Copyright © Philip M. Parker, INSEAD. Terms of Use.
Definition: Attractor |
AttractorNoun1. An entertainer who attracts large audiences; "he was the biggest drawing card they had". 2. A characteristic that provides pleasure and attracts people. Source: WordNet 1.7.1 Copyright © 2001 by Princeton University. All rights reserved. |
(From Wikipedia, the free Encyclopedia)
Attractors are the pinnacle and origin of chaos theory.An attractor is a 'set', 'curve', or 'space' that a system irreversibly evolves to if left undisturbed. It is other-wise known as a 'limit set'. There are three types of attractors; point attractors, periodic attractors and strange attractors, all of which are discussed below.
Example
For instance, if you drop a book, it will land on the floor, and stop moving. This final state is the attractor of the system of "the book dropping". The book has now lost its potential energy, and is in a state of equilibrium. The type of attractor exhibited by this phenomena is known as a 'point attractor', because the limit set consists of a single point: position = constant, velocity = zero, acceleration = zero. Mathematically stated (see differential equations), we say:
Phase space
The trajectory representation of a single-variable system is:
That is, state(x) is a function of time(t). Similarly, for a multi-variable system, we express x as a vector:
And say that:
The phase space representation of a single-variable system, however, expresses the change of state of the system with respect to time(dx/dt) as a function of the current state of the system:
Or, in vector notation:
Where F is a transformation matrix (see control systems) or tensor describing a nonlinear transformation, mapping x onto a new coordinate system:
As time approaches infinity (t → ∞), the coordinate system contracts into a limit set, or attractor.
The three types of attractors
Point attractor
A point attractor is a fixed point that a system evolves towards, such as a falling book, a damped pendulum, or the halting state of a computer.
Periodic attractor (a.k.a. limit cycle)
A periodic attractor is a repeating loop of states. 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.
Strange attractor
A strange attractor is a non-periodic attractor. This is the most common type of attractor. It is characterized by a set of coupled nonlinear partial differential equations. The first strange attractor discovered was the Lorenz attractor, discovered by the meteorologist Edward Lorenz, while simulating weather on a computer.
The Lorenz attractor is defined by a set of 3 coupled nonlinear differential equations:
where a = 10, b = 28, c = 8 / 3. Strange attractors have fractal structure.
These last two types of attractors are exhibited by what are called dissipative systems. Dissipative systems are systems not in thermodynamic equilibrium, but constantly "evolving towards" equilibrium. That is, they are characterized by a flow of entropy, and mutually, a flow of energy.
Further reading
- Edward N. Lorenz (1996) The Essence of Chaos ISBN 0295975148
- James Gleick (1988) Chaos: Making a New Science ISBN 0295975148
External link
- A gallery of polynomial strange attractors
Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Attractor."
Synonyms: AttractorSynonyms: attraction (n), attractive feature (n), draw (n), drawing card (n). (additional references) |
Crosswords: Attractor |
| Specialty definitions using "attractor": Edward Lorenz ♦ Lorenz attractor. (references) |
| Domain | Title | ||
Books |
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Music |
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Source: compiled by the editor from various references; see credits. | |||
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| "UH 03" by Lucien Aréstegüi Commentary: "URBAN HABITAT 03 A look at a luxury suite, spider-styliez. You've got your loft, with a great view, and a nice Attractor (tm)." |
Source: photographs selected by the editor, with permission from the photographers. |
| "Attractor" is generally used as a noun (singular) -- approximately 100.00% of the time. "Attractor" is used about 80 times out of a sample of 100 million words spoken or written in English. Its rank is based on over 700,000 words used in the English language. Some parts-of-speech are not covered due to the samples used by the British National Corpus. (note: percents less than one-hundredth of one percent have been omitted) |
| Parts of Speech | Percent | Usage per 100 Million Words | Rank in English |
| Noun (singular) | 100% | 80 | 37,112 |
Source: compiled by the editor from several corpora; see credits.
Expressions using "attractor": basin of an attractor ♦ great Attractor ♦ lorenz attractor. Additional references. | |
| Hypenated Usage | |
Ending with "attractor": strange-attractor. | |
| Source: compiled by the editor from various references; see credits. | |
| The following statistics estimate the number of searches per day across the major English-language search engines as identified by various trade publications. Hyperlinks lead to commercial use of the expression at Amazon.com. |
| Expression | Frequency per Day |
strange attractor | 8 |
attractor | 7 |
attractor lorenz | 5 |
attractor great | 3 |
attractor female | 3 |
attractor lite traffic | 3 |
fish attractor | 3 |
attractor field technique | 2 |
attractor robust strange | 2 |
| Source: compiled by the editor from various references; see credits. | |
| Language | Translations for "attractor"; alternative meanings/domain in parentheses. | |
French | attracteur périodique (periodic attractor), attracteur de basse dimension (attractor of low dimension), attracteur d'équilibre stationnaire (stationary equilibrium attractor), attracteur chaotique (chaotic attractor, strange attractor), attracteur étrange (chaotic attractor, strange attractor), grand attracteur (great attractor), bassin d'un attracteur (basin of an attractor). (various references) | |
German | Attraktor niedriger Dimension (attractor of low dimension), stationärer Gleichgewichtspunkt (stationary equilibrium attractor), seltsamer Attraktor (strange attractor), periodischer Attraktor (periodic attractor), Einzugsbereich eines Attraktors (basin of an attractor), chaotischer Attraktor (chaotic attractor, strange attractor), befremdlicher Attraktor (chaotic attractor, strange attractor). (various references) | |
Greek | στάσιμο σημείο ισορροπίας (stationary equilibrium attractor), περιοδικός χώρος έλξης (periodic attractor), παράξενος χώρος έλξης-χαοτικός χώρος έλξης (chaotic attractor, strange attractor), χώρος έλξης μικρού αριθμού διαστάσεων (attractor of low dimension). (various references) | |
Italian | attrattore strano (chaotic attractor, strange attractor), attrattore periodico (periodic attractor), attrattore caotico (chaotic attractor, strange attractor), attrattore a bassa dimensionalità (attractor of low dimension), punto di equilibrio stazionario (stationary equilibrium attractor), bacino di un attrattore (basin of an attractor). (various references) | |
Japanese Kanji | アトピー性皮膚炎 (ad, ad impact, add-on, add-on module, adobe, advertisement, at random, atmosphere, atom, atomic, atopic dermatitis, atrium, attraction, attractive, attribute, autoload, studio). (various references) | |
Japanese Katakana | アトラクター . (various references) | |
Pig Latin | attractoray.(various references) | |
Spanish | atractor periódico (periodic attractor), atractor extraño (chaotic attractor, strange attractor), atractor de baja dimensión (attractor of low dimension), atractor caótico (chaotic attractor, strange attractor), punto de equilibrio estacionario (stationary equilibrium attractor). (various references) | |
| Source: compiled by the editor from various translation references. | ||
Derivations | |
Words beginning with "attractor": attractors. (additional references) | |
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"Attractor" is suggested in spellcheckers for the following: Attaturk, Attranto, ttractor. (additional references) | |
| Source: compiled by the editor, based on several corpora (additional references). | |
| Words rhyming with "attractor" (pronounced 'At*tract"or'): Acceptor, Assertor, Assessor, Assistor, Assizor, Chantor, Circumventor, Co-assessor, Collector, Compressor, Conductor, Confessor, Conjector, Connector, Consignor, Constrictor, constructor, Contractor, Contradictor, Conveyor, Corrector, Countor, Cruor, Debtor, Decolor, Deflector, Deforceor, Devisor, Duressor, Embraceor, Encolor, Escheator, flexor, grantor, ignitor, inductor, inspector, instructor, INVENTOR, investor, Mainor, Maintainor, manor, mayor, Miscolor, misdemeanor, Nonconductor, Objector, Oppressor, Overcolor. (additional references) |
Scrabble® Enable2K-Verified Anagrams | |
| Words within the letters "a-a-c-o-r-r-t-t-t" | |
-2 letters: attract, tractor. | |
-3 letters: carrot, cottar, tartar, trocar. | |
-4 letters: actor, aorta, attar, carat, cotta, ottar, taroc, tarot, tatar, tract. | |
-5 letters: acta, arco, carr, cart, coat, orca, orra, rato, roar, rota, taco, tact, taro, tart, tora, torc, torr, tort, trot. | |
| Words containing the letters "a-a-c-o-r-r-t-t-t" | |
+1 letter: attractors. | |
+5 letters: ultrapatriotic. | |
| Source: compiled by the editor from various references; see credits. SCRABBLE® is a registered trademark. All intellectual property rights in and to the game are owned in the U.S.A and Canada by Hasbro Inc., and throughout the rest of the world by J.W. Spear & Sons Limited of Maidenhead, Berkshire, England, a subsidiary of Mattel Inc. Mattel and Spear are not affiliated with Hasbro. | |
| 1. Definition 2. Synonyms 3. Crosswords 4. Usage: Commercial | 5. Images: Digital Art 6. Usage Frequency 7. Expressions 8. Expressions: Internet | 9. Translations: Modern 10. Derivations 11. Rhymes 12. Anagrams | 13. Bibliography |
Copyright © Philip M. Parker, INSEAD. Terms of Use.
