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Topic: Attractor

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	Strange Attractor
		A chaotic attractor is a set of states in a system's state space with very special properties.
		Chaotic attractors themselves are quite orderly---their often elegant, geometric structures are fixed and unchanging---despite the fact that the trajectories moving within them appear unpredictable.
		One result of the stretch-and-fold aspect of chaotic attractors is that they are fractals---some cross-section of them reveals similar structure on all scales.
	www.exploratorium.edu /complexity/CompLexicon/strange.html (202 words)

	Center for Nonlinear Science - What is an attractor?
		Roughly speaking, an attractor is what the behavior of a system settles down to or that to which it is attracted.
		Imagine that you are taking the pulse, blood pressure and temperature of a person every hour, and you want to graph the relationships among all three vital signs as they change over time.
		In nonlinear science, this trajectory is referred to as an attractor.
	www.twu.edu /cns/attractor.html (126 words)

	The Lorenz Attractor, a thing of beauty
		Listen (mov or midi) to the Lorenz attractor.
		The lorenz attractor was first studied by Ed N. Lorenz, a meterologist, around 1963.
		It was derived from a simplified model of convection in the earths atmosphere.
	local.wasp.uwa.edu.au /~pbourke/fractals/lorenz (401 words)

	Attractor - Definition, explanation
		Geometrically, an attractor can be a point, a curve, a manifold, or even a complicated set with fractal structures known as a strange attractor.
		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.
		The Hénon attractor and the Lorenz attractor are examples of strange attractors.
	www.calsky.com /lexikon/en/txt/a/at/attractor.php (825 words)

	Chaotic Attractors
		This means that for a dynamical system whose attractor is chaotic, if the conditions are disturbed by the slightest amount, the behavior from that point on will begin to diverge such that after a time it will have no relationship to what it would have been in the absence of that disturbance.
		When we disturbed dynamical systems that were on their attractor, be it a point attractor or a periodic attractor, the state point in phase space temporarily wandered off but after the transient died away they returned to the attractor.
		Here the attractor instead of being a finite number of loops as it was for the periodic attractors, is an infinite bundle of loops in the vicinity of the time axis circle.
	www.mcasco.com /cattr1.html (2147 words)

	Vortex attractor - Patent 6595753
		Such a driveshaft configuration may be incorporated as a portion of a suspended attractor (at the attractor end of the cable), as a portion of or substitute for an attached arm, or on a hand-held device.
		A vortex attractor may be provided at an end of a rigid or flexible arm or handle to create a toy in the form of a hollow tube or wand, which, when the impellers are caused to spin, creates a low pressure area capable of attracting and holding objects.
		The vortex attractor described herein generates a generally cylindrical vortex fluid flow component, an inner toroidal vortex, and an outer toroidal vortex, and as these forces act upon an object to draw it closer, the effects of external ambient fluid are reduced and efficiency is achieved by low fluid resistance.
	www.freepatentsonline.com /6595753.html (18018 words)

	Attractor Fields
		Each level on his Map of Consciousness is associated with a distinct attractor field and that field predominates in the experience of the person at that level of consciousness.
		According to Hawkins, individuals are born with a certain level of consciousness, hence the attractor field is already in place at birth.
		Traditionally, the student seeks out a teacher at a higher level of consciousness, and the attractor field of the teacher adds the necessary energy for the student to expand his or her attractor field.
	www.changingconsciousness.org /attractor_fields.htm (542 words)

	Strange Attractor (Site not responding. Last check: )
		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)

	Attractor (Site not responding. Last check: )
		The attractor could be called the final stable pattern of system dynamics.
		The attractor is the reason why we call chaotic systems deterministic or in principal predictable.
		There are several attractors that chaos theory considers but it is beyond the scope of this paper.
	www.wesleyan.edu /synthesis/GROUP1/FINAL/attract.htm (205 words)

	Rossler Attractor - Scholarpedia
		The Rössler attractor is the most simple chaotic attractor from the topological point of view, that is, it is a simple stretched and folded ribbon.
		The Rössler attractor can therefore be viewed as the trivial suspension - given a discrete map f of an n-dimensional manifold M, it is always possible to construct a flow on an n+1-dimensional manifold - of the Logistic map (both obey the Sharkovsky Ordering).
		Bob Rosen first saw the spiral-chaos' simplified attractor slowly take shape on the slow desktop plotter with the built-in close to machine-language computer, and loved this illustration of his analogous-systems theorem (a long line), as he said.
	www.scholarpedia.org /article/Rossler_Attractor (1214 words)

	Discrete Dynamical Networks and their Attractor Basins
		Attractor basins are constructed with algorithms that directly compute the pre-images of network states[16, 17, 21].
		The frequency of reaching a given attractor type indicates the relative size of the basin of attraction, and other data are extracted such as the number of basins, and the length of transients and attractor cycles.
		In the graphic convention[16, 19], the length of edges decreases with distance away from the attractor, and the diameter of the attractor cycle approaches an upper limit with increasing period.
	journal-ci.csse.monash.edu.au /ci/vol06/wuensche/wuensche.html (7614 words)

	Myswizard » Attractor
		Geometrically, an attractor can be a point, a curve, a manifold, or even a complicated set with fractal structures known as a strange attractor.
		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.
		A time series corresponding to this attractor is a quasiperiodic series: A discretely sampled sum of Nt periodic functions (not necessarily sine waves) with incommensurate frequencies.
	www.myswizard.com /2006/08/17/attractor (1028 words)

	Falling all the way: Cascade diagrams
		This concept is the same as we have seen before: the attractor of a sequence of iterates is the set A of all points of accumulation of the orbit.
		The stable attractor of a dynamical system may be discovered, at least numerically, by simply letting the system run long enough.
		If the attractor is a stable 4-cycle, for instance, the 4 points in that cycle will be recorded 250 times each.
	www.math.okstate.edu /mathdept/dynamics/lecnotes/node54.html (757 words)

	Attractor - Scholarpedia
		The word "attractor", as used in dynamical systems, has nothing at all to do with its use in gravitational theory [[1]].
		Perhaps the first such examples were the Lorenz attractors and the Hénon attractors, which have been widely studied, and the Ueda attractors (Figure 4).
		The term attractor is sometimes used for any set which contains a dense orbit and has an attracting basin of positive measure, omitting the second condition in the definition of measure attractor.
	www.scholarpedia.org /article/Attractor (2269 words)

	Invariant density and finite-time Lyapunov exponents for nonhyperbolic dynamics on Henon attractor
		In order to determine whether the invariant set is hyperbolic or nonhyperbolic, we first need to calculate the angles between stable and unstable manifolds for points x belonging to the set.
		As Dr. Daniel Lathrop suggested, I was looking for correlation between the invariant density and angle between stable and unstable manifolds for points on the attractor.
		Angle vs. invariant density on the Henon attractor.
	www.glue.umd.edu /~alekseyz/715project/715project.htm (1448 words)

	Attractor - AGIRI.org
		The mathematical definition of an attractor says, roughly, that an attractor is a set of system states to which the system gravitates after it iterates for long enough.
		Generally a subsystem may settle into an attractor after a while, but then be perturbed out of it by input from some other part of the system.
		If the wings or parts of the attractor are labeled with symbols, then the symbol-sequences associated with the system's trajectories may be taken as the words in a formal grammar, which leads to the field of Symbolic Dynamics.
	www.agiri.org /wiki/index.php?title=Attractor&printable=yes (232 words)

	Great Attractor
		Some astronomers believe that the Great Attractor may be centered on the rich cluster known as Abell 3627; others propose that, while there may be a cluster of galaxies in the area of the Great Attractor, the large-scale movement of so many superclusters is probably due to the gravitational pull of all clusters combined.
		One argument against the existence of the Great Attractor is that no one has detected signs of infalling galaxies behind the Attractor.
		On the other hand, it is possible that this infall may be counteracted by the mass of the more distant Shapley Concentration whose galaxies may be tugging the Great Attractor galaxies the other way.
	www.daviddarling.info /encyclopedia/G/Great_Attractor.html (234 words)

	Attractor of Henon map
		The attractor of the above applet is colored based of the value of the coarse-grained expansion rate, and it will be explained later.
		At the curves of the attractor, the orbital expansion rate takes negative values, thus they are colored with yellow.
		And the sharp area of the attractor also form a curve, as you can see when you expand it, thus it is also yellow.
	brain.cc.kogakuin.ac.jp /~kanamaru/Chaos/e/Henon (647 words)

	Attractors (Site not responding. Last check: )
		Attractors are geometric forms that characterize long-term behaviour in the phase space.
		Roughly speaking, an attractor is what the behaviour of a systems settles down to, or is attracted to.
		In a strange attractor periodic orbits are unstable and act as repellors.
	www.christianhubert.com /hypertext/Attractors.html (323 words)

	AGFX-Software- Aurora_Attractor (Site not responding. Last check: )
		This is the simplest of the polynomial attractor equations.
		The same attractor was also created in Modeler using point polys which where then used to create the particle effects with the emitters set to emit from the vertex normal.
		The second part is another single attractor with two different parameters being animated over time as the camera first moves around the attractor and then through it to show the dimensionality of attractors.
	www.auroragrafx.com /Software/Attr/index.shtml (4034 words)

	Chaos: The Four Attractors
		With the Point attractor in play a person is invariably drawn to one particular activity, or repelled from another, like the positive or negative poles of electromagnetic energy.
		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.
		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)

	CS 585 Stange Attractor
		A strange attractor exists in a system where behavior is random within a constraint.
		The current attractor should be serializable into a file with an *.atr extension.
		When the application is minimized and then restored the attractor should be displayed, not redrawn.
	www.csun.edu /~renzo/cs585/attract2005.htm (1019 words)

	Complicity and the Brain: Dynamics in Attractor Space
		Attractors can have semantic content (see here) and exist on time scales that are commensurate with the time scales on which animals have to act.
		In humans the dynamics in attractor space is operating in a large enough system, with enough attractors to flip around so that it becomes possible for self-organization to become operative on this level and lead to the emergence of features one level up from the dynamics in attractor space.
		When we connect several Hopfield nets by sending their current attractor as output to other nets in the neighborhood, all we get is one larger system that will follow its own dynamics, and that depending on its initial state will converge towards a point, cyclic, or strange attractor.
	alifegames.sourceforge.net /project/ComplicityBrain.html (9609 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.
		This implementation processes only the first 1500 iterations of the Lorenz Attractor.
		The Lorenz Attractor is often attributed to Ed.
	www.levitated.net /daily/levLorenzAttractor.html (127 words)

	Rossler Attractor (Site not responding. Last check: )
		Rossler's attractor is not a famous attractor, but is a rather nice attractor which draws a nifty picture.
		Rossler's attractor displays a type of banding, which suggests that perhaps it is related to the Cantor set.
		Another interesting fact about Rossler's attractor is that it has a half-twist in it, which makes it look somewhat like a Möbius strip (what you get when you take a strip of paper, half-twist it once, and tape the ends together.
	www.zeuscat.com /andrew/chaos/rossler.html (317 words)

	2 attractor paper w fig
		response is in the lower attractor, it is not synchronized to the drive circuit (except in
		When the drive circuit attractor is inverted from the attractor in Fig.
		The out-of-sync attractor for the response circuit appears to be going unstable.
	chaos-mac.nrl.navy.mil /Section_Stuff/Papers/2_attractor_sync/_2_attractor_paper_w_fig04.html (199 words)

	fUSION Anomaly. Strange Attractors
		The Attractor may come as a point, in which case, it gives a steady state where no change is made.
		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.
		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)

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