41. Chaos And The Solar System Article by Paul Trow about the development of the theory and its astronomic insights. http://ptrow.com/articles/ChaosandSolarSystem5.htm

Chaos and the Solar System by Paul Trow Mathematical theories do not usually get much public attention. A recent exception is the theory of chaos, which emerged on the scientific world in the 1970�s, and has since received extensive coverage by the media and in a number of books aimed at a general audience. The term �chaos� has even made its way into several popular science fiction movies. Part of the fascination with this theory has to do its claim that chaos � which is inherently more interesting than order - is a pervasive feature of the world around us. Chaos, we are told, is responsible for the unpredictability of the weather and the fluctuations of the stock market. We can observe it in ecological systems, the rhythms of the human body, and the turbulence of a mountain stream. Surprisingly, although chaos is all around us here on Earth, the mathematician Henri Poincare first discovered it, late in the nineteenth century, in the mathematics underlying the solar system. Before explaining just what Poincare discovered, let us recall a little of the background the background that led up to it. In a sense, chaos theory is as a belated reaction to the principle of determinism, which dominated science for over three hundred years. Newton established this principle through his second law of motion, force equals mass times acceleration, from which it follows that if we know all of the forces acting on a system, we should � at least in theory - be able to predict how it will evolve over time. Determinism gave rise to the metaphor of the clockwork universe, which, when once wound up, will evolve forever in a predetermined manner.

42. Chaos - Dissidia Wiki - Characters, Equipment, Guides, And More chaos is the main antagonist in Dissidia. As the God of Discord, he summons villains from the worlds of Final Fantasy I to XII (except XI), in order to tip the balance of good http://dissidia.wikia.com/wiki/Chaos

Wikia Skip to Content Skip to Wiki Navigation Skip to Site Navigation Wikia Navigation Start a wiki Entertainment Fall TV Glee ... Dissidia Wiki Dissidia Wiki Navigation Dissidia Wiki Characters Cosmos Chaos ... Shop Random Page Wiki Activity Watchlist Recent changes Talk Chaos Edit Read more: Character Edited by A Wikia contributor View full history Chaos is the main antagonist in Dissidia . As the God of Discord, he summons villains from the worlds of Final Fantasy I to XII (except XI), in order to tip the balance of good and evil. He wages war on Cosmos , the Goddess of Harmony, to gain control of the world. The God of Discord Added by Orochi Freeza Contents Fighting Chaos Chaos' Brave Attacks Ground Attacks Air Attacks ... Trivia Fighting Chaos Edit Chaos' style is fittingly named Master of Bedlam . Unleashing the mightiest of earth and fire based attacks, Chaos wreaks utter havoc and destruction upon his foes. His attacks cover a very large range and is capable of instantly warping to his opponent's position. When fighting Chaos, players may find him intimidating due to his sheer size and strength. However, here are a few tips for fighting Chaos, including his attacks. Chaos comes equipped with a summon, Shinryu. Unlike the player's summons, Shinryu regenerates during the battle, allowing Chaos to use Shinryu continuously during a single phase of battle. Shinryu's ability is

43. The Chaos Game Outlines Barnsley s chaos game, in which a random number generator is used to produce various fractals. http://www.jcu.edu/math/vignettes/ChaosGame.htm

Vignette 9 The Chaos Game The Chaos Game is played as follows: On a sheet of paper, mark the three vertices of an equilateral triangle. (Variations of the game use triangles of other shapes.) Mark the vertices A B and C , as shown below. With a pencil or pen, mark any other point chosen at random on the paper. We will call this point P . You should mark the point, but don't label it. Now roll an ordinary 6-faced die. If the die comes up 1 or 2, measure half the distance from P to vertex A , and plot a new point there. (Remember where this point is, but don't label it.) If the die shows 3 or 4, do the same thing, but instead go half the distance toward vertex B . If the die shows 5 or 6, go halfway to vertex C . Continue this process, using your newly marked points as the new starting points for each move. Play for about 30,000 moves or until you get tired whichever comes later. The Chaos Game It seems intuitively clear that "chaos" would be a good word to describe this game. After all, you are marking 30,000 points, each of which is selected by applying a random process the roll of a die. And each game should progress differently, since there is randomness involved in each move. After 30 rolls of the die in one play of the game, the following points were plotted: Of course, if you start with a point within the boundaries of the triangle, then all of the points will stay within the triangle. So it is not unexpected that all of these points are contained within the triangle. But is there any other pattern that we do not yet see? Let's continue to play the game, this time for a total of 100 rolls:

44. Chaos -- From Wolfram MathWorld chaos is a tricky thing to define. In fact, it is much easier to list properties that a system described as chaotic has rather than to give a precise definition of chaos. http://mathworld.wolfram.com/Chaos.html

Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Interactive Demonstrations Chaos "Chaos" is a tricky thing to define. In fact, it is much easier to list properties that a system described as "chaotic" has rather than to give a precise definition of chaos. Gleick (1988, p. 306) notes that "No one [of the chaos scientists he interviewed] could quite agree on [a definition of] the word itself," and so instead gives descriptions from a number of practitioners in the field. For example, he quotes Philip Holmes (apparently defining "chaotic") as, "The complicated aperiodic attracting orbits of certain, usually low-dimensional dynamical systems." Similarly, he quotes Bai-Lin Hao describing chaos (roughly) as "a kind of order without periodicity." It turns out that even textbooks devoted to chaos do not really define the term. For example, Wiggins (1990, p. 437) says, "A dynamical system displaying sensitive dependence on initial conditions on a closed invariant set (which consists of more than one orbit) will be called chaotic ." Tabor (1989, p. 34) says, "By a chaotic solution to a deterministic equation we mean a solution whose outcome is very sensitive to initial conditions (i.e., small changes in initial conditions lead to great differences in outcome) and whose evolution through phase space appears to be quite random." Finally, Rasband (1990, p. 1) says, "The very use of the word 'chaos' implies some observation of a system, perhaps through measurement, and that these observations or measurements vary unpredictably. We often say observations are chaotic when there is no discernible regularity or order."

45. The Tundra Bastille Images and information about chaos! characters. http://members.tripod.com/~VampiressKemira/index.html

Build your own FREE website at Tripod.com Share: Facebook Twitter Digg reddit document.write(lycos_ad['leaderboard']); document.write(lycos_ad['leaderboard2']); Welcome to the Tundra Bastille! As you enter through the dark wooden door, your senses are assualted by a variety of images and sounds. You can almost hear the creak of floorboards, and smell the blood that stains the walls. To your right, you see a large, ornately carved bronze door decorated with lights that still glow strongly, despite the wear of the centuries. You press your ear to the door, and can faintly hear the sound of people clapping. You try the knob, but in vain-it's locked, and has obviously been so for quite a while, due to the rust gathering on the iron. Throwing your hands up, you venture further into the large room. Directly in front of you are a stairwell, ascending up into darkness, and a set of doors. One is a stone opening, with nothing between them- even the hings have rusted away-and an odd little door. Several doorframes descend into the walls before reaching a shining bronze door, which also happens to be locked. Giving up, you wander The stone archway Up the stairs souls have passed through these halls Vampiress Kimera city.of.angels@usa.net

46. Chaos - Warhammer 40K Wiki - Space Marines, Chaos, Planets, And More chaos refers to the universal spiritual force represented by the often malevolent intelligent entities comprised of psychic energy that live in the Warp, composed mostly of http://warhammer40k.wikia.com/wiki/Chaos

Wikia Skip to Content Skip to Wiki Navigation Skip to Site Navigation Wikia Navigation Start a wiki Entertainment Fall TV Glee ... Warhammer 40k Warhammer 40k Navigation Top Content Editor's pick Most visited Highest voted ... Fenris Random Page Wiki Activity Watchlist Recent changes Talk Chaos Login to edit Read more: C Chaos Edited by Montonius View full history The Chaos Star, Symbol of Chaos Undivided Added by GreaterBad Chaos refers to the universal spiritual force represented by the often malevolent intelligent entities comprised of psychic energy that live in the Warp , composed mostly of daemons , but the term also encompasses those mortals who have thrown in their lot with Chaos, ranging from simple peasants and/or laborers who serve as Chaos Cultists, to Traitor Imperial Guardsmen, warriors, Imperial nobles, planetary governors, and even the mighty Chaos Space Marines and Traitor Titan Legions . Chaos is also itself the psychic energy that composes Warp space. Chaos is almost synonymous with the Warp - the two concepts are inseparable: Chaos is the limitless ocean of spiritual and emotional energy that defines the Immaterium. It is a great and raw force of change and power, and is both physically and spiritually corrupting. The most gifted mortals, psykers, can utilize this energy, thus making them capable of abilities which transcend the laws of the material universe. However, the malevolent power of Chaos can gradually corrupt a psyker, tainting his mind and body. The most powerful entities of Chaos are the four great Chaos Gods, also known as the Ruinous Powers, who each embody one aspect of the greater force of Chaos and can be worshipped individually or as an entire pantheon. The iconic symbol of Chaos is the eight-pointed star, representing the infinite possibilities of Chaos.

47. Cyber Fiends - Group chaos! Comics Official Online Chapter of the Fiend Club. http://cyberfiends.yuku.com/

48. Interactivate: Chaos The following discussions and activities are designed to lead the students to explore various incarnations of chaos. This lesson is best implemented with students working in http://www.shodor.org/interactivate/lessons/Chaos/

@import "/common-1.9/ui/default/css/main.css"; @import "/common-1.9/ui/interactivate/css/main.css"; @import "/interactivate/public/css/main.css"; @import "/common-1.9/ui/xforms/xforms.css"; Interactivate Jump To: Activities Discussions Lessons Tools Assessments Dictionary Textbooks Standards Version 1.0 Browse: By Subject (broad) By Topic (specific) By Audience By Resource Type Chaos Shodor Interactivate Lessons Abstract The following discussions and activities are designed to lead the students to explore various incarnations of chaos. This lesson is best implemented with students working in teams of 2, alternating being the "driver" and the "recorder" using the computer activities. Objectives Upon completion of this lesson, students will: have experimented with several chaotic simulations have built a working definition of chaos have reinforced their knowledge of basic probability and percents Standards Addressed: Please select a standards alignment California Content Standards Common Core State Standards NCTM North Carolina Standard Course of Study South Carolina Academic Standards for Mathematics Texas Essential Knowledge and Skills Grade 5 Number Sense 1.0 Students compute with very large and very small numbers, positive integers, decimals, and fractions and understand the relationship between decimals, fractions, and percents. They understand the relative magnitudes of numbers

49. Chaos - Definition Of Chaos At YourDictionary.com noun. the disorder of formless matter and infinite space, supposed to have existed before the ordered universe; extreme confusion or disorder; Archaic an abyss; chasm http://www.yourdictionary.com/chaos

50. MySpace - JAPMAN - 32 - Male - Margate, US - Myspace.com/japman Photos, scans, chaos! Top Ten lists. http://www.myspace.com/japman

51. Chaos chaos is from the Greek word Khaos, meaning 'gaping void'. There are many explanations as to who or what chaos is, but most theories state that it was the void from which all http://www.pantheon.org/articles/c/chaos.html

52. Ecometry Introduction to chaos, attractors and dynamic systems theory. Includes mathematical formulation, images and references. http://www.bentamari.com/

53. Chaos - Greek Mythology Link Greek Mythology Link a collection of myths retold by Carlos Parada, author of Genealogical Guide to Greek Mythology. http://homepage.mac.com/cparada/GML/Chaos.html

Document belonging to the Greek Mythology Link , a web site created by Carlos Parada , author of Genealogical Guide to Greek Mythology Characters Places Topics ... About Chaos Chaos. Painting by C. Parada (but Chaos—the Hesiodic—cannot be represented). “In truth at first Chaos came to be …” writes Hesiod, “but next wide-bosomed Earth …” The name Chaos, we learn, comes from and means unfilled expanse. The Hesiodic Chaos is understood as a “Gaping Chasm,” the empty space, the void, or the place where everything else exists. “These considerations,” writes Aristotle ( Phys “would lead us to suppose that place is something distinct from bodies, and that every sensible body is in place. Hesiod too might be held to have given a correct account of it when he made Chaos first … If this is its nature, the potency of place must be a marvelous thing, and take precedence of all other things. For that without which nothing else can exist, while it can exist without the others, must needs be first; for place does not pass out of existence when the things in it are annihilated.” Unlike all phenomena, Chaos is beyond change: it undergoes no transformations. Therefore the peculiar manner of being of this

54. Chaos (Final Fantasy)/Dissidia - The Final Fantasy Wiki Has More Final Fantasy I chaos is the primary antagonist and the Final Boss of Dissidia Final Fantasy. He is the god of discord that opposes Cosmos, the goddess of harmony, both being equal in power. http://finalfantasy.wikia.com/wiki/Chaos_(Final_Fantasy)/Dissidia

Wikia Skip to Content Skip to Wiki Navigation Skip to Site Navigation Wikia Navigation Start a wiki Entertainment Fall TV Glee ... Final Fantasy Wiki Final Fantasy Wiki Navigation Featured articles Final Fantasy XIII Dissidia Final Fantasy Cloud Strife ... Final Fantasy VII Random Page Wiki Activity Watchlist Recent changes Talk Chaos (Final Fantasy)/Dissidia Edit Chaos (Final Fantasy) Read more: Villains Dissidia Final Fantasy Characters Edited by Yeah 93 View full history At the end of the dream...even chaos tears itself apart! Chaos is the primary antagonist and the Final Boss of Dissidia Final Fantasy . He is the god of discord that opposes Cosmos , the goddess of harmony, both being equal in power. However, Chaos summons villains from other worlds to seize control of the Crystals , tipping the balance of power in his favor and setting the stage for the game's events. Chaos is voiced by Norio Wakamoto in the Japanese release, and Keith David in the English release. He is set to return, along with the other characters from Dissidia , to Dissidia 012 Final Fantasy Contents Appearance Story Shade Impulse Battle ... Trivia Appearance Edit Chaos's appearance is based on his original artwork by Yoshitaka Amano . He appears as a four-arm fiend in dark and red hues, with wings sprouting from his back and a demonic face with large horns. He also has an alternate form that can be changed to in battle, which is a palette swap based on the in-game sprite from the original

55. Chaos - HammerWiki, The Warhammer Online Wiki - Zones, Quests, Guilds, And More This article describes the background and the forces that make up chaos. For information about the army and the playable careers, see the article on the Raven Host. http://warhammeronline.wikia.com/wiki/Chaos

Wikia Skip to Content Skip to Wiki Navigation Skip to Site Navigation Wikia Navigation Start a wiki Entertainment Fall TV Glee ... HammerWiki HammerWiki Navigation Gameplay Combat RvR PvE ... Community talk Random Page Wiki Activity Watchlist Recent changes Talk Chaos Edit Read more: Chaos Edited by Heaven's Agent View full history The eight-pointed star represents Chaos Undivided and is also used by followers of the individual Gods, arguably the most prominent symbol in Warhammer. Added by Pendrako This article describes the background and the forces that make up Chaos . For information about the army and the playable careers , see the article on the Raven Host For information on the Tome of Knowledge unlocks, see the bestiary Chaos is a term used variously to describe a mutating and corrupting force from the Realm of Chaos which manifests in the world as the Winds of Magic ; the mortal (whether humans or any other race ) and daemonic servants of "Chaos"; the Chaos Gods Tzeentch Nurgle Khorne and Slaanesh and as a broad term for all of these together. Contents Introduction Origins of Chaos Overview of the Chaos Gods Tzeentch, the Changer of Ways

56. Chaos Theory: A Brief Introduction | IMHO What exactly is chaos? The name chaos theory comes from the fact that the systems that the theory describes are apparently disordered, but chaos theory is really about http://www.imho.com/grae/chaos/chaos.html

IMHO In My Humble Opinion Log in Home Chaos Theory: A Brief Introduction What exactly is chaos? The name "chaos theory" comes from the fact that the systems that the theory describes are apparently disordered, but chaos theory is really about finding the underlying order in apparently random data. When was chaos first discovered? The first true experimenter in chaos was a meteorologist, named Edward Lorenz. In 1960, he was working on the problem of weather prediction. He had a computer set up, with a set of twelve equations to model the weather. It didn't predict the weather itself. However this computer program did theoretically predict what the weather might be. Figure 1: Lorenz's experiment: the difference between the starting values of these curves is only .000127. (Ian Stewart, Does God Play Dice? The Mathematics of Chaos, pg. 141) One day in 1961, he wanted to see a particular sequence again. To save time, he started in the middle of the sequence, instead of the beginning. He entered the number off his printout and left to let it run. When he came back an hour later, the sequence had evolved differently. Instead of the same pattern as before, it diverged from the pattern, ending up wildly different from the original. (See figure 1.) Eventually he figured out what happened. The computer stored the numbers to six decimal places in its memory. To save paper, he only had it print out three decimal places. In the original sequence, the number was .506127, and he had only typed the first three digits, .506.

57. Chaos - Wiktionary A vast chasm or abyss. The unordered state of matter in classical accounts of cosmogony Any state of disorder, any confused or amorphous mixture or conglomeration. 1977 http://en.wiktionary.org/wiki/chaos

chaos Definition from Wiktionary, the free dictionary Jump to: navigation search Chaos (disambiguation) on Wikipedia Wikipedia See also Chaos Contents English Etymology Pronunciation Noun ... edit English edit Etymology From Ancient Greek khaos vast chasm, void In Early Modern English used in the sense of the original Greek word. In the meaning primordial matter from the 16th century. Figurative usage in the sense "confusion, disorder" from the 17th century. The technical sense in mathematics and science dates to the 1960s. edit Pronunciation IPA /ˈkeɪ.ɒs/ SAMPA /keIQs/ Audio (US) file Rhymes: -eɪɒs edit Noun chaos usually uncountable plural chaoses obsolete A vast chasm or abyss The unordered state of matter in classical accounts of cosmogony Any state of disorder, any confused or amorphous mixture or conglomeration. , Irwin Edman, Adam, the Baby, and the Man from Mars‎ , page 54 or out of these chaoses order may be made, out of this ferment a clear wine of life. There are chaoses that have gone too far for retrieval obsolete rare A given medium ; a space in which something exists or lives; an environment , Robert Burton, The Anatomy of Melancholy , II.ii.3:

58. Chaos Research Group At The University Of Tennessee Interdisciplinary research group at the University of Tennessee concerned with deterministic nonlinear dynamic aspects. Includes overview, publications, bibliography, monographs, glossary and project information. http://www-chaos.engr.utk.edu/

Chaos Research Group The University of Tennessee and Oak Ridge National Laboratory will host Dynamics Days in Knoxville, Tennessee, 2008 January 3-6. Please visit the site for up-to-date information. Overview Personnel Research Publications (with viewable abstracts and downloadable texts) Chaos bibliographies (lists of references on specific subjects) Links to related sites on the WWW Site map What's new (updated 2007-06-14) "Chaos" quotations Patents - patents held by group members sci.nonlinear FAQ - Meiss's Frequently Asked Questions (with answers) Miscellania - random stuff Local server information Overview The Chaos Research Group studies deterministic chaos and nonlinear dynamics in engineering systems and is located within the College of Engineering at the University of Tennessee . This group closely collaborates with the researchers at the Oak Ridge National Laboratory The Chaos Research Group is an interdisciplinary team of faculty, students and engineering staff which studies the nature of complex, nonlinear engineering systems to achieve a better understanding of the underlying physical processes, to develop better diagnostics, or to control these systems in situations in which conventional control might be infeasible or too costly. Personnel Research Publications Bibliographies ... Quotations Please email comments about this page to www-adm@www-chaos.engr.utk.edu

59. Chaos - RelicWiki Like the Space Marines, chaos Marines are one of the most elite fighting forces in the Warhammer 40,000 universe. But chaos also draws on the power of the Warp and their hordes http://wiki.reliccommunity.com/Chaos

Chaos From RelicWiki Jump to: navigation search This article is part of the Dawn of War Player's Guide guide discussion A Chaos Marine Like the Space Marines, Chaos Marines are one of the most elite fighting forces in the Warhammer 40,000 universe. But Chaos also draws on the power of the Warp and their hordes of daemons and followers to create a dangerously brutal and unpredictable fighting force. Chaos uses hordes of Cultist, sorcerous abilities, and warp-spawned daemons to throw enemies off guard and then finish them off with the cold, calculating brutality of Space Marines who have lived and fought for thousands of years. Contents Backstory Dawn of War Winter Assault Dark Crusade ... The Dawn of War Player's Guide Backstory At the birth of the Imperium of Man, fully half of the Emperor's most trusted Space Marine Legions turned against him in a bitter civil war known as the Horus Heresy. Brother fought brother, and Mankind stood upon the very brink of extinction in this civil war. After Warmaster Horus was defeated, the fallen Space Marines were banished to the Eye of Terror. Ten thousand years after their defeat, those same traitors still launch their Black Crusades out of the Eye of Terror, intent upon nothing less then the utter destruction of the Imperium and the death of its weakling Emperor. Now and forever they had become Chaos Space Marines, despised and feared as traitors and heretics throughout the galaxy.

60. James A. Yorke Professor of mathematics and physics at the University of Maryland, U.S., known to the general public for coining the mathematical term of chaos in 1975. Includes publications and contact information. http://www-chaos.umd.edu/~yorke/

James A. Yorke Distinguished University Professor of Mathematics and Physics Institute for Physical Sciences and Technology (IPST) University of Maryland, College Park, MD 20742 A.B., Columbia University Ph.D., Mathematics, University of Maryland at College Park After Professor Yorke earned his bachelors degree from Columbia University in 1963, he came to the University of Maryland for graduate studies, in part because of interdisciplinary opportunities offered by the faculty of IPST. IPST is an Institute established in 1950 and committed to interdisciplinary research in the sciences. After receiving his doctoral degree in 1966 in Mathematics, Yorke stayed at the University as a member of IPST. Today he holds the title of Distinguished University Professor and also is a member of the Mathematics and Physics Departments. Professor Yorke's current research projects range from chaos theory and weather prediction and genome research to the population dynamics of the HIV/AIDS epidemic. He is perhaps best known to the general public for coining the mathematical term "chaos" with T.Y. Li in a 1975 paper entitled

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