康尼島（英語：），又译科尼島，是位於美國紐約市布魯克林區的半島，原本為一座海島，其面向大西洋的海灘是美國知名的休閒娛樂區域。居民大多集中位於半島的西側，約有六萬人左右，範圍西至希捷社區，東至布萊登海灘和曼哈頓海灘，而北至葛瑞福山德社區。 二十世紀前葉在美國極為知名的太空星際樂園即是以康尼島作為主要的腹地，該樂園在二次大戰後開始衰退，並持續荒廢了許久。在最近幾年，康尼島因為凱斯班公園的開幕而重新繁榮起來，凱斯班公園是職棒小聯盟球隊布魯克林旋風的主要球場。旋風隊在當地十分受到歡迎，每季開賽時都會吸引許多球迷到場觀戰。 ..

Anjos da guarda são os anjos que segundo as crenças cristãs, Deus envia no nosso nascimento para nos proteger durante toda a nossa vida. Argumenta-se que a Bíblia sustenta em algumas ocasiões a crença do anjo da guarda: "Vou enviar um anjo adiante de ti para ..

Altay Cumhuriyeti (Rusça: Респу́блика Алта́й / Respublika Altay; Altay Türkçesi: Алтай Республика / Altay Respublika), Rusya'nın en güneyinde yer alan, federasyona bağlı bir özerk cumhuriyet. Orta Asya'da Asya kıtasının coğrafî merkezinin hemen kuzeyinde ve ..

沙羅週期長度為18年11天，本週期包含70次日食，其中公元3000年以前有49次。 註：下表各項數據均為食分最大地點的情況。寬度指該地點食甚時刻月球的本影（全食時）或偽本影（環食時）落在地表的寬度，持續時間指該地點食既到生光的時間，即全食或環食的持續時間，全環食（亦稱混合食）發生時，食分最大處為全食。最後兩項參數不適用於偏食。 本周期最終結束於3378年6月17日。

希西家王 (希伯來語：，英語：）是猶大末年的君主，也是猶大國歷史中極尊重上帝的君王，在位29年。終年54歲。他在位的年份有兩種說法：其一是前715年-前687年；另一種是前716年-前687年。他的德行在其前後的猶大列王中，没有一個能及他。其希伯來名字的意思是“被神加力量”。 希西家的父親亞哈斯是一個背逆上帝的君王。因此在希西家當政之初的猶大國，無論政治，宗教上都极其黑暗。根據《聖經》記載，因为北國以色列被亞述攻滅，亞述王可以趁勢来攻打猶大國；又猶大的先王亞哈斯曾封鎖了聖殿之路，引導舉國崇拜偶像，大大得罪上帝。若非上帝的憐憫，為了堅定向大衛家所說的應許，猶大國的暫得幸存。希西家在二十五歲就登基作王，且正在國家危急之秋，由於行耶和華上帝眼中看為正的事，因而得上帝的憐憫，得以成功脫離亞述大軍的攻擊和一場致死的大病。他樂於聽從當代先知以賽亞的指導，使他為上帝大發熱心。 ..

The OnePlus 2 (also abbreviated as OP2) is a smartphone designed by OnePlus. It is the successor to the OnePlus One. OnePlus revealed the phone on 28 July 2015 via virtual reality, using Google's Cardboard visor and their own app. OnePlus sold out 30,000 units ..

兴隆街镇，是中华人民共和国四川省内江市资中县下辖的一个乡镇级行政单位。 兴隆街镇下辖以下地区： 兴隆街社区、兴松村、玄天观村、三元村、金星村、三皇庙村、双桥村、红庙子村、华光村、高峰村、芦茅湾村、篮家坝村、五马村和解放村。

Национальная и университетская библиотека (словен. Narodna in univerzitetna knjižnica, NUK), основанная в 1774 году, — один из важнейших образовательных и культурных учреждений Словении. Она располагается в центре столицы Любляна, между улицами Турьяшка (Turjaška ..

Mauser M1924 (или M24) — серия винтовок компании Mauser, использовавшихся в армиях Бельгии и Югославии. Внешне напоминают чехословацкие винтовки vz. 24, в которых использовались стандартный открытый прицел, патроны калибра 7,92×57 мм (или 8×57 мм), укороченные ..

第三条道路（英語：），又称新中间路线（Middle Way），是一种走在自由放任资本主义和传统社会主义中间的一种政治经济理念的概称。它由中间派所倡导，是社会民主主义的一个流派，英国工党称其为「现代化的社会民主主义」。它的中心思想是既不主张纯粹的自由市场，也不主张纯粹的社會主義，主张在两者之间取折衷方案。 第三条道路不只单单是走在中间，或只是一种妥协或混合出来的东西，第三条道路的提倡者看到了社会主义和资本主义互有不足之处，所以偏向某一极端也不是一件好事，第三条道路正正是揉合了双方主义的优点，互补不足而成的政治哲学。 ..

In chaos theory, the **butterfly effect** is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state.

The term, closely associated with the work of Edward Lorenz, is derived from the metaphorical example of the details of a tornado (the exact time of formation, the exact path taken) being influenced by minor perturbations such as the flapping of the wings of a distant butterfly several weeks earlier. Lorenz discovered the effect when he observed that runs of his weather model with initial condition data that were rounded in a seemingly inconsequential manner would fail to reproduce the results of runs with the unrounded initial condition data. A very small change in initial conditions had created a significantly different outcome.^{[1]}

The idea that small causes may have large effects in general and in weather specifically was earlier recognized by French mathematician and engineer Henri Poincaré and American mathematician and philosopher Norbert Wiener. Edward Lorenz's work placed the concept of *instability* of the Earth's atmosphere onto a quantitative base and linked the concept of instability to the properties of large classes of dynamic systems which are undergoing nonlinear dynamics and deterministic chaos.^{[2]}

In *The Vocation of Man* (1800), Johann Gottlieb Fichte says "you could not remove a single grain of sand from its place without thereby ... changing something throughout all parts of the immeasurable whole".

Chaos theory and the sensitive dependence on initial conditions were described in the literature in a particular case of the three-body problem by Henri Poincaré in 1890.^{[3]} He later proposed that such phenomena could be common, for example, in meteorology.^{[4]}

In 1898, Jacques Hadamard noted general divergence of trajectories in spaces of negative curvature. Pierre Duhem discussed the possible general significance of this in 1908.^{[3]}

The idea that the death of one butterfly could eventually have a far-reaching ripple effect on subsequent historical events made its earliest known appearance in "A Sound of Thunder", a 1952 short story by Ray Bradbury about time travel.^{[5]}

In 1961, Lorenz was running a numerical computer model to redo a weather prediction from the middle of the previous run as a shortcut. He entered the initial condition 0.506 from the printout instead of entering the full precision 0.506127 value. The result was a completely different weather scenario.^{[6]}

Lorenz wrote:

"At one point I decided to repeat some of the computations in order to examine what was happening in greater detail. I stopped the computer, typed in a line of numbers that it had printed out a while earlier, and set it running again. I went down the hall for a cup of coffee and returned after about an hour, during which time the computer had simulated about two months of weather. The numbers being printed were nothing like the old ones. I immediately suspected a weak vacuum tube or some other computer trouble, which was not uncommon, but before calling for service I decided to see just where the mistake had occurred, knowing that this could speed up the servicing process. Instead of a sudden break, I found that the new values at first repeated the old ones, but soon afterward differed by one and then several units in the last decimal place, and then began to differ in the next to the last place and then in the place before that. In fact, the differences more or less steadily doubled in size every four days or so, until all resemblance with the original output disappeared somewhere in the second month. This was enough to tell me what had happened: the numbers that I had typed in were not the exact original numbers, but were the rounded-off values that had appeared in the original printout. The initial round-off errors were the culprits; they were steadily amplifying until they dominated the solution." (E. N. Lorenz,

The Essence of Chaos, U. Washington Press, Seattle (1993), page 134)^{[7]}

In 1963, Lorenz published a theoretical study of this effect in a highly cited, seminal paper called *Deterministic Nonperiodic Flow*^{[8]}^{[9]} (the calculations were performed on a Royal McBee LGP-30 computer).^{[10]}^{[11]} Elsewhere he stated:

One meteorologist remarked that if the theory were correct, one flap of a sea gull's wings would be enough to alter the course of the weather forever. The controversy has not yet been settled, but the most recent evidence seems to favor the sea gulls.

^{[11]}

Following suggestions from colleagues, in later speeches and papers Lorenz used the more poetic butterfly. According to Lorenz, when he failed to provide a title for a talk he was to present at the 139th meeting of the American Association for the Advancement of Science in 1972, Philip Merrilees concocted *Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?* as a title.^{[12]} Although a butterfly flapping its wings has remained constant in the expression of this concept, the location of the butterfly, the consequences, and the location of the consequences have varied widely.^{[13]}

The phrase refers to the idea that a butterfly's wings might create tiny changes in the atmosphere that may ultimately alter the path of a tornado or delay, accelerate or even prevent the occurrence of a tornado in another location. The butterfly does not power or directly create the tornado, but the term is intended to imply that the flap of the butterfly's wings can *cause* the tornado: in the sense that the flap of the wings is a part of the initial conditions of an inter-connected complex web; one set of conditions leads to a tornado while the other set of conditions doesn't. The flapping wing represents a small change in the initial condition of the system, which cascades to large-scale alterations of events (compare: domino effect). Had the butterfly not flapped its wings, the trajectory of the system might have been vastly different—but it's also equally possible that the set of conditions without the butterfly flapping its wings is the set that leads to a tornado.

The butterfly effect presents an obvious challenge to prediction, since initial conditions for a system such as the weather can never be known to complete accuracy. This problem motivated the development of ensemble forecasting, in which a number of forecasts are made from perturbed initial conditions.^{[14]}

Some scientists have since argued that the weather system is not as sensitive to initial conditions as previously believed.^{[15]} David Orrell argues that the major contributor to weather forecast error is model error, with sensitivity to initial conditions playing a relatively small role.^{[16]}^{[17]} Stephen Wolfram also notes that the Lorenz equations are highly simplified and do not contain terms that represent viscous effects; he believes that these terms would tend to damp out small perturbations.^{[18]}

While the "butterfly effect" is often explained as being synonymous with sensitive dependence on initial conditions of the kind described by Lorenz in his 1963 paper (and previously observed by Poincaré), the butterfly metaphor was originally applied^{[19]} to work he published in 1969^{[20]} which took the idea a step further. Lorenz proposed a mathematical model for how tiny motions in the atmosphere scale up to affect larger systems. He found that the systems in that model could only be predicted up to a specific point in the future, and beyond that, reducing the error in the initial conditions would not increase the predictability (as long as the error is not zero). This demonstrated that a deterministic system could be "observationally indistinguishable" from a non-deterministic one in terms of predictability. Recent re-examinations of this paper suggest that it offered a significant challenge to the idea that our universe is deterministic, comparable to the challenges offered by quantum physics.^{[21]}^{[22]}

The butterfly effect in the Lorenz attractor time 0 ≤ *t*≤ 30 (larger)*z*coordinate (larger)These figures show two segments of the three-dimensional evolution of two trajectories (one in blue, and the other in yellow) for the same period of time in the Lorenz attractor starting at two initial points that differ by only 10 ^{−5}in the x-coordinate. Initially, the two trajectories seem coincident, as indicated by the small difference between the*z*coordinate of the blue and yellow trajectories, but for*t*> 23 the difference is as large as the value of the trajectory. The final position of the cones indicates that the two trajectories are no longer coincident at*t*= 30.An animation of the Lorenz attractor shows the continuous evolution.

Recurrence, the approximate return of a system towards its initial conditions, together with sensitive dependence on initial conditions, are the two main ingredients for chaotic motion. They have the practical consequence of making complex systems, such as the weather, difficult to predict past a certain time range (approximately a week in the case of weather) since it is impossible to measure the starting atmospheric conditions completely accurately.

A dynamical system displays sensitive dependence on initial conditions if points arbitrarily close together separate over time at an exponential rate. The definition is not topological, but essentially metrical.

If *M* is the state space for the map , then displays sensitive dependence to initial conditions if for any x in *M* and any δ > 0, there are y in *M*, with distance *d*(. , .) such that and such that

for some positive parameter *a*. The definition does not require that all points from a neighborhood separate from the base point *x*, but it requires one positive Lyapunov exponent.

The simplest mathematical framework exhibiting sensitive dependence on initial conditions is provided by a particular parametrization of the logistic map:

which, unlike most chaotic maps, has a closed-form solution:

where the initial condition parameter is given by . For rational , after a finite number of iterations maps into a periodic sequence. But almost all are irrational, and, for irrational , never repeats itself – it is non-periodic. This solution equation clearly demonstrates the two key features of chaos – stretching and folding: the factor 2^{n} shows the exponential growth of stretching, which results in sensitive dependence on initial conditions (the butterfly effect), while the squared sine function keeps folded within the range [0, 1].

The butterfly effect is most familiar in terms of weather; it can easily be demonstrated in standard weather prediction models, for example. The climate scientists James Annan and William Connolley explain that chaos is important in the development of weather prediction methods; models are sensitive to initial conditions. They add the caveat: "Of course the existence of an unknown butterfly flapping its wings has no direct bearing on weather forecasts, since it will take far too long for such a small perturbation to grow to a significant size, and we have many more immediate uncertainties to worry about. So the direct impact of this phenomenon on weather prediction is often somewhat wrong."^{[23]}

The potential for sensitive dependence on initial conditions (the butterfly effect) has been studied in a number of cases in semiclassical and quantum physics including atoms in strong fields and the anisotropic Kepler problem.^{[24]}^{[25]} Some authors have argued that extreme (exponential) dependence on initial conditions is not expected in pure quantum treatments;^{[26]}^{[27]} however, the sensitive dependence on initial conditions demonstrated in classical motion is included in the semiclassical treatments developed by Martin Gutzwiller^{[28]} and Delos and co-workers.^{[29]}. The random matrix theory and simulations with quantum computers prove that one version of the butterfly effect in quantum mechanics does not exist
^{[30]}.

Other authors suggest that the butterfly effect can be observed in quantum systems. Karkuszewski et al. consider the time evolution of quantum systems which have slightly different Hamiltonians. They investigate the level of sensitivity of quantum systems to small changes in their given Hamiltonians.^{[31]} Poulin et al. presented a quantum algorithm to measure fidelity decay, which "measures the rate at which identical initial states diverge when subjected to slightly different dynamics". They consider fidelity decay to be "the closest quantum analog to the (purely classical) butterfly effect".^{[32]} Whereas the classical butterfly effect considers the effect of a small change in the position and/or velocity of an object in a given Hamiltonian system, the quantum butterfly effect considers the effect of a small change in the Hamiltonian system with a given initial position and velocity.^{[33]}^{[34]} This quantum butterfly effect has been demonstrated experimentally.^{[35]} Quantum and semiclassical treatments of system sensitivity to initial conditions are known as quantum chaos.^{[26]}^{[33]}

The journalist Peter Dizikes, writing in *The Boston Globe* in 2008, notes that popular culture likes the idea of the butterfly effect, but gets it wrong. Whereas Lorenz suggested correctly with his butterfly metaphor that predictability "is inherently limited", popular culture supposes that each event can be explained by finding the small reasons that caused it. Dizikes explains: "It speaks to our larger expectation that the world should be comprehensible – that everything happens for a reason, and that we can pinpoint all those reasons, however small they may be. But nature itself defies this expectation."^{[36]}

- Actuality and potentiality
- Avalanche effect
- Behavioral cusp
- Butterfly effect in popular culture
- Cascading failure
- Causality
- Chain reaction
- Clapotis
- Determinism
- Domino effect
- Dynamical systems
- Fractal
- Great Stirrup Controversy
- Innovation butterfly
- Kessler syndrome
- Law of unintended consequences
- Norton's dome
- Point of divergence
- Positive feedback
- Representativeness heuristic
- Ripple effect
- Snowball effect
- Traffic congestion
- Tropical cyclogenesis

- ↑ Lorenz, Edward N. (March 1963). <0130:dnf>2.0.co;2 "Deterministic Nonperiodic Flow".
*Journal of the Atmospheric Sciences*.**20**(2): 130–141. Bibcode:1963JAtS...20..130L. doi:10.1175/1520-0469(1963)020<0130:dnf>2.0.co;2. - ↑ "Butterfly effect - Scholarpedia".
*www.scholarpedia.org*. Archived from the original on 2016-01-02. Retrieved 2016-01-02. - 1 2 Some Historical Notes: History of Chaos Theory Archived 2006-07-19 at the Wayback Machine
- ↑ Steves, Bonnie; Maciejewski, AJ (September 2001).
*The Restless Universe Applications of Gravitational N-Body Dynamics to Planetary Stellar and Galactic Systems*. USA: CRC Press. ISBN 0750308222. Retrieved January 6, 2014. - ↑ Flam, Faye (2012-06-15). "The Physics of Ray Bradbury's "A Sound of Thunder"".
*The Philadelphia Inquirer*. Archived from the original on 2015-09-24. Retrieved 2015-09-02. - ↑ Gleick, James (1987).
*Chaos: Making a New Science*. Viking. p. 16. ISBN 0-8133-4085-3. - ↑ Motter, Adilson E.; Campbell, David K. (2013). "Chaos at fifty".
*Physics Today*.**66**(5): 27–33. arXiv:1306.5777. Bibcode:2013PhT....66e..27M. doi:10.1063/PT.3.1977. - ↑ Lorenz, Edward N. (March 1963). <0130:DNF>2.0.CO;2 "Deterministic Nonperiodic Flow".
*Journal of the Atmospheric Sciences*.**20**(2): 130–141. Bibcode:1963JAtS...20..130L. doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2. ISSN 1520-0469. - ↑ Google Scholar citation record
- ↑ "Part19". Cs.ualberta.ca. 1960-11-22. Archived from the original on 2009-07-17. Retrieved 2014-06-08.
- 1 2 Lorenz, Edward N. (1963). "The Predictability of Hydrodynamic Flow" (PDF).
*Transactions of the New York Academy of Sciences*.**25**(4): 409–432. doi:10.1111/j.2164-0947.1963.tb01464.x. Archived (PDF) from the original on 10 October 2014. Retrieved 1 September 2014. - ↑ Lorenz: "Predictability", AAAS 139th meeting, 1972 Archived 2013-06-12 at the Wayback Machine Retrieved May 22, 2015
- ↑ "The Butterfly Effects: Variations on a Meme".
*AP42 ...and everything*. Archived from the original on 11 November 2011. Retrieved 3 August 2011. - ↑ Woods, Austin (2005).
*Medium-range weather prediction: The European approach; The story of the European Centre for Medium-Range Weather Forecasts*. New York: Springer. p. 118. ISBN 978-0387269283. - ↑ Orrell, David; Smith, Leonard; Barkmeijer, Jan; Palmer, Tim (2001). "Model error in weather forecasting".
*Nonlinear Processes in Geophysics*.**9**(6): 357–371. Bibcode:2001NPGeo...8..357O. doi:10.5194/npg-8-357-2001. - ↑ Orrell, David (2002). "Role of the metric in forecast error growth: How chaotic is the weather?".
*Tellus*.**54A**(4): 350–362. Bibcode:2002TellA..54..350O. doi:10.3402/tellusa.v54i4.12159. - ↑ Orrell, David (2012).
*Truth or Beauty: Science and the Quest for Order*. New Haven: Yale University Press. p. 208. ISBN 978-0300186611. - ↑ Wolfram, Stephen (2002).
*A New Kind of Science*. Wolfram Media. p. 998. ISBN 978-1579550080. - ↑ Lorenz: "Predictability", AAAS 139th meeting, 1972 Archived 2013-06-12 at the Wayback Machine Retrieved May 22, 2015
- ↑ Lorenz, Edward N. (June 1969). "The predictability of a flow which possesses many scales of motion".
*Tellus*.**XXI**(3): 289–297. Bibcode:1969TellA..21..289L. doi:10.1111/j.2153-3490.1969.tb00444.x. - ↑ Tim, Palmer (19 May 2017). "The Butterfly Effect - What Does It Really Signify?".
*Oxford U. Dept. of Mathematics Youtube Channel*. Retrieved 13 February 2019. - ↑ Emanuel, Kerry (26 March 2018). "Edward N. Lorenz and the End of the Cartesian Universe".
*MIT Department of Earth, Atmospheric, and Planetary Sciences Youtube channel*. Retrieved 13 February 2019. - ↑ "Chaos and Climate". RealClimate. Archived from the original on 2014-07-02. Retrieved 2014-06-08.
- ↑ Heller, E. J.; Tomsovic, S. (July 1993). "Postmodern Quantum Mechanics".
*Physics Today*.**46**(7): 38–46. Bibcode:1993PhT....46g..38H. doi:10.1063/1.881358. - ↑ Gutzwiller, Martin C. (1990).
*Chaos in Classical and Quantum Mechanics*. New York: Springer-Verlag. ISBN 0-387-97173-4. - 1 2 Rudnick, Ze'ev (January 2008). "What is...Quantum Chaos" (PDF).
*Notices of the American Mathematical Society*. Archived (PDF) from the original on 2009-10-02. - ↑ Berry, Michael (1989). "Quantum chaology, not quantum chaos".
*Physica Scripta*.**40**(3): 335–336. Bibcode:1989PhyS...40..335B. doi:10.1088/0031-8949/40/3/013. - ↑ Gutzwiller, Martin C. (1971). "Periodic Orbits and Classical Quantization Conditions".
*Journal of Mathematical Physics*.**12**(3): 343. Bibcode:1971JMP....12..343G. doi:10.1063/1.1665596. - ↑ Gao, J. & Delos, J. B. (1992). "Closed-orbit theory of oscillations in atomic photoabsorption cross sections in a strong electric field. II. Derivation of formulas".
*Physical Review A*.**46**(3): 1455–1467. Bibcode:1992PhRvA..46.1455G. doi:10.1103/PhysRevA.46.1455. PMID 9908268. - ↑ Yan, Bin; Sinitsyn, Nikolai A. (2020). "Recovery of Damaged Information and the Out-of-Time-Ordered Correlators".
*Physical Review Letters*.**125**: 040605. doi:10.1103/PhysRevLett.125.040605. - ↑ Karkuszewski, Zbyszek P.; Jarzynski, Christopher; Zurek, Wojciech H. (2002). "Quantum Chaotic Environments, the Butterfly Effect, and Decoherence".
*Physical Review Letters*.**89**(17): 170405. arXiv:quant-ph/0111002. Bibcode:2002PhRvL..89q0405K. doi:10.1103/PhysRevLett.89.170405. PMID 12398653. - ↑ Poulin, David; Blume-Kohout, Robin; Laflamme, Raymond & Ollivier, Harold (2004). "Exponential Speedup with a Single Bit of Quantum Information: Measuring the Average Fidelity Decay".
*Physical Review Letters*.**92**(17): 177906. arXiv:quant-ph/0310038. Bibcode:2004PhRvL..92q7906P. doi:10.1103/PhysRevLett.92.177906. PMID 15169196. - 1 2 Poulin, David. "A Rough Guide to Quantum Chaos" (PDF). Archived from the original (PDF) on 2010-11-04.
- ↑ Peres, A. (1995).
*Quantum Theory: Concepts and Methods*. Dordrecht: Kluwer Academic. - ↑ Lee, Jae-Seung & Khitrin, A. K. (2004). "Quantum amplifier: Measurement with entangled spins".
*Journal of Chemical Physics*.**121**(9): 3949–51. Bibcode:2004JChPh.121.3949L. doi:10.1063/1.1788661. PMID 15332940. - ↑ Dizikes, Petyer (8 June 2008). "The meaning of the butterfly". The Boston Globe. Archived from the original on 18 April 2016. Retrieved 8 June 2016.

- James Gleick,
*Chaos: Making a New Science*, New York: Viking, 1987. 368 pp. - Devaney, Robert L. (2003).
*Introduction to Chaotic Dynamical Systems*. Westview Press. ISBN 0670811785. - Hilborn, Robert C. (2004). "Sea gulls, butterflies, and grasshoppers: A brief history of the butterfly effect in nonlinear dynamics".
*American Journal of Physics*.**72**(4): 425–427. Bibcode:2004AmJPh..72..425H. doi:10.1119/1.1636492. - Bradbury, Ray. "A Sound of Thunder." Collier's. 28 June 1952

Look up in Wiktionary, the free dictionary.butterfly effect |

- Weather and Chaos: The Work of Edward N. Lorenz. A short documentary that explains the "butterfly effect" in context of Lorenz's work.
- The Chaos Hypertextbook. An introductory primer on chaos and fractals
- The meaning of the butterfly: Why pop culture loves the 'butterfly effect,' and gets it totally wrong, Peter Dizikes,
*The Boston Globe*, June 8, 2008 - New England Complex Systems Institute - Concepts: Butterfly Effect
- The Chaos Hypertextbook. An introductory primer on chaos and fractals
- ChaosBook.org. Advanced graduate textbook on chaos (no fractals)
- Weisstein, Eric W. "Butterfly Effect".
*MathWorld*.

© 2019 raptorfind.com. Imprint, All rights reserved.