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“洛伦兹系统”是由[[爱德华-诺顿-洛伦兹|爱德华-洛伦兹]]最先提出的一种由[[常微分方程]]构成的系统。值得注意的是，在一些特定参数和初始条件下，它的解是[[混沌理论|混沌]]的。更确切的说，“洛伦兹吸引子”其实是洛伦兹系统所有的混沌解。人们通常所说的"[[蝴蝶效应]]"源于洛伦兹吸引子的现实意义：即在任何物理系统中，在对初始条件不完全了解的情况下，即使是蝴蝶拍打翅膀引起的微小扰动都可以让我们无法成功的预测系统的未来进程。对物理系统来说，即使它可以被完整的测定，但人们仍然不能完全预测它（即使排除了量子效应也不行）。洛伦兹吸引子绘制成的图形看起来就像一只蝴蝶。这也是“蝴蝶效应”这一词的由来。

“洛伦兹系统”是由[[爱德华-诺顿-洛伦兹|爱德华-洛伦兹]]最先提出的一种由[[常微分方程]]构成的系统。值得注意的是，在一些特定参数和初始条件下，它的解是[[混沌理论|混沌]]的。更确切的说，“洛伦兹吸引子”其实是洛伦兹系统所有的混沌解。人们通常所说的"[[蝴蝶效应]]"源于洛伦兹吸引子的现实意义：即在任何物理系统中，在对初始条件不完全了解的情况下，即使是蝴蝶拍打翅膀引起的微小扰动都可以让我们无法成功的预测系统的未来进程。对物理系统来说，即使它可以被完整的测定，但人们仍然不能完全预测它（即使排除了量子效应也不行）。洛伦兹吸引子绘制成的图形看起来就像一只蝴蝶。这也是“蝴蝶效应”这一词的由来。

（关于这一词的由来需要参考书籍《The essence of chaos》）引用原文如下：(未翻译)The thing that has made the origin of the phrase a bit uncertain

 

is a peculiarity of the first chaotic system that I studied in detail.

 

Here an abbreviated graphical representation of a special collection

（关于这一词的由来需要参考书籍《The essence of chaos》）引用原文如下：(未翻译)The thing that has made the origin of the phrase a bit uncertainis a peculiarity of the first chaotic system that I studied in detail.Here an abbreviated graphical representation of a special collectionof states known as a “strange attractor” was subsequently foundto resemble a butterfly, and soon became known as the butterfly.In Figure 2 we see one butterfly; a representative of a closely relatedspecies appears on the inside cover of Gleick’s book. A number ofpeople with whom I have talked have assumed that the butterflyeffect was named after this attractor. Perhaps it was.Some correspondents have also called my attention to RayBradbury’s intriguing short story “A Sound of Thunder,” writtenlong before the Washington meeting. Here the death of a prehistoricbutterfly, and its consequent failure to reproduce, change theoutcome of a present-day presidential election.Before the Washington meeting I had sometimes used a sea gullas a symbol for sensitive dependence. The switch to a butterfly wasactually made by the session convenor, the meteorologist PhilipMerilees, who was unable to check with me when he had to submitthe program titles. Phil has recently assured me that he was notfamiliar with Bradbury’s story. Perhaps the butterfly, with itsseeming frailty and lack of power, is a natural choice for a symbolof the small that can produce the great.Other symbols have preceded the sea gull. In George R.Stewart’snovel Storm, a copy of which my sister gave me for Christmas whenshe first learned that I was to become a meteorology student, ameteorologist recalls his professor’s remark that a man sneezing inChina may set people to shoveling snow in New York. Stewart’sprofessor was simply echoing what some real-world meteorologistshad been saying for many years, sometimes facetiously, sometimesseriously<ref>{{cite book | last1=Lorenz | first1=Edward N. | title=The Essence of Chaos | publisher=UCL Press | isbn=978-1-85-728454-6 | year=1993}}</ref>

of states known as a “strange attractor” was subsequently found

 

to resemble a butterfly, and soon became known as the butterfly.

In Figure 2 we see one butterfly; a representative of a closely related

 

species appears on the inside cover of Gleick’s book. A number of

people with whom I have talked have assumed that the butterfly

effect was named after this attractor. Perhaps it was.

Some correspondents have also called my attention to Ray

Bradbury’s intriguing short story “A Sound of Thunder,” written

long before the Washington meeting. Here the death of a prehistoric

butterfly, and its consequent failure to reproduce, change the

outcome of a present-day presidential election.

Before the Washington meeting I had sometimes used a sea gull

as a symbol for sensitive dependence. The switch to a butterfly was

actually made by the session convenor, the meteorologist Philip

Merilees, who was unable to check with me when he had to submit

the program titles. Phil has recently assured me that he was not

familiar with Bradbury’s story. Perhaps the butterfly, with its

seeming frailty and lack of power, is a natural choice for a symbol

of the small that can produce the great.

Other symbols have preceded the sea gull. In George R.Stewart’s

novel Storm, a copy of which my sister gave me for Christmas when

she first learned that I was to become a meteorology student, a

meteorologist recalls his professor’s remark that a man sneezing in

China may set people to shoveling snow in New York. Stewart’s

professor was simply echoing what some real-world meteorologists

had been saying for many years, sometimes facetiously, sometimes

==概述==

==概述==

== Gallery ==

== Gallery ==

<gallery>

<gallery>

File:Lorenz system r28 s10 b2-6666.png|A solution in the Lorenz attractor plotted at high resolution in the x-z plane.

File:Lorenz system r28 s10 b2-6666.png|A solution in the Lorenz attractor plotted at high resolution in the x-z plane. x-z平面上对洛伦兹吸引子其中一个解的高清图。

File:Lorenz attractor.svg|A solution in the Lorenz attractor rendered as an SVG.

File:Lorenz attractor.svg|A solution in the Lorenz attractor rendered as an SVG.以SVG形式呈现的洛伦兹吸引子的解。

File:A Lorenz system.ogv|An animation showing trajectories of multiple solutions in a Lorenz system.

File:A Lorenz system.ogv|An animation showing trajectories of multiple solutions in a Lorenz system.动画显示了洛伦兹系统中多个解的轨迹。

File:Lorenzstill-rubel.png|A solution in the Lorenz attractor rendered as a metal wire to show direction and [[Three-dimensional space|3D]] structure.

File:Lorenzstill-rubel.png|A solution in the Lorenz attractor rendered as a metal wire to show direction and [[Three-dimensional space|3D]] structure.洛伦兹吸引子的一个解被渲染成金属线，以显示方向和[[三维空间|3D]]结构。

File:Lorenz.ogv|An animation showing the divergence of nearby solutions to the Lorenz system.

File:Lorenz.ogv|An animation showing the divergence of nearby solutions to the Lorenz system.动画显示出在洛伦兹系统的解附近会出现发散的情况。

File:Intermittent Lorenz Attractor - Chaoscope.jpg|A visualization of the Lorenz attractor near an intermittent cycle.

File:Intermittent Lorenz Attractor - Chaoscope.jpg|A visualization of the Lorenz attractor near an intermittent cycle.洛伦兹吸引子在一个间歇循环附近。

File:Lorenz apparition small.gif|Two streamlines in a Lorenz system, from rho=0 to rho=28 (sigma=10, beta=8/3)

File:Lorenz apparition small.gif|Two streamlines in a Lorenz system, from rho=0 to rho=28 (sigma=10, beta=8/3)洛伦兹系统中的两条流线，从rho=0到rho=28（sigma=10，beta=8/3）。

File:Lorenz(rho).gif| Animation of a Lorenz System with rho- dependence

File:Lorenz(rho).gif| Animation of a Lorenz System with rho- dependence 动画展示出洛伦兹系统具有rho-依赖性。

</gallery>

</gallery>