is possible to make good long-term predictions about how a system will act. A chaotic system can actually develop in a way that appears very smooth and ordered. Determinism Sir Isaac Newton Determinism is the belief that every action is the result of preceding actions. It began as a philosophical belief in Ancient Greece thousands of years ago and was introduced into science around 1500 A.D. with the idea that cause and effect rules govern science. Sir Isaac Newton was closely associated with the establishment of determinism in modern science. His laws were able to predict systems very accurately. They were deterministic at their core because they implied that everything that would occur would be based entirely on what happened right before. The Newtonian model of the universe is often depicted as a billiard game in which the outcome unfolds mathematically from the initial conditions in a pre-determined fashion, like a movie that can be run forwards or backwards in time. Determinism remains as one of the more important concepts of physical science today. Early Chaos

6. Chaos At Maryland CHAOS COMPLEXITY THEORY Below are links to chaos theory and weblinks to fractal pictures. More important links on the new site above. The new site above gives the reader an idea of what Chaos is without using the math involved. http://www-chaos.umd.edu/

The idea that many simple nonlinear deterministic systems can behave in an apparently unpredictable and chaotic manner was first noticed by the great French mathematician . Other early pioneering work in the field of chaotic dynamics were found in the mathematical literature by such luminaries as Birkhoff Cartwright Littlewood Levinson ... Smale , and Kolmogorov and his students, among others. In spite of this, the importance of chaos was not fully appreciated until the widespread availability of digital computers for numerical simulations and the demonstration of chaos in various physical systems. This realization has broad implications for many fields of science, and it is only within the past decade or so that the field has undergone explosive growth. It is found that the ideas of chaos have been very fruitful in such diverse disciplines as biology, economics, chemistry, engineering, fluid mechanics, physics, just to name a few. Chaos is a multidisciplinary science, and this is reflected in the fact that the members of the group are affiliated with diverse departments and institutions: Department of Physics Department of Mathematics Department of Electrical Engineering Institute for Physical Sciences and Technology (IPST) ... Applied Math and Scientific Computation (AMSC) Since the mid-1970s, the Chaos Group at Maryland has done extensive research in various areas of chaotic dynamics ranging from the theory of

7. A Theory Of Everything: Virtual Chaos - Welcome chaos theory A Brief Introduction What exactly is chaos? Put simply, it is the idea that it is possible to get completely random results from normal equations. http://www.virtualchaos.org/

A Theory of Everything Virtual Chaos VirtualChaos.Org. "More than at any time in history mankind faces a crossroads. One path leads to despair and utter hopelessness, the other to total extinction. Let us pray that we have the wisdom to choose correctly." - Woody Allen Here we offer another choice... Welcome to Virtual Chaos You are visitor number Thank you for taking the time to visit and consider the ideas that we have put forth in an attempt to help explain how the world around us, and within us, works. We have done our best to try and make the information we present understandable to as many people as possible. We try to put the ideas in a format that the layperson can read and understand, but will not bore the steeped scientist to death. We ask you to check back with this site, as it is constantly evolving as new ideas are conceived, new questions asked, and new explanations offered. What is Virtual Chaos? Virtual Chaos is a Theory of Everything . A Theory of Everything is designed to explain how everything works with a single set of rules. These rules would have to apply to all known (and unknown) phenomena and work with all of them. We have tried to break Virtual Chaos using everything we could think of, testing it against Relativity, Quantum Mechanics, Gyroscopes, Solar systems, Metaphysics, Religion and anything else we could think of. The result: It ended up uniting everything in a common framework.

8. Chaos Theory Resources - Fractals - Directories - Links A Directory of Internet resources on chaos theory and fractals. http://www.academicinfo.net/mathchaos.html

Home Keyword Search Subject Index Reference Desk ... Student Center Academic Info Mathematics Sciences Mathematics Chaos Theory We Need Your Help Please take a minute to make a $10 tax-deductible donation. Academic Info is made possible by the generous financial support of users like you. Academic Info 19-143rd ST SW Lynnwood, WA 98037 The Chaos Page page is sponsored by How would you like to sponsor this page? For a $100 tax-deductible donation you, your organization, department, or company are acknowledged here as a sponsor of the Chaos Theory page. Email us at madin@academicinfo.net for details. A Beginner's Guide to Chaos "This page was created to give a short introduction into some of the concepts and creations of Chaos Science. Chaos is very much related to fractal images which many view as both breathtaking artistically and thought provoking intellectually. It's written in fairly simple language and is intended primarily for beginners, however, an understanding of some basic mathematics and math terminology is required. Sections include: What is Chaos ; Calculator Chaos ; What are Fractals ; What is Fractal Dimensions.

9. Chaos Theory's Home Page Metal band from Trenton, New Jersey. History, band member profiles, contact information and links to MP3s. http://members.aol.com/chaosthory/

Chaos Theory has broken up, we'd like to thank everyone for their support over the years. Any correspondence can be done through chaosthory@aol.com The remaining members of Chaos Theory are currently holding auditions for their new project Circle's End We are a heavy alternative band, something you'd see on an Ozzfest, Warped Tour, and Tattoo the Earth. Influences- Punk, thrash, hard core, groove, NU metal, harmonies, etc. A sound all it's own. We just need the last few parts to complete the puzzle. We want to be musicians for life, and not be a fad...more of a pioneer. We need: Lead Guitarist, Bassist, 2nd vocalist (if you can play guitar or bass and sing that is a huge plus) and a keyboardist/sampler/alt. percussionist. Here is the plan. Learn enough cover songs to pull off a cover band front. Use the majority of the proceeds to finance our original material. Play both original and cover shows in the "A & B" circuit by summer. We've already got management in place and shows booked (starting 7/03) We want to be playing out hard core by summer (4 nights +) 94.1 WYSP/KRock/WSOU heavy party music/80's

10. Fractional Sanity - Fractals And Chaos Theory Fractals and chaos theory. Fractals and chaos theory have not only had a dramatic impact on mathematics, but also art and computer visualization. http://thor.prohosting.com/~nraak/chaostheory.htm

Fractals and Chaos Theory Mathematical Chaos Fractals and chaos theory have not only had a dramatic impact on mathematics, but also art and computer visualization. Some people might argue that chaos and fractals were around long before the invention of computers, especially considering Poincare’s researches, and the fact that Cantor had invented an infinite set, that was essentially a "fractal". However it was not until computers began to be used extensively in numerical research in the 1960's that chaos and fractals would become a fully-fledged area of mathematics to display themselves in a dizzying array of colours and infinite descent that so many people have seen. So how did it begin? Most mathematical physics is based around the study and solution of Differential Equations. Differential Equations are just like every other sort of equation, in which something on one side has to equal something on the other side, for example For the above equation we are usually given the values of y and c, and asked to solve the equation for t. Thus we have one side equaling the other side, and we are asked to find certain values of t that makes this true. Differential equations are of exactly the same form, except instead of solving for simple values or functions, we are asked to solve for functions that relate the rate of change of one value to another. For clarity consider the following example.

11. Chaos Theory And Education Describes how chaos theory can impact educational theory. Explains chaos theory and gives examples in education. http://www.libraryreference.org/chaos.html

Chaos Theory and Education Michael Lorenzen The universe is a chaotic place. It is full of uncertainty and it can be difficult to predict exactly what is going to happen at any given time be it the present or the far future. Scientists and mathematicians have developed a theory to explain this phenomenon. It is called chaos theory and it is highly relevant to the field of teaching. Education is an uncertain endeavor. Not only is it difficult to exactly predict what will happen in the class each day, it is nearly impossible to ascertain what the best course of education for any given person or class may be. The reasons for this are simple. Education is connected to the rest universe and as such is fully subject to the chaos that naturally exists in reality. It is easy to see from this description that all work, be it professional or not, is subject to the whims of chaos. Any one in public service, be it a doctor or a cashier at Quality Dairy, deals with uncertainty while dealing with the public. It is impossible to predict with certain accuracy what is going to happen next. Even less public driven jobs have this uncertainty. The long term is even worse. How can any given action be used to explain why something happens later? Sometimes good guesses can be made. ("Hey, maybe I should have told that guy to stop smoking.") Still, it is difficult in to prove causality in most cases. There are usually several alternate explanations for every occurrence. Education and teaching are forced to deal with chaos. The initial, and all subsequent conditions, are not know to an infinite degree of accuracy with any given student or class. Hence, chaos must ensue. This chaos can be seen in two ways. First, every class session is uncertain until it occurs. Despite the best developed lesson plans and class management techniques, the class will be subject to an infinite number of possible occurrences. Second, it is difficult to see the connection between teaching and learning. How can a teacher know what is taught is best for the student's learning in the short and long terms. Sometimes, good assumptions can be made by studying students. However, all students are subject to a variety of chaos in their lives at school and in the world. Which effect beyond teaching could have effected the result? Educators will always deal with uncertainty in both how and what they should teach.

12. Chaos Theory: An Anchorage, Alaska Paintball Team A recreational and tournament team based in Anchorage. Pictures, game variations, and links. http://www.paintballchaos.com/

Theoretically Speaking... Well, the weather here is just crazy bizarre. It's been a strange winter, but still no indoor field.. =( Element has opened Goose Lake for a couple of days recently, but that may not last, depending on snow. A new Tournament Series has been announced, planned to take place between AK Village and Element over the summer. There is also a HUGE scenario planned for May down towards Homer at Mount Olsen. For details on both of these, zoom over to our Increasingly Popular Alaskan Forum . They are listed under the Scheduled Events Board. Element will be updating their website sometime in March, In the mean time, check it out at www.elementpaintball.com Welcome to our Website! Thanks for Visiting! All images and logos are the property of Chaos Theory or have been used by permission. Please do not display or link to them without permission from Chaos Theory e-mail us at: mail@paintballchaos.com Paintball team "Chaos Theory" is based in Anchorage, Alaska and was formed in 1998. We pride ourselves in remaining candid, easy to get along with, and fair. We may not be the best, but by god, we are the sexiest! More Paintball Sites: Here's what's going on in our Forum!

13. Billiards And Chaos Theory An interactive applet that shows billiard motion in various shaped tables.Category Science Math Chaos and Fractals Chaos......The Billiards Simulation. Polygon Table, Circle Table, Stadium Table, Ellipse Table.Documentation. Derya Davis, Mathematics and Physics; Carin Ewing, Philosophy;. http://serendip.brynmawr.edu/chaos/home.html

The Billiards Simulation Polygon Table Circle Table Stadium Table Ellipse Table ... Derya Davis , Mathematics and Physics; Carin Ewing , Philosophy; Zhenjian He , Computer Science and Mathematics; Tina Shen , Computer Science Advisors: Bogdan Butoi , Victor Donnay, and Deepak Kumar To Dynamical Systems To Serendip Forum ... Serendip Home Send us your comments at Serendip

14. Chaos Theory: Printable Version An Introduction to chaos theory and Fractal Geometry. The very name chaos theory seems to contradict reason, in fact it seems somewhat of an oxymoron. http://www.duke.edu/~mjd/chaos/chaosp.html

An Introduction to Chaos Theory and Fractal Geometry Author: Manus J. Donahue III "Physicists like to think that all you have to do is say, these are the conditions, now what happens next?" -Richard P. Feynman An interesting question arises from many skeptics concerning why chaos has just recently been noticed. If chaotic systems are so mandatory to our every day life, how come mathematicians have not studied chaos theory earlier? The answer can be given in one word: computers. The calculations involved in studying chaos are repetitive, boring and number in the millions. No human is stupid enough to endure the boredom; however, a computer is always up to the challenge. Computers have always been known for their excellence at mindless repetition; hence, the computer is our telescope when studying chaos. For, without a doubt, one cannot really explore chaos without a computer. Before advancing into the more precocious and advanced areas of chaos, it is necessary to touch on the basic principle that adequately describes chaos theory, the Butterfly Effect. The Butterfly Effect was vaguely understood centuries ago and is still satisfactorily portrayed in folklore: "For want of a nail, the shoe was lost;

15. SCTPLS Site Has Moved! Change your Bookmark! The web site for the Society for chaos theory in Psychologyand Life Sciences has moved! If you are not forwarded automatically http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/cspls.html

Change your Bookmark! The web site for the Society for Chaos Theory in Psychology and Life Sciences has moved! If you are not forwarded automatically ... Click here for the new location

16. THE THIRD CULTURE Collected works and ideas of intellectuals whose work bridges the gap that C.P. Snow identified as existing between traditional intellectuals and the sciences. Topics include physics, evolutionary biology, philosophy, psychology, artificial life, chaos theory, neural nets, fractals, and others. http://www.edge.org/3rd_culture/index.html

Home About Edge Features Edge Editions ... Edge Search The Third Culture The third culture consists of those scientists and other thinkers in the empirical world who, through their work and expository writing, are taking the place of the traditional intellectual in rendering visible the deeper meanings of our lives, redefining who and what we are. In the past few years, the playing field of American intellectual life has shifted, and the traditional intellectual has become increasingly marginalized. A 1950s education in Freud, Marx, and modernism is not a sufficient qualification for a thinking person in the 1990s. Indeed, the traditional American intellectuals are, in a sense, increasingly reactionary, and quite often proudly (and perversely) ignorant of many of the truly significant intellectual accomplishments of our time. Their culture, which dismisses science, is often nonempirical. It uses its own jargon and washes its own laundry. It is chiefly characterized by comment on comments, the swelling spiral of commentary eventually reaching the point where the real world gets lost. In 1959 C.P. Snow published a book titled The Two Cultures. On the one hand, there were the literary intellectuals; on the other

17. Choas In The CNS Paper Tutorial on chaos theory and selforganizing systems in the brain. Freeman Neurophysiology Lab, UC Berkeley. http://sulcus.berkeley.edu/FLM/MS/WJF_man2.html

CHAOS IN THE CNS: THEORY AND PRACTICE Walter J. Freeman Abstract The Limbic System Memory Some pivotal questions are: How does the organized neural activity that initiates and sustains voluntary behavior arise in the limbic system? What observable forms does it take? How does it depend on past experience? How does it achieve flexibility in adapting to unpredictably changing environments? An optimal starting point for answers is study of the neural mechanisms for memory, of its role in coding information, and of its role in classical and operant conditioning, which voluntary behavior incorporates and transcends. A principal focus of research has been the ganglia of invertebrates, in the hope that an understanding of the biological basis of memory through the anatomy and physiology of single neurons in simpler nervous systems might lead to the discovery of universal mechanisms of memory in the modifiable synapses (Alkon, 1992). The Hippocampus In regard to applications with neuropsychiatric patients, Alkon concludes (p. 225): "The awesome tasks of treatment must include restructuring the memory banks, reorienting the mind itself." Herein one can begin to see why this enterprise may fail, if the synapse is conceived as an address in a computer memory, which can be re-written as part of a new ''program". We know that memory is fallible, and that the human psyche can generate images, ideas, and articulations that transcend the limits of computers and neuropsychiatry (Sacks, 1985). A noncomputational approach is required (Globus, 1992).

18. Chaos Theory History JUDY PETREE'S HOMEPAGE GO TO CHAOS INDEX GO TO PART 2 INSTABILITY Part 1 Historyof chaos theory Be sure to check out Author's Homepage links in Footnotes http://www.wfu.edu/~petrejh4/HISTORYchaos.htm

JUDY PETREE'S HOMEPAGE GO TO CHAOS INDEX GO TO PART 2: INSTABILITY Part 1: History of Chaos Theory Be sure to check out Author's Homepage links in Footnotes Introduction Real life never goes as smoothly as this music. Click icon. The word "chaos" might have first appeared in Hesiod 's Theogeny (@700 B.C.E.) in Part I: "At the beginning there was chaos, nothing but void, formless matter, infinite space." Later in Milton's Paradise Lost : "In the beginning, how the heav'ns and earth rose out of chaos". Both Shakespeare ( Othello ) and Henry Miller ( Black Spring ) refer to chaos. In these instances one inferred that chaos was an undesirable disordered quality. Historically our vernacular incorporated this idea of disorder into chaos; dictionaries defined chaos as turmoil, turbulence, primordial abyss, and biblical references to Tohu and Bohu had the same referential character of undesired randomness. Scientifically, Chaos implied the existence of the undesirable randomness, but the self-organization concept at the edge of chaos denoted the order we get out of chaos. The American essayist and historian Henry Adams (1858-1918) expressed the scientific meaning of "chaos" succinctly: "Chaos often breeds life, when order breeds habit".

19. In The Wake Of Chaos (Stephen Kellert) Book exposes the actual philosophical implications of chaos theory. http://dannyreviews.com/h/Wake_of_Chaos.html

Danny Yee's Book Reviews Subjects Titles Authors ... Latest In the Wake of Chaos Stephen H. Kellert The University of Chicago Press 1993 A book review by Danny Yee "Chaos" has rapidly approached "quantum" as the favourite scientific buzz-word of crackpots, pseudo-scientists, and others of that ilk. Even in the humanities and social sciences chaos theory is less often used to model phenomena than invoked as support for outré metaphysical claims or sweeping generalisations about the demise of Western science. As an exposition of the philosophical implications of chaos theory, Kellert's In the Wake of Chaos is therefore an important work. Kellert begins by defining chaos theory as "the qualitative study of unstable aperiodic behavior in deterministic nonlinear dynamical systems". He goes on to explain this in non-technical language, but he doesn't provide a general introduction to chaos theory: readers are expected to have read at least popular accounts of the subject. Chapter two addresses the topics of predictability and sensitive dependence on initial conditions. Kellert argues that the problems of prediction raised by chaos theory require a new form of impossibility, between theoretical impossibility (violation of accepted laws of nature) and practical impossibility (ruled out by human limitations). He suggests the term

20. Www.students.uiuc.edu/~ag-ho/chaos/chaos.html Similar pages chaos theory A Brief Introductionchaos theory A Brief Introduction. What exactly is chaos? chaos theory also coversthe reverse finding the order in what appears to be completely random data. http://www.students.uiuc.edu/~ag-ho/chaos/chaos.html

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