Talk:Lorenz attractor

Three models

The three coupled differential equations model convection rolls in the atmosphere. Do the three variables x, y, and z describe the position of a small cell of air? If not, then to what physical attribute do they apply?

No, X, Y and Z are the coefficients of the main terms in a series expansion of the stream function (its curl gives the velocity components) and of the temperature distribution. See e.g. [1], or even better the original [2]. —The preceding unsigned comment was added by 81.14.185.86 (talk) 11:07, 28 December 2006 (UTC).

Fractal

> The Lorenz attractor, named for Edward N. Lorenz, is a fractal structure

In what sense exactly is this a fractal? It does not seem to be self-similar at arbitrary scale.
208.82.105.24 (talk) 23:42, 29 May 2009 (UTC)Brad White

Plain English

"is a non-linear three-dimensional deterministic dynamical system derived from the simplified equations of convection rolls arising in the dynamical equations of the atmosphere" means nothing to anybody but the already educated. This is not a suitable explanation of what the Lorenz attractor is. We need to remove such technical barriers to Wikipedia entries. This is an encyclopedia for all not just for maths geeks 199.4.27.1 14:23, 24 April 2006 (UTC)

very good point. Have tried to make some improvements, especially to that horrendous opening. -- GWO

Referencing

The article improved significantly since the last time I've read it (about 6 months ago) and some interesting facts were added. However now it lacks references. Specifically:

• 2001 Tucker work
• applications in lasers and dynamos (I found only info about the waterwheel at [1])

Broken links

It seems that the links to the java simulations under the images are broken. I think the website has been taken down, it seems to redirect to a portugese web-site provider now. 144.32.212.71 12:10, 16 February 2007 (UTC)

Just a temporary problem. Tó campos 18:34, 16 February 2007 (UTC)

Raleigh number transition

Following the link to the applet, I noticed the value of rho where chaos is noted as beginning is at most 23, which is lower than this article's 24.74. Is this a typo? 67.189.108.27 06:13, 4 August 2007 (UTC)

According to the formula ρ = ... (which should be ρ <) the critical value is 470/19 ~ 24.74. Incidentaly, does anyone know where I can find a published derivation of this formula? John_Perram, 7 July 2011. — Preceding unsigned comment added by John Perram (talk • contribs) 04:35, 7 July 2011 (UTC)

What is it?

What set, exactly, is the Lorenz attractor? Every model I've seen is a model of trajectories of solutions, not a model of the attractor itself. Is the Lorenze attractor a set? Is it just the 2 equilibria? Is there a homoclinic orbit connecting the equilibria? SmaleDuffin 19:04, 19 October 2007 (UTC)

Octave source code

I am no octave person, but I wanted to see the result of what was given and it didn't work. I copied the code exactly as it was given.

octave-3.0.5:1> ## Lorenz Attractor equations solved by ODE Solve
octave-3.0.5:1> ## x' = sigma*(y-x)
octave-3.0.5:1> ## y' = x*(rho - z) - y
octave-3.0.5:1> ## z' = x*y - beta*z
octave-3.0.5:1> function dx = lorenzatt(X)
>     rho = 28; sigma = 10; beta = 8/3;
>     dx = zeros(3,1);
>     dx(1) = sigma*(X(2) - X(1));
>     dx(2) = X(1)*(rho - X(3)) - X(2);
>     dx(3) = X(1)*X(2) - beta*X(3);
>     return
> end
octave-3.0.5:2> ## Using LSODE to solve the ODE system.
octave-3.0.5:2> clear all
octave-3.0.5:3> close all
octave-3.0.5:4> lsode_options("absolute tolerance",1e-3)
octave-3.0.5:5> lsode_options("relative tolerance",1e-4)
octave-3.0.5:6> t = linspace(0,25,1e3); X0 = [0,1,1.05];
octave-3.0.5:7> [X,T,MSG]=lsode(@lorenzatt,X0,t);
error: error creating function handle "@lorenzatt"
error: evaluating argument list element number 1
octave-3.0.5:7> T
error: `T' undefined near line 7 column 1
octave-3.0.5:7> MSG
error: `MSG' undefined near line 7 column 1
octave-3.0.5:7> plot3(X(:,1),X(:,2),X(:,3))
error: `X' undefined near line 7 column 7
error: evaluating argument list element number 1
octave-3.0.5:7> view(45,45)
octave-3.0.5:8>

--Sidious1741 (talk) 22:01, 24 April 2010 (UTC)

At least the following works: put the first part into a file called lorenzatt.m, start octave, and execute the latter part in the octave shell. —Preceding unsigned comment added by 213.157.86.71 (talk) 16:31, 6 November 2010 (UTC) The typo is the extra line at beginning of main script: A "clear all" command will erase the definition of previous function "lorenzatt". Just remove this line will do. — Preceding unsigned comment added by 111.243.7.30 (talk) 10:19, 8 December 2016 (UTC)

Where's the definition of a lorenz attractor?

No one answered the first person to ask this question over 4 years ago, so I'll ask it again. The first sentence says the attractor is an example corresponding to its oscillator. Does that mean something? It seems like the rest of the article does not belong here as the other wikian posted. Somebody please write an article that explains what a lorenz attractor is. If it's just another name for the oscillator, then say so and make this article merely point to the oscillator article. Ywaz (talk) 15:51, 4 February 2012 (UTC)

Moving contents to "Lorenz system"

Almost everything in this article is about the Lorenz System (i.e. a system of differential equations), not the Lorenz Attractor (which arises in the study of the Lorenz System). It's like having all the information about New York City in the article about the Statue of Liberty: it's absurd. Right now, the article about the "Lorenz system" redirects to the article about the "Lorenz attractor". Imagine if "New York City" redirected to "Statue of Liberty"... Here is what I'm going to do: I'm going to move the bulk of the "Lorenz attractor" article to the "Lorenz system" article, and then I'm going to redirect the "Lorenz attractor" article to the corresponding section (heading) within the "Lorenz system" article. Drttm (talk) 23:09, 14 March 2012 (UTC) Re:

Not disagreeing with your "move", but you seem to have done it by a cut-and-paste of the article contents. This is a really bad idea because it splits up the history of the article and its contributors. A proper page move would have been the correct action - see Wikipedia:How to fix cut-and-paste moves. You may need to ask an admin to help you sort this out. Gandalf61 (talk) 13:20, 16 March 2012 (UTC)