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Topic: Edward Lorenz

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Lorenz attractor

Strange attractor

Butterfly effect

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Edge of chaos

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	Edward N. Lorenz (Site not responding. Last check: 2007-10-18)
		In the early 1960's using a simple system of equations to model convection in the atmosphere, Edward Lorenz, an MIT meteorologist, ran headlong into "sensitivity to initial conditions".
		In Lorenz's meteorological computer modeling, he discovered the underlying mechanism of deterministic chaos: simply-formulated systems with only a few variables can display highly complicated behavior that is unpredictable.
		In his famous 1963 paper Lorenz picturesquely explains that a butterfly flapping its wings in Beijing could affect the weather thousands of miles away some days later.
	www.exploratorium.edu /complexity/CompLexicon/lorenz.html (215 words)

	Edward Norton Lorenz - Wikipedia, the free encyclopedia
		Edward Norton Lorenz is an American mathematician and meteorologist, and a contributor to the chaos theory and inventor of the strange attractor notion.
		Edward Norton Lorenz was born in West Haven, Connecticut, on May 23, 1917.
		Lorenz went on to explore the underlying mathematics and published his conclusions in a seminal work in titled Deterministic Nonperiodic Flow, in which he described a relatively simple system of equations that resulted in a pattern of infinite complexity, the Lorenz attractor.
	en.wikipedia.org /wiki/Edward_Lorenz (339 words)

	Edward Norton Lorenz -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-18)
		Edward Norton Lorenz is an American mathematician and meteorologist, and a contributor to the (Click link for more info and facts about chaos theory) chaos theory and inventor of the (An attractor for which the approach to its final point in phase space is chaotic) strange attractor notion.
		Lorenz studied the way air moves around in the (The envelope of gases surrounding any celestial body) atmosphere, for which he build a mathematical model.
		Lorenz went on to explore the underlying mathematics and published his conclusions in a seminal work in titled Deterministic Nonperiodic Flow, in which he described a relatively simple system of equations that resulted in a pattern of infinite complexity, the (Click link for more info and facts about Lorenz attractor) Lorenz attractor.
	www.absoluteastronomy.com /encyclopedia/e/ed/edward_norton_lorenz.htm (617 words)

	The Essence of Chaos by Edward Lorenz (Site not responding. Last check: 2007-10-18)
		Edward Lorenz is a professor of meteorology at MIT who wrote the first clear paper about what has come to be known as Chaos.
		Lorenz himself of course first found the characteristics of chaos in weather patterns and in the book he recounts in a very interesting way how he made his discovery.
		Lorenz showed that with a set of simple differential equations seemingly very complex turbulent behaviour could be created that would previously have been considered as random.
	www1.dragonet.es /users/markbcki/lorenz.htm (436 words)

	Edward Lorenz
		Edward Lorenz is best known for his work with meteorology (mee•tee•uh•RAH•luh•jee), the science of weather.
		Edward Lorenz was born in West Haven, Connecticut, on May 23, 1917.
		Edward Lorenz developed an idea that was later called chaos to describe disorder in weather forecasting.
	www.harcourtschool.com /activity/biographies/lorenz (397 words)

	Levitated \| Lorenz Attractor \| Macromedia Flash open source
		The Lorenz Attractor is a solution to a set of differential equations originally developed to model small scale atmospheric behavior.
		The Lorenz Attractor is often attributed to Ed.
		Lorenz, who presented a paper to the New York Academy of Science in 1963 as the butterfly effect.
	www.levitated.net /daily/levLorenzAttractor.html (127 words)

	Introduction to Chaos Theory
		Lorenz's new system is three-dimensional, the three variables: x, y and z correspond to the location of a point in geometric space.
		Lorenz's system, although simple in the eyes of a physicist or mathematician, is actually an insolvable problem except by numerical means.
		Lorenz was the first to recognize this erratic behavior as something other than error, and that everyone had been trying to view the world through a microscope.
	www.gweep.net /~rocko/sufficiency/node10.html (1628 words)

	Chaos-Page 2 (Site not responding. Last check: 2007-10-18)
		Edward was unsuccessful with the accuracy of the prediction.
		Edward Lorenz continued to analyze the aspects of chaos finding that if all elements are controled the results have some sort of a boundary and the results look like a loop or fractual.
		All though Edward was looked at as the father of chaos he was not the first one to discover its wonders.
	www.colorado.edu /physics/phys2900/homepages/Tim.Brenner/public/Page-2.html (250 words)

	LORENZ, EDWARD N. - CIRS (Site not responding. Last check: 2007-10-18)
		LORENZ, EDWARD N. Professor Emeritus, Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, USA.
		Professor Emeritus Edward N. Lorenz has been investigating the extent to which weather is predictable.
		Professor Lorenz is also studying the long-term properties of highly simplified mathematical models of the atmosphere and similar systems.
	www.cirs-tm.org /investigadores/investigadores.php?id=520 (242 words)

	chaos theory - a Whatis.com definition - see also: butterfly effect (Site not responding. Last check: 2007-10-18)
		Lorenz, a meteorologist, was running computerized equations to theoretically model and predict weather conditions.
		Lorenz reentered the number from his printout, taken half-way through the sequence, and left it to run.
		In a 1963 paper for the New York Academy of Sciences, Lorenz had quoted an unnamed meteorologist's assertion that, if chaos theory were true, a single flap of a single seagull's wings would be enough to change the course of all future weather systems on the earth.
	whatis.techtarget.com /definition/0,,sid9_gci759332,00.html (805 words)

	Lorenz Awarded Kyoto Prize (Site not responding. Last check: 2007-10-18)
		Professor Emeritus Edward N. Lorenz SM '43 of the Department of Earth and Planetary Sciences has been awarded the 1991 Kyoto Prize for the basic sciences for his pioneering work on the study of mathematically chaotic systems in nature.
		Lorenz later discovered that the chaos inherent in atmosphere circulation made it impossible to forecast the weather over any given area of the globe more than about 10 days in advance.
		Lorenz, who is at the National Center for Atmospheric Research in Boulder, CO, could not be reached for comment.
	www-tech.mit.edu /V111/N29/kyoto.29n.html (366 words)

	Mastering Chaos
		To demonstrate synchronized chaos initially, Pecora created a computer simulation based on the chaotic Lorenz system, which is named after American meteorologist Edward N. Lorenz, who in 1963 discovered chaotic behavior in a computer study of the weather.
		Plotting the trajectory of the Lorenz system in state space reveals what is known as the Lorenz chaotic attractor [see "Chaos," by James P. Crutchfield, J. Doyne Farmer, Norman H. Packard and Robert S. Shaw; SCIENTIFIC AMERICAN, December 1986].
		Four years ago Edward Ott, Celso Grebogi and James A. Yorke of the University of Maryland developed a scheme in which a chaotic system can be encouraged to follow one particular unstable orbit through state space.
	www.fortunecity.com /emachines/e11/86/mastring.html (5534 words)

	Edward Lorenz Article, EdwardLorenz Information (Site not responding. Last check: 2007-10-18)
		Edward Norton Lorenz (born May 23, 1917), a research meteorologist at MIT, observed that minute variations in the initial values of variables in his primitive computer weather model (c.1960) would result in grossly divergent weather patterns.
		This sensitive dependenceon initial conditions came to be known as the Butterfly effect.
		He went on to explore the underlying mathematics and published his conclusions in a seminal work in the annals of chaos theory, Deterministic Nonperiodic Flow, in which he described arelatively simple system of equations that resulted in a pattern of infinite complexity, the Lorenz attractor.
	www.anoca.org /weather/initial/edward_lorenz.html (182 words)

	Lorenz Attractor (Site not responding. Last check: 2007-10-18)
		Edward Lorenz, a meteorologist, modelled the location of a moving particle subject to atmospheric forces and obtained a system of three differential equations.
		Lorenz saw that slight differences in one variable had profound effects on the outcome of the whole system, a result of "sensitive dependence on initial conditions".
		To illustrate what this means, Lorenz has said that a butterfly flapping its wings in Brazil could stir up a hurricane in Texas.
	www.cat.cc.md.us /~gwillgin/lorenz.htm (102 words)

	Strange Attractors - Lorenz Butterfly (Site not responding. Last check: 2007-10-18)
		Edward Lorenz in 1960 while attempting to create a weather forecasting program on a computer in his MIT laboratory.
		Upon a closer examination, Lorenz found that rounding off his input values (from five or six decimals to three) was having a profound effect on the system.
		Lorenz found that the simplest way to describe his system was by using the three above equations.
	www.cs.colby.edu /projects/2002-03/donahue/lorentz.htm (367 words)

	People in Chaos (Site not responding. Last check: 2007-10-18)
		Edward Lorenz was born in 1917 and has worked at MIT since 1946.
		His paper "Deterministic Nonperiodic Flow" in 1963 marked the beginnning of a new area of research in chaos, that of atmospheric prediction, which is now one of the most famous areas of chaotic research.
		The Lorenz attractor is named after him, after his work on the Butterfly Effect.
	students.bath.ac.uk /ma2bs/people.html (451 words)

	Edward van de Vendel
		Het omslag is iets gewijzigd, maar het binnenwerk is niet veranderd.
		Edward de tekst voor schreef en Carll Cneut de tekening voor maakt, en dat in het najaar bij Uitgeverij De Eenhoorn verschijnt.
		Edward schreef twee liedteksten, en Isabelle Vandenabeele maakte er keramisch werk bij.
	www.edwardvandevendel.com /DreamHC/Page2.html (4414 words)

	UW Press: Search Books in Print
		In The Essence of Chaos, Lorenz presents to the general reader the features of this "new science," with its far-reaching implications for much of modern life, from weather prediction to philosophy, and he describes its considerable impact on emerging scientific fields.
		Lorenz uses examples from everyday life, and simple calculations, to show how the essential nature of chaotic systems can be understood.
		Appendixes present the first publication of Lorenz's seminal paper "Does the Flap of a Butterfly's Wing in Brazil Set Off a Tornado in Texas?"; the mathematical equations from which the copious illustrations were derived; and a glossary.
	www.washington.edu /uwpress/search/books/LORESS.html (564 words)

	The Essence of Chaos (Site not responding. Last check: 2007-10-18)
		For Lorenz, sensitive dependence on initial conditions is central to an acceptable definition of chaos.
		Lorenz explains: "The states of any system that do occur again and again, or are approximated again and again, more and more closely, therefore belong to a rather restricted set.
		Lorenz notes, "To [Poincaré, chaos] was the phenomenon that rendered the three-body equations too complex to be solved, rather than the principal subject of a future field of investigation" (121).
	mtprof.msun.edu /Win1995/Cofrev.html (1296 words)

	Lorenz Attractor
		Lorenz had assumed that the difference, only one part in a thousand, would be inconsequential; however, due to the recursive nature of the equations, little errors would first cause tiny errors, which would then affect the resulting next calculation a bit more, which would affect the output of the next run even more.
		A term Lorenz coined to describe sensitive dependence on initial conditions is the "butterfly effect." This is another thought experiment which is hardly testable: imagine that there exist two earths, so that an incorporeal observer could compare events on one earth to another.
		Lorenz happened to choose 8/3, which is now the most common number used to draw the attractor.
	www.zeuscat.com /andrew/chaos/lorenz.html (1713 words)

	Index (Site not responding. Last check: 2007-10-18)
		Lorenz cannot break with the Cold War framework that focuses on the role of the U.S. and the struggle against Communism.
		Lorenz believes that the progressive coalitions of earlier eras, and Meany's struggle with the ILO in the 1970s, prove that dedicated populists working within the framework of American political pluralism, and committed to the ILO's tripartite structure, can force governments and corporations to take workers' rights into account.
		In passing Lorenz alludes to the theory that the ILO owes its very existence to the strength of European socialism and the Russian Revolution.
	slash.autonomedia.org /print.pl?sid=02/01/24/1616213 (694 words)

	Making Order Out of Chaos: Edward Lorenz
		One of the earliest pioneers of chaos theory was Edward Lorenz.
		Lorenz was a meteorologist at the Maachussetts Institute of Technology.
		When Lorenz entered the numbers to recreate the scenerio, he the printout provided him with numbers to the thousandth position (such as.617).
	library.thinkquest.org /12170/history/lorenz.html (286 words)

	Chaos Theory: A Brief Introduction
		From this idea, Lorenz stated that it is impossible to predict the weather accurately.
		However, this discovery led Lorenz on to other aspects of what eventually came to be known as chaos theory.
		Lorenz had discovered something revolutionary; now he had to wait for someone to discover him.
	www.imho.com /grae/chaos/chaos.html (2838 words)

	Intro to Fractals (Site not responding. Last check: 2007-10-18)
		Edward Lorenz, however, was a meteorologist with a strong mathematical background who had an early computer at his disposal.
		Lorenz learned that certain patterns were usually followed by other patterns and believed he was on the path to completely accurate weather prediction.
		Lorenz realized that to accurately predict weather in the long term would require almost infinitesimal sensing and readjustment of initial conditions.
	home.comcast.net /~laellis/Chaos (3094 words)

	No. 652: The Butterfly Effect
		Lorenz rounded off the fourth decimal place of the starting number on the second day.
		Suddenly, Lorenz saw that the weather would change utterly if you started things out just a little differently.
		Lorenz had taken the first step on the road to showing that our world is far more chaotic than we dreamed.
	www.uh.edu /engines/epi652.htm (413 words)

	The Essence of Chaos (The Jessie and John Danz Lecture Series): Current Amazon U.S.A. One-Edition Data (Site not responding. Last check: 2007-10-18)
		Lorenz analyzes specific chaotic functions, gives you the math (equations are in the appendix) and generally accomplishes what the title suggests - that is, exploring the essence of chaos.
		Edward Lorenz takes a complicated topic and makes it accessible for all people, regardless of prior knowledge of chaos theory.
		Lorenz gives a brief history of chaos and explains how it is used in the study of mathematics, meteorology, economics, music, and other fields.
	www.ferretexpert.info /stuff-0295975148.html (327 words)

	The Butterfly Effect (Site not responding. Last check: 2007-10-18)
		This is illustrated in the accompanying applet of the Lorenz Attractor.
		This is an illustration of the butterfly effect - the idea in meteorology that the flapping of a butterfly's wing will create a disturbance that in the chaotic motion of the atmosphere will become amplified eventually to change the large scale atmospheric motion, so that the long term behavior becomes impossible to forecast.
		The "Butterfly Effect" is often ascribed to Lorenz.
	www.cmp.caltech.edu /~mcc/chaos_new/Lorenz.html (348 words)

	KNAW > News > Press releases (Site not responding. Last check: 2007-10-18)
		Mr Lorenz will be presented with his medal on Wednesday 12 May at the headquarters of the Royal Netherlands Meteorological Institute (KNMI) in De Bilt, the Netherlands.
		The Royal Netherlands Academy is awarding the medal to Lorenz for his contribution to the science of weather and climate forecasting.
		Lorenz, the founder of chaos theory, discovered that a small disturbance of the atmosphere in one location can have major consequences for the weather in another.
	www.knaw.nl /cfdata/news/pressrelease_detail.cfm?nieuws__id=247 (425 words)

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