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Topic: Strange attractor

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	Attractor - Wikipedia, the free encyclopedia
		Until the 1960s, as evidenced by textbooks of that era, attractors were thought of as being geometrical subsets of the phase space: points, lines, surfaces, volumes.
		Strange attractors are often differentiable in a few directions and like a Cantor dust (and therefore not differentiable) in others.
		The Hénon attractor and the Lorenz attractor are examples of strange attractors.
	en.wikipedia.org /wiki/Strange_attractor (899 words)

	Jo Alyson Parker
		strange attractor evolves in the multi-dimensionality of state- space, as trajectories at times diverge and at times almost converge, but never intersect, attracted to the unstable attracting point or points that they can never attain.
		One important feature of the strange attractor is that, as the trajectory moves through state space, the "memory" of initial conditions is lost as new information replaces it.
		Reframing my earlier discussion in terms of attractors, I would argue that in the linear (auto)biographical novel, the birth of the protagonist initiates a (narrative) trajectory that is attracted to the fixedpoint of the protagonist's death, whether symbolic or real.
	www.altx.com /ebr/w(ebr)/essays/parker.html (3787 words)

	Larry D. Bradley: Strange Attractors
		Strange attractors are unique from other phase space attractors in that one does not know exactly where on the attractor the system will be.
		Strange attractors are also unique in that they never close on themselves - the motion of the system never repeats (non-periodic).
		The Lorenz attractor was the first strange attractor, but there are many systems of equations that give rise to chaotic dynamics.
	www.pha.jhu.edu /~ldb/seminar/attractors.html (383 words)

	Attractor -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-20)
		In ((physics) a phase space togther with a transformation of that space) dynamical systems, an attractor is a set to which the system evolves after long enough time.
		Until the (The decade from 1960 to 1969) 1960s, as evidenced by contemporaneous textbooks, attractors were thought of as being geometrical subsets of the phase space: points, lines, surfaces, volumes.
		An attractor is informally described as strange if it has (Click link for more info and facts about non-integer) non-integer dimension or if the dynamics on the attractor are (Click link for more info and facts about chaotic) chaotic.
	www.absoluteastronomy.com /encyclopedia/a/at/attractor.htm (967 words)

	Strange Attractor (Site not responding. Last check: 2007-10-20)
		Chaotic attractors have geometric structures that are fixed and unchanging---despite the fact that the trajectories moving within them appear unpredictable.
		The attractor shape shown at the top of this document, reminds a seashell and is typical of attractors.
		The attractor is superimposed and is the result of continuing this procedure many many times or, in scientific terms,the limit set.
	www.ba.infn.it /~zito/strange.html (443 words)

	Fractals and the Rossler attracter (Site not responding. Last check: 2007-10-20)
		The Collins Reference Dictionary of mathematics states the definition of a strange attractor as...such that its Hausdorf Dimension is non-integral, or else dependant on initial conditions...
		So by definition a strange attractor is an object which is neither a point, a line, or a plane!.
		For example, the dimension of the Rossler Attractor is estimated at between 2.01 and 2.02.
	www.ocf.berkeley.edu /~trose/rossler.html (1035 words)

	2.1 Strange Attractors
		The most famous strange attractor is undoubtedly the Lorenz attractor -- a three dimensional object whose body plan resembles a butterfly or a mask.
		The Lorenz attractor, named for its discoverer Edward N. Lorenz, arose from a mathematical model of the atmosphere.
		The mathematical equivalent of rolling and folding and rolling and folding is the origin of sensitive dependence in the Lorenz attractor as well as in the much simpler quadratic mapping (which we will revisit in the remaining sections of this chapter).
	www.hypertextbook.com /chaos/21.shtml (2641 words)

	Corante > Strange Attractor > Welcome to Strange Attractor (Site not responding. Last check: 2007-10-20)
		In Strange Attractor, Suw picks out patterns from the apparent chaos that is the blogosphere.
		The thing about strange attractors is that they bring their own kind of beautiful order to chaos, but it is still chaos.
		These, I sort of gather are 2-dimensional slices of the multi-dimensional wanderings of a strange attractor, kinda like that dead dude who was sliced into wafers and scanned for med students to play with.
	www.corante.com /strange/archives/005237.php (3136 words)

	Strange attractor (Site not responding. Last check: 2007-10-20)
		The type of attractor exhibited by thisphenomena is known as a 'point attractor', because the limit set consists of a single point: position = constant, velocity =zero, acceleration = zero.
		A planet orbiting around a star is an example of a periodic attractor.Also, an undamped pendulum and an infinite loop on a digital computer are examples of periodic attractors.
		The first strange attractor discovered was the Lorenz attractor, discovered by the meteorologist Edward Lorenz, while simulating weatheron a computer.
	www.therfcc.org /strange-attractor-5706.html (428 words)

	the_futures-lab
		STRANGE ATTRACTOR is a science fiction film which presents a psychedelic inversion of the ADAM & EVE story.
		What is unique about STRANGE ATTRACTOR is that it is using cutting edge graphic techniques to convey a complex and subtle story in a way that would be inconceivable with conventional film technology.
		Since STRANGE ATTRACTOR is a dream diary, the issue of "point of view" remains somewhat ambiguous, as does the relationship between reality and dreaming.
	www.futures-lab.com /article.cml-id=21.htm (1969 words)

	Attractors
		In general, an attractor is a region in the space of possible states which the system can enter but not leave.
		Imagine that each attractor corresponds to a lake or sea, and that the trajectories leading into an attractor correspond to the rivers and streams flowing into those lakes.
		Similarly, each attractor has a basin, which is the surrounding region in state space such that all trajectories starting in that region end up in the attractor.
	pespmc1.vub.ac.be /ATTRACTO.html (968 words)

	fUSION Anomaly. Strange Attractors
		Torus attractor, picture walking on a large doughnut, going over, under and around its outside surface area, circling, but never repeating exactly the same path you went before.
		A scientist by the name of Edward Lorenz is credited with the discovery of the 'strange attractor', which is a point in phase space which attracts the movements of molecules into spiral patterns.
		Some of the spiral patterns surrounding a single attractor are reminiscent of the spiral patterns carved on ancient monoliths, known as 'cup and ring' markings.
	fusionanomaly.net /strangeattractors.html (1084 words)

	Chaos: The Four Attractors
		With the Point attractor there is typically a fixation on one desire, or revulsion, and all else is put aside until it is satisfied or destroyed.
		With the Torus Attractor there is a high degree of irregularity and complexity in the pattern, particularly when compared to the Circuit or Point attractors.
		An example of the Torus attractor at work would be a more complex set of attracting events which occur to a person on many levels over a course of a year, and repeat again, year in and year out.
	www.fractalwisdom.com /FractalWisdom/fourattr.html (1469 words)

	Draft: Various Chapters
		The algorithm for determining a global Poincare surface of section is applied to a previously studied dynamical system on R^2 \times S^1 and a one-parameter family of embeddings of the strange attractor it generates in R^3.
		We establish conditions for distinguishing between two topologically identical strange attractors that are enclosed by identical bounding tori, one of which is generated by a flow restricted to that torus, the other of which is generated by a flow in a different bounding torus and either imaged or lifted into the first bounding torus.
		Strange attractors can exhibit bifurcations just as periodic orbits in these attractors can exhibit bifurcations.
	einstein.drexel.edu /~bob/Papers_Progress.html (441 words)

	Chaos: Henon's Strange Attractor - Robert J Morton (Site not responding. Last check: 2007-10-20)
		Each point on the display shows where the orbit of the system's 3-Dimensional strange attractor passes through the x-y plane of the screen.
		The Hénon strange attractor is an attractor to which all these real-world attractors are attracted.
		It is formed from those other attractors when normal space is bent and folded to form a particular phase space in which this 'attractor of attractors' looks simple.
	www.robmorton.20m.com /maths/chaos/henon/henon.htm (329 words)

	The Strange Attractor Within
		Tornados have a “limit cycle” attractor that tries to keep the air moving in a circle around the center of the funnel.
		I believe the strange attractor is what drives the pattern of the human psyche, giving rise to behavioral, interactional and cognitive patterns commonly referred to as a psychological Type.
		The strange attractors can also be divided into four similar, but not identical, groups that account for the four temperament patterns.
	www.16types.com /Request.jsp?lView=ViewArticle&Article=OID:293923&Page=OID:293924 (1072 words)

	STRANGE ATTRACTORS
		Strange Attractors is part of the independent comics movement, said movement being years-old now, and enjoying explosive growth--even in these dark days of The Distributor Wars.
		Strange Attractors tells the tale of Sophie, the curator of The Museum of Lost Things, and her Freud-spouting robot side-kick, Roshi, as they adventure through a future world of SuperScience, Magic, robots, Rangerettes, and retro-futuristic romance and adventure.
		Strange Attractors original pages are for sale in our push to finance our first trade paperback, a compilation of Strange Attractors 1-7, featuring an introduction by Dave Sim and a preface by Norman Spinrad.
	www.ac.wwu.edu /~marks/strange.html (664 words)

	strange. The American Heritage® Dictionary of the English Language: Fourth Edition. 2000.
		strange, peculiar, odd, queer, quaint, outlandish, singular, eccentric, curious These adjectives describe what deviates from the usual or customary.
		Strange refers especially to what is unfamiliar, unknown, or inexplicable: All summer I traveled through strange lands.
		Eccentric refers particularly to what is strange and departs strikingly from the conventional: His musical compositions were innovative but eccentric.
	www.bartleby.com /61/37/S0793700.html (320 words)

	Example: Duffing Equation
		We believe that the orbits shown in Figure 5.5 correctly identify all the period one and some of the period three orbits embedded in the strange attractor at these parameter values.
		By superimposing the orbits in Figure 5.5 onto one another, we recover the picture of the strange attractor shown in the upper left-hand corner of Figure 5.5.
		Each of these periodic orbits is a knot, and the periodic orbits of the strange attractor are interwoven (tied together) in a very complicated pattern.
	cnls.lanl.gov /People/nbt/Book/node140.html (498 words)

	Working with Chaos with BrainMaker Neural Networks
		A Strange attractor is an attractor for which there is not an equilibrium point.
		In the chaotic cotton production system, what you learn by seeing the Strange attractor is that there is some sort of a feedback mechanism, there is an analytic solution to what the system is doing and there is feedback around the analytic solution.
		You get Strange attractors when you look at the population of foxes over the years as it grows and shrinks.
	www.calsci.com /Chaos.html (362 words)

	FranklinCovey > Effectiveness Zone > Knowledge Expo > "The Strange Attractor" by Stephen R. Covey
		To get the Strange Attractor, you need a vision or strategic purpose that everyone can buy into and feel good about, and have a value system based on principles, reinforced by a 360-degree information system and sustained by the universal conscience, the source of the mission statement.
		When you give up control and involve people in a genuine process of developing a common purpose and value system where they own the Strange Attractor, you begin to see everyone pulling together in the same direction according to their roles and level of skill.
		When the Strange Attractor is present, people may actually be absent without impairing the operation.
	www.franklincovey.com /ez/library/strange.html (1913 words)

	Experimental Techniques (Site not responding. Last check: 2007-10-20)
		Specifically, a strange attractor is an attractor that is a fractal ;.
		That is, the term strange refers to a static geometric property of the attractor.
		We mention this distinction because it is possible for an attractor to be strange (a fractal), but not chaotic (exhibit sensitive dependence on initial conditions) [25].
	www.drchaos.net /drchaos/Book/node82.html (213 words)

	Attractors Everywhere - Order from Chaos
		Now this need not be a fixed equilibrium point like we saw above, we can have attractors that follow an orbit (like that of the planets round the sun) or we may have a system that never returns to the same place - this we call a 'Strange Attractor'.
		We try to navigate from attractor to attractor, using energy to climb to the top of a nearby hill - changing state, so that we can reach a better valley, a new (hopefully more rewarding) steady state - or attractor.
		The formation of these mental attractors, if such there are, and their changes with learning is an interesting problem in developmental or Evolutionary Psychology.
	www.calresco.org /attract.htm (1631 words)

	Wyoming: is old faithful a strange attractor?
		Three-dimensional state-space reconstruction of eruption time data provides strong evidence of a strange attractor quite similar to the Rossler attractor.
		Seismic activity is believed to be a perturbation shifting Old Faithful into a new chaotic state with a different shape to the strange attractor.
		"Strange attractor" is a specialized term employed in chaos analysis.
	www.science-frontiers.com /sf071/sf071g16.htm (291 words)

	Chaos: Strange Attractor (Site not responding. Last check: 2007-10-20)
		We need to escape from the deterministic influence of the point, circuit and torus attractors into the unpredictability of the Strange Attractor.
		There is no apparent order at all to the actions of the Strange attractor.
		Still another important Strange Attractor that appears in odd places throughout Nature is called the Feigenbaum fractal.
	www.fractalwisdom.com /FractalWisdom/strange.html (190 words)

	Strange Attractor images compiled by CALResCo
		It is seen that the solutions are all contained within a definite figure, which we call the 'strange attractor'.
		One feature of attractors such as these is that initial values outside the structure are sucked into the attractor, and then can no longer escape (rather like a fl hole).
		The region for which this is true is called the basin of attraction, and the trajectory of a point until it reaches the attractor is called the transient.
	www.calresco.org /pic5/img5a.htm (421 words)

	Strange Attractor's Chris Scofield: The Stylus Interview Series - Article - Stylus Magazine
		Strange Attractors Audio House became the name for the record label, and it was officially born on Halloween 2000 with the debut release by the Lowdown.
		CS: Strange Attractors is a term used in physical science, namely chaos theory.
		To summarize, basically a Strange Attractor is the name of a pattern that erupts from chaos—order from disorder.
	www.stylusmagazine.com /feature.php?ID=809&PHPSESSID=084675339241921d9ef6a379ce27829d (1853 words)

	Further: Strange Attractor and beyond
		When the 5,300-year-old body of a Stone Age man was discovered entombed in a glacier in the Italian Alps in 1991, it was hailed as one of the most significant archeological finds ever.
		These were strange, often accidental deaths of people who had come into close contact with the frozen corpse, dubbed Oetzi.
		There may also be a spontaneous Disinformation vs Strange Attractor performance in the space sometime next week.
	www.strangeattractor.co.uk /further (1717 words)

	Chaos Theory and Strange Attractors
		The darker area outside the main body of the attractor will yield values that tend to infinity, and the lighter area is pulled into the attractor.
		The attractors plotted by Spirofractal are polynomials, or other fairly simple functions, that use either two real variables, or one complex variable (which amounts to the same thing).
		But a small minority of the possible functions give rise to strange attractors, and in many cases these have beautiful patterns.
	www.alunw.freeuk.com /chaos.html (837 words)

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