Copyright © Philip M. Parker, INSEAD. Terms of Use.
Definition: Chaotic |
ChaoticAdjective1. Lacking a visible order or organization. 2. Completely unordered and unpredictable and confusing. Source: WordNet 1.7.1 Copyright © 2001 by Princeton University. All rights reserved. |
Date "chaotic" was first used in popular English literature: sometime before 1550. (references) |
(From Wikipedia, the free Encyclopedia)
This article is about the mythological concept. See Chaos theory for the mathematics and physics term. In Greek mythology, Chaos is the primeval state of existence from which the first gods appeared. The word "chaos" means "gaping void" in Greek. As a god, Chaos was the nothingness out of which the first objects of existence appeared. These first beings, described as children of Chaos alone, were Gaia, Tartarus and Eros, sometimes also including Nyx and Erebus. Ovid described Chaos in Metamorphoses as "rather a crude and indigested mass, a lifeless lump, unfashioned and unframed, of jarring seeds and justly Chaos named." According to some sources Chaos was the offspring of Chronos.Ovid. Metamorphoses; Hesiod. Theogony. (123-132) In Chinese mythology, Chaos is the name of a god which has no eyes and no ears. Once he invited two friends to his place, the two friends offer to craft two eyes and two ears on his face so that he can sense. But he soon died when he finally got his eyes and ears.
Also a cat Muppet character in the children's television show Sesame Park.
Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Chaos."
(From Wikipedia, the free Encyclopedia)
Established in the 1960s, chaos theory deals with dynamical systems that, while in principle deterministic, have a high sensitivity to initial conditions, because their governing equations are nonlinear. Examples for such systems are the atmosphere, plate tectonics, economies, and population growth.
Description of the theory
A non-linear dynamical system can in general exhibit one or more of the following types of behaviour:
The type of behaviour may depend on the initial state of the system and the values of its parameters, if any.
- forever at rest
- forever expanding (only for unbounded systems)
- in periodic motion
- in quasi-periodic motion
- in chaotic motion
Chaotic motion
The most famous type of behaviour is chaotic motion, a non-periodic complex motion which has given name to the theory. In order to classify the behaviour of a system as chaotic, the system must be
Sensitivity on the initial conditions means that two such systems with however small a difference in their initial state eventually will end up with a finite difference between their states (However, two deterministic systems with identical initial conditions will remain identical).
- bounded,
- sensitive on the initial conditions,
- transitive and
- The periodic orbits must be dense.
An example of such sensitivity is the well-known butterfly effect, whereby the flapping of a butterfly's wings produces tiny changes in the atmosphere which over the course of time cause it to diverge from what it would have been and potentially cause something as dramatic as a tornado to occur. Other commonly known examples of chaotic motion are the mixing of colored dyes and airflow turbulence.
Transitivity means that application of the transformation on any given Interval I1 stretches it until it overlaps with any other given Interval I2.
The fourth condition means that for any point in the system and any real number ε > 0 there is another point with distance d ≤ ε which is located on an periodic orbit.
Strange attractors
One way of visualizing chaotic motion, or indeed any type of motion, is to make a phase diagram of the motion. In such a diagram time is implicit and each axis represents one dimension of the state. For instance, a system at rest will be plotted as a point and a system in periodic motion will be plotted as a simple closed curve.
A phase diagram for a given system may depend on the initial state of the system (as well as on a set of parameters), but often phase diagrams reveal that the system ends up doing the same motion for all initial states in a region around the motion, almost as though the system is attracted to that motion. Such attractive motion is fittingly called an attractor for the system and is very common for forced dissipative systems.
While most of the motion types mentioned above give rise to very simple attractors, such as points and circle-like curves called limit cycles, chaotic motion gives rise to what are known as strange attractors, attractors that can have great detail and complexity. For instance, a simple three-dimensional model of the Lorenz weather system gives rise to the famous Lorenz attractor. The Lorenz attractor is perhaps one of the best known chaotic system diagrams, probably because not only was it one of the first, but it is one of the most complex and as such gives rise to a very interesting pattern which looks like the eyes of an owl.
Strange attractors have fractal structure.
History
The theory has roots back to around 1950 when it first became evident for some scientists that linear theory, the prevailing system theory at that time, simply could not explain the observed behaviour of certain experiments like that of the logistic map. The main catalyst for the development of chaos theory was the electronic computer. Much of the mathematics of chaos theory involves the repeated iteration of simple mathematical formulas, which would be impractical to do by hand. Moore's law and the availability of cheaper computers has greatly increased the extent of chaos theory. As of 2003, chaos theory continues to be a very active area of research.
An early pioneer of the theory was Edward Lorenz whose interest in chaos came about accidentally through his work on weather prediction in 1961. Lorenz was using a basic computer to run his simulation of the weather. He wanted to see a sequence of data again and to save time he started the simulation in the middle of its course. He was able to do this by entering a printout of the data corresponding to conditions in the middle of his simulation which he had calculated last time.
To his surprise the weather that the machine began to predict was completely different to the weather calculated before. Lorenz tracked this down to only bothering to enter 3-digit numbers in to the simulation, whereas the computer had last time worked with 5-digit numbers. This difference is tiny and the consensus at the time would have been that it should have had practically no effect. However Lorenz had discovered that small changes in initial conditions produced large changes in the long-term outcome.
The importance of chaos theory can be illustrated by the following observations:
- In popular terms, a linear system is exactly equal to the sum of its parts, whereas a non-linear system can be more than the sum of its parts. This mean that in order to study and understand the behaviour of a non-linear system one need in principle to study the system as a whole and not just its parts in isolation.
- It has been said that if the universe is an elephant, then linear theory can only be used to describe the last molecule in the tail of the elephant and chaos theory must be used to understand the rest. Or, in other words, almost all interesting real-world systems are described by non-linear systems.
Mathematical theory
Mathematicians have devised many additional ways to make quantitative statements about chaotic systems. These include
- fractal dimension of the attractor
- Lyapunov exponents
- recurrence plots
- Poincaré maps
- bifurcation diagrams
Minimum complexity of a chaotic system
Many simple systems can also produce chaos without relying on partial differential equations, such as the logistic equation, which describes population growth over time.
Even discrete systems can heavily depend on initial conditions, such as cellular automata. Stephen Wolfram has investigated a cellular automaton with this property, termed by him rule 30.
Other examples of chaotic systems
See also: fractal, Dynamical systems and chaos theory, Benoit Mandelbrot, Mandelbrot set, Julia set, predictability, Mitchell Feigenbaum
- Double pendulum
- Logistic map
References
- Chaotic and Fractal Dynamics, by Francis C. Moon, ISBN 0471545716
Further Reading
The Beauty of Fractals, by H.-O. Peitgen and P.H. Richter Chaotic Evolution and Strange Attactors, by David Ruelle Computers, Pattern, Chaos, and Beauty, by Clifford A. Pickover Fractals, by Hans Lauwerier Fractals Everywhere, by Michael Barnsley The Fractal Geometry of Nature, by Benoit Mandelbrot Order Out of Chaos, by Ilya Prigogine and Isabelle Stengers The Science of Fractal Images, by Heinz-Otto Peitgen and Dietmar Saupe, Eds. Chaos Theory and Education Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Chaos theory."
Synonyms: ChaoticSynonyms: disorderly (adj), helter-skelter (adj). (additional references) |
| Context | Synonyms within Context (source: adapted from Roget's Thesaurus). |
Disorder | Immethodical; unsymmetric, unsystematic; untidy, slovenly; dislocated; out of sorts; promiscuous, indiscriminate; chaotic, anarchical; unarranged; (see arrange; ); confused; deranged; topsy-turvy; (inverted); shapeless; disjointed, out of joint. |
| Source: adapted from Roget's Thesaurus. | |
Crosswords: Chaotic |
| English words defined with "chaotic": Semichaotic. (references) |
| Specialty definitions using "chaotic": basin of an attractor, Buckle ♦ Fractals ♦ Lorenz attractor ♦ mandelbug ♦ Nonlinear Dynamics, NoteCards ♦ Running the floor. (references) |
| Domain | Usage | |
Movie/TV Titles | Zoids: Chaotic Century (2002) | |
Source: compiled by the editor from various references; see credits. | ||
| Domain | Title | ||
Books |
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Theater & Movies | |||
Music |
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Source: compiled by the editor from various references; see credits. | |||
| Subject | Topic | Quote |
Health | In some cases, the first and only manifestation of hypertrophic cardiomyopathy is sudden death, caused by a chaotic heartbeat. (references) | |
The onset is predominantly in the first year of life. Characteristic features of IS, sometimes called West syndrome, include myoclonic seizures, hypsarrhythmia (abnormal, chaotic electroencephalogram), and mental retardation. (references) | ||
Business | After a chaotic start, due mainly to inadequate regulations and lack of information, the new healthcare system seems to be settling down. Healthcare providers have themselves been most critical of the progress of reforms. (references) | |
This coupled with limited information about the world automotive market and the dominant Soviet philosophy; the local population was deprived of an opportunity to have any access to foreign made cars. After the independence of 1991, there was a 2-3 year period in Uzbekistan that can be described as chaotic for most of the sectors of the economy including automotive. (references) | ||
Economic History | Zimbabwe | The government of Zimbabwe's chaotic land reform program, couple with recurrent interference with and intimidation of the judiciary, has led to a sharp drop in investor confidence. (references) |
Serbia and Montenegro | Consequently, the Serbian king, Petar Karadjordjevic, was able to exploit the chaotic conditions in Montenegro at the war's end, paving the way for the violent and unwanted Serbian annexation of Montenegro. (references) | |
Equatorial Guinea | Although Equatorial Guinea lacks a well-established democratic tradition comparable to the developed democracies of the West, it has progressed toward developing a participatory political system out of the anarchic, chaotic, and repressive conditions of the Macias years. (references) | |
Human Rights | Kuwait | There were no developments in the investigations into the extrajudicial killings that occurred during the chaotic period after the country's liberation in February 1991. (references) |
Political Economy | PARAGUAY | Even though land taxes are low, chaotic land title records make land tax evasion the norm. (references) |
DOMINICAN REPUBLIC | A chaotic land tenure system and the unwillingness of large landowners to modernize impede investment in modern agricultural techniques. (references) | |
Political Rights | Venezuela | Faced with the prospect of a chaotic and contested election, the CNE decided at the last minute to serve as a friend of the court in a pending suit by two NGO's before the Supreme Court seeking delay of the election. (references) |
Source: compiled by the editor from ICON Group International, Inc.; see credits. | ||
| Speaker | Term | Phrase(s) |
Harry S. Truman | 1945-1953 | The end of the war in Europe found Germany in a chaotic condition. |
Source: compiled by the editor from various references. | ||
| "Chaotic" is generally used as an adjective (general or positive) -- approximately 99.77% of the time. "Chaotic" is used about 444 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 |
| Adjective (general or positive) | 99.77% | 443 | 13,068 |
| Noun (proper) | 0.23% | 1 | 339,140 |
| Total | 100.00% | 444 | N/A |
Source: compiled by the editor from several corpora; see credits.
| Hyphenated Usage | |
Beginning with "chaotic": chaotic-looking. | |
Ending with "chaotic": emotionally-chaotic, near-chaotic, non-chaotic. | |
| 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. |
| Language | Translations for "chaotic"; alternative meanings/domain in parentheses. | |
Albanian | kaotik. (various references) | |
Arabic | فوضوي (anarchic, anarchist, confused, disarrayed, disordered, lawless, messy, mixed up, skinhead), مشوش (become confused, confused, deranged, disarranged, disarrayed, disordered, disorganized, disturbed, disturber, higgledy-piggledy, hugger mugger, jumbled up, messy, mixed, muddled, muddy, promiscuous, unsettled), هيولي. (various references) | |
Bulgarian | хаотичен (promiscuous, undigested). (various references) | |
Chinese | 混乱 (Clamorous, Confusion, Disarray, Disordered, disorganise, disorganised, Disorganize, Disorganized, Disorganizing, mess, Muddle, Muddled, Muddling, ravel). (various references) | |
Czech | chaotický (amorphous, disorganized, in chaos, messy), zmatený (addle-brained, addle-pated, bemused, bewildered, confused, disordered, embroiled, in confusion, mazy, mixed, muddy, screwed up, turbid). (various references) | |
Dutch | chaotisch. (various references) | |
Esperanto | kaosa, ĥaosa. (various references) | |
Farsi | پرهرج ومرج , بی نظم (Amorphous). (various references) | |
Finnish | sekasortoinen (disordered). (various references) | |
French | chaotique. (various references) | |
German | chaotisch (disorganized, shambolic). (various references) | |
Greek | χαώδησ (abyssal, snafu), χαώδης (disorderly, shambolic), χαοτικός. (various references) | |
Hebrew | של תו"ו ובו"ו, פרוע (disorderly, rampant, rank, riotous, tumultuous, turbulent, unruly, wild). (various references) | |
Hungarian | zűrzavaros (anarchic, anarchical, deranged, mazy), kaotikus. (various references) | |
Indonesian | semrawut (disorganized), kisruh (anarchic, confused, disorganized), awut-awutan (haphazard, tangled, tousled), amburadul (disorder, disorganized). (various references) | |
Italian | caotico (messy, pell mell). (various references) | |
Japanese Kanji | 混沌としている (to be chaotic). (various references) | |
Japanese Katakana | ""と"としている (to be chaotic). (various references) | |
Korean | 혼돈되". (various references) | |
Malay | kacau. (various references) | |
Manx | fud y cheilley (at variance, confused, confusing, confusion, dishevelled, disorder, disordered, embarrassed, flustered, mixed up, muddle, muddled, perplexed, tangled, topsy-turvy), corvaalagh. (various references) | |
Papiamen | kaótiko. (various references) | |
Pig Latin | aoticchay.(various references) | |
Portuguese | caótico (promiscuous). (various references) | |
Romanian | confuz (abashed, addle, bewildered, blurred, confused, crabbed, dim, embarrassed, faint, gloomily, hazy, hugger mugger, misty, muddy, muzzy, nebulous, stodgy, turbid, vague, washy, wrongheaded), haotic (chaotically, loose). (various references) | |
Russian | хаотический (shambolic). (various references) | |
Serbo-Croatian | haotičan. (various references) | |
Spanish | caótico (pell mell, pellmell). (various references) | |
Swedish | kaotisk (disorganized, jumbly, snafu). (various references) | |
Turkish | karman çorman (all mixed up, confused, crabbed, crabby, higgledy-piggledy, messy, mussy, pell mell, pellmell, ragged, topsyturvy), karmakarışık (all in a tumble, all mixed up, at sixes and sevens, confused, disheveled, dishevelled, embroiled, haywire, helter-skelter, higgledy-piggledy, hurly burly, in complete disorder, intricate, mess, messy, mussy, out of order, pell mell, pellmell, promiscuous, snafu), düzensiz (desultory, disordered, disorderly, disorganized, erratic, excursive, fitful, freehand, haywire, hugger mugger, huggermugger, indigested, inordinate, irregular, jerky, nonuniform, non-uniform, out of order, out of square, out of trim, out-of-balance, patchily, patchy, ragged, rambling, snatchy, snuffy, unequal, unkempt, unsteady, untidy). (various references) | |
Ukrainian | хаотичний (amorphous). (various references) | |
Vietnamese | lộn xộn (confused, farraginous, jumbly, messy, promiscuous, shop, skimble-scamble, straggling, straggly, topsyturvy, turbid, wild), hỗn loạn (lawless, topsyturvy, troublous, turbulent), hỗn độn (messy, mussy, rough). (various references) | |
Welsh | anhrefnus (disorderly, untidy). (various references) | |
| Source: compiled by the editor from various translation references. | ||
Derivations | |
Words beginning with "chaotic": chaotically. (additional references) | |
| |
"Chaotic" is suggested in spellcheckers for the following: caotic, cautic, Chaitow, Chakoti, chaltic, chaortic, chaot, chaote, chaoticum, chastic, Chatou, Chauliac, chautic, chemtech, chiottes, choatic, chotain, choti, chotic, Ghayoit, haptic, kaotic, Khatori, rhaetic. (additional references) | |
| Source: compiled by the editor, based on several corpora (additional references). | |
| # of Phoneme Matches | Pronunciation | Word(s) rhyming with "chaotic" (pronounced kāÄ"tik) |
| 4 | -Ä" t i k | antibiotic, aquatic, astronautic, despotic, erotic, exotic, hypnotic, idiotic, narcotic, neurotic, patriotic, psychotic, quixotic, robotic, semiotic, symbiotic, unpatriotic. |
| 3 | -t i k | acetic, acoustic, acrobatic, aerobatic, aesthetic, agnostic, alphabetic, altruistic, amniotic, anachronistic, analytic, anesthetic, antagonistic, Antarctic, antic, anticlimactic, antiseptic, aortic, apathetic, apocalyptic, apologetic, apoplectic, arctic, aristocratic, arithmetic, aromatic, arthritic, artistic, ascetic, asthmatic, asymptomatic, atavistic, atheistic, athletic, attic, authentic, autistic, autocratic, automatic, axiomatic, ballistic, bombastic, bureaucratic, capitalistic, catalytic, cathartic, caustic, characteristic, charismatic, chauvinistic, chiropractic, cinematic, climactic, climatic, coloristic, cosmetic, critic, cryptic, cultic, cystic, democratic, dendritic, deterministic, diabetic, diagnostic, diagrammatic, dialectic, diamagnetic, didactic, dietetic, diplomatic, diuretic, dogmatic, domestic, dramatic, drastic, drumstick, dualistic, dynastic, ecclesiastic, eclectic, ecliptic, ecstatic, elastic, electrolytic, electromagnetic, electrostatic, emblematic, emetic, empathetic, emphatic, energetic, enigmatic, enthusiastic, enzymatic, epigenetic, epileptic, erratic, euphemistic, evangelistic, expressionistic, extragalactic, fanatic, fantastic, fatalistic, ferromagnetic, feudalistic, fiberoptic, frantic, frenetic, futuristic, galactic, genetic, geomagnetic, gigantic, granitic, gymnastic, halophytic, hectic, hedonistic, hemolytic, hepatic, heretic, hermaphroditic, holistic, homeostatic, homiletic, humanistic, hyperkinetic, iconoclastic, idealistic, idiomatic, idiosyncratic, imperialistic, impressionistic, individualistic, inelastic, interscholastic, jingoistic, journalistic, kinesthetic, kinetic, lactic, legalistic, linguistic, logistic, lymphatic, magnetic, majestic, masochistic, materialistic, mathematic, mechanistic, melodramatic, militaristic, monastic, monochromatic, monopolistic, moralistic, mystic, narcissistic, nationalistic, naturalistic, neritic, novelistic, numismatic, oligopolistic, onomastic, operatic, opportunistic, optic, optimistic, orthodontic, pancreatic, pantheistic, paralytic, paramagnetic, parasitic, parasympathetic, parthenogenetic, paternalistic, pathetic, patristic, pectic, pedantic, peptic, peripatetic, pessimistic, phonetic, phosphatic, plastic, pluralistic, pneumatic, poetic, polytheistic, porphyritic, posttraumatic, pragmatic, primitivistic, prismatic, problematic, programmatic, propagandistic, prophetic, prophylactic, prostatic, prosthetic, psychoanalytic, psychosomatic, psychotherapeutic, puristic, realistic, relativistic, rheumatic, ritualistic, romantic, rustic, sadistic, sarcastic, schematic, scholastic, semantic, semiautomatic, sensationalistic, septic, simplistic, skeptic, socialistic, static, statistic, stylistic, surrealistic, sycophantic, sympathetic, symptomatic, synergistic, synthetic, systematic, tactic, technocratic, terroristic, thematic, theocratic, therapeutic, thermoplastic, thrombolytic, transatlantic, traumatic, triptych, unapologetic, unauthentic, uncharacteristic, undemocratic, undiplomatic, unenthusiastic, unrealistic, unsympathetic, voyeuristic. |
Source: compiled by the editor (additional references); see credits. | ||
Scrabble® Enable2K-Verified Anagrams | |
| Words within the letters "a-c-c-h-i-o-t" | |
-2 letters: aitch, cacti, catch, chiao, chico, coach, coact, coati. | |
-3 letters: chao, chat, chia, chic, chit, ciao, coat, coca, iota, itch, oath, ohia, otic, tach, taco, thio. | |
-4 letters: act, ait, cat, chi, cot, hao, hat, hic, hit, hot, ich, oat, oca, tao, tho, tic. | |
-5 letters: ah, ai, at, ha, hi, ho, it, oh, ta, ti, to. | |
| Words containing the letters "a-c-c-h-i-o-t" | |
+1 letter: cathodic, catholic, thoracic, trochaic. | |
+2 letters: catholics, chromatic, laccolith, stomachic, trochaics. | |
+3 letters: achromatic, anchoritic, cataphoric, catholicoi, catholicon, catholicos, chalcocite, chromatics, cytopathic, escharotic, hypotactic, laccoliths, octarchies, phagocytic, scholastic, stochastic, stomachics, theocratic. | |
+4 letters: achondritic, anacoluthic, catholicate, catholicity, catholicize, catholicons, chalcocites, chaotically, chemotactic, chocolatier, cholestatic, chromatinic, cyclothymia, dichromatic, escharotics, euchromatic, laccolithic, macrophytic, masochistic, ochlocratic, outcatching, outcoaching, phonotactic, phototactic, prothoracic, scholastics, scholiastic, sociopathic, sycophantic, theocracies. | |
| 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: Modern | 5. Usage: Commercial 6. Quotations: Non-fiction 7. Quotations: Speeches 8. Usage Frequency | 9. Expressions 10. Expressions: Internet 11. Translations: Modern 12. Derivations | 13. Rhymes 14. Anagrams 15. Bibliography |
Copyright © Philip M. Parker, INSEAD. Terms of Use.
