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The edit on 29th August apparently broke the section with Python Code (compare the previous version from 26th August where the section dedicated to Python was a very clean, concise piece of code) - the part in question is below the Mathematica section. I do not want to simply restore the previous version but would like to request a review by competent editors who may have more knowledge about this topic than me.

I've just been working on a javascript based interactive demo of the Lorenz system, which you're welcome to use on this page if you want: http://highfellow.github.com/lorenz-attractor/attractor.html

The code is open source: https://github.com/highfellow/lorenz-attractor

A javascript based demo seems better to me than the link to the wolfram demo, which needs special software to run. Highfellow (talk) 20:18, 11 December 2012 (UTC)[reply]

I decided to add the link myself under 'external links' - I think this will be more useful to people than the existing links to interactive demos, as it is entirely based on html / css / javascript. Highfellow (talk) 21:20, 16 December 2012 (UTC)[reply]

The above comment (and this one) belong in a labeled section. Meanwhile, I'll mention that your Javascript rendition of the Lorenz attractor would be better if 1) it did not erase itself, and 2) if it rendered different portions of the attractor in different colors so it was easier to understand.96.11.154.131 (talk) 22:51, 8 August 2020 (UTC)[reply]

Shall we put a dot at the end of an image caption's sentence or not? Sofia Koutsouveli (talk) 16:07, 16 March 2014 (UTC)[reply]

I've heard that the "chaotic" solutions to the Lorentz system are "non-repeating". Would it not be technically more correct to say that they have "probability zero" of repeating? Should this point be addressed in the article? - dcljr (talk) 22:38, 16 October 2017 (UTC)[reply]

It would be extremely incorrect to even mention the word "repeating" unless it is stated clearly just exactly what is meant by the word. As it is, I have no idea exactly what you mean by it.96.11.154.131 (talk) 22:48, 8 August 2020 (UTC)[reply]

The differential equations were recently modified to use the Newton/dot notation (${\displaystyle {\dot {x}}}$) for the derivative with respect to time. This is clearly not wrong, but I think it makes it more daunting to readers who have only a general understanding of mathematics. I think the Liebniz notation is more widely understood (${\displaystyle {\frac {dx}{dt}}}$), and would be a better choice here. If nobody objects I would suggest reverting the change. Tim.spears (talk) 19:27, 25 October 2017 (UTC)[reply]

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The introduction to any article should seek to contain the most fundamental points about the subject in question. With that in mind, I'll note that while the shape of the Lorenz attractor may, in fact, resemble a butterfly, it more importantly describes what is the now proverbial effect of a 'butterfly flapping its wings in China', i.e. that in any physical system, in the absence of perfect knowledge of the initial conditions (and independently of any quantum effects), our ability to predict its future course will always fail. Physical systems can be completely deterministic and yet still be inherently unpredictable. It is this point that makes the Lorenz attractor so pivotal in our understanding of the world. That the plot of the curve may also be seen as the shape of a butterfly only serves to obscure this more fundamental point. I am therefore going to remove the shape-resemblance part.

Unfortunately, in Wikipedia's eagerness to say everything that can be said as soon as possible, this article presents the equations in too much generality (the first time a reader sees them), with unspecified constants instead of the standard values, which are mentioned first in the section titled Analysis.

It would be much better to start with the standard constants, and then mention in a later section that the standard equations have been generalized to a wider class of differential equations.

This should be obvious, but unfortunately is not.96.11.154.131 (talk) 22:45, 8 August 2020 (UTC)[reply]

Response by one user: I respectfully disagree with the above comment. Lorenz's (1963) original derivation of these equations (Sec. 5) requires no assumption about the 3 constants except that they are positive, and he carries out a linear stability analysis of the general system in Sec. 6 of the paper. It is only in Sec. 7, when he discusses numerical simulation, that the so-called standard values for these constants are actually introduced and used. The citation and link to Lorenz's paper is on the main page; it's open access. You can see for yourself. Duncanpark (talk) 06:59, 9 August 2020 (UTC)[reply]

I addressed the issue in my revision of Jan. 5, therefore, I am requesting removal of the "original research" tag in this section. Everything in this section is in Lorenz's original 1963 paper, which is available open access for anyone to verify. Moreover, the information is also available in the textbooks already cited there (Hilborn; Pomeau et al). Please discuss any objections to removing the "original research" tag.Duncanpark (talk) 02:51, 13 January 2022 (UTC)[reply]

Update: Seeing no discussion or objection, I am taking the liberty of removing the tag. Duncanpark (talk) 01:03, 12 April 2022 (UTC)[reply]

Finally, in the Analysis section, the article mentions:

"Lorenz used the values σ = 10, β = ⁠8/3⁠ and ρ = 28."

But these parameters should be much easier to find in the article. Preferably in the Overview section where, unfortunately for readers, the differential equations of the Lorenz system are presented in an absurdly general form rather than the usual equations of Lorenz himself.

I say we should present the standard equations first and then, later in the article include the general form.

It's not as though the extra electrons will cause global warming. 2601:200:C000:1A0:5CB3:EB76:C957:9110 (talk) 13:12, 4 August 2022 (UTC)[reply]

I respectfully disagree with the above comment. Lorenz's (1963) original derivation of these equations (Sec. 5) requires no assumption about the 3 constants except that they are positive, and he carries out a linear stability analysis of the general system in Sec. 6 of the paper. It is only in Sec. 7, when he discusses numerical simulation, that the so-called standard values for these constants are actually introduced and used. The citation and link to Lorenz's paper is on the main page; it's open access. You can see for yourself. Duncanpark (talk) 21:48, 2 November 2025 (UTC)[reply]

I think the article should explain more clearly whether the "Lorentz butterfly effect" is a permanent theoretical problem or just a temporary one that'll lose significance after an exact solution is found for the Navier-Stokes equation system?

The connection between "Lorentz butterfly effect" and the gravitational Three-Body Problem could also be addressed in the article, as they seem to be closely related. 77.234.84.45 (talk) 18:48, 3 January 2025 (UTC)[reply]

The Navier-Stokes equations depend on the shape of the space they are defined on, as well as on the initial conditions. So it is extremely unlikely that exact solutions will ever be found that even cover a large number of cases, no less all cases.

But even if the Navier-Stokes equations were solved explicitly, that would have no bearing on the butterfly effect in general, since the butterfly effect — often called "sensitive dependence on initial conditions" — occurs in an enormous variety of dynamical systems having no relationship to Navier-Stokes systems. (Even if the Lorenz system itself was derived by a modification of Navier-Stokes equations.) 2601:204:F181:9410:C2D:543E:305D:77FD

A few questions should be addressed in this article. Are the following known or unknown, and if known, what are the answers? Here I am specifically referring to the *standard* parameters of the Lorenz attractor 10, 8/3, 28:

1. Is the Lorenz attractor a closed subset of 3-dimensional space?

2. Is the Lorenz system hyperbolic in a neighborhood of the Lorenz attractor?

3. Is the Lorenz system as a whole structurally stable?

These are extremely basic questions that one would like to know about any interesting dynamical system. If any of these are known, I hope someone knowledgeable about them will add them to the article, and if they are unknown at this time, that is also definitely worth adding to the article. 2601:204:F181:9410:C2D:543E:305D:77FD (talk) 05:32, 3 June 2025 (UTC)[reply]

User:Bwshen, who is blocked, seems to have engaged in COI editing on this page, by citing sources for which he was an author. Bwshen is likely Bo-Wen Shen, who is an author of many sources cited on this page, and I imagine that many of these citations were added by Bwshen, though I haven't checked them all. I'm not too knowledgeable about this topic myself, so it would help if somebody else could help decide if all of these sources merit inclusion in this article. It's possible that they do, but there should be independent verification of this. The same issue arises on Butterfly effect and Chaos theory. Truthnope (talk) 10:01, 1 November 2025 (UTC)[reply]

I would tend to agree. For example, the section on Generalized Lorenz System specifically discusses Shen's works, but there are several other "generalized Lorenz systems" in the literature. There is no particular reason I know of why Shen's merits special attention on wikipedia compared to the others. Unfortunately I don't have the time to clean up the page. Duncanpark (talk) 01:02, 13 November 2025 (UTC)[reply]

Hi Everyone, as a new member of the editing community of Wiki, i couldn't help but notice that the page of Lorenz Attractor was merged with this page. These, although are quite similar are by no means the same; Where the Lorenz system sets a equations that describe the behavior OF the Lorenz attractor. The Lorenz attractor is a specific solution of the Lorenz system, it is known by its butterfly shape. the system is deterministic, where the attractor is a subset of phase space where systems to the system converge. although they go hand in hand i believe firmly that there is so much more content that is not covered here in Lorenz system that could be.

if anyone has any reasons for this not going ahead please let me know (i might not reply for a day or two),

JG

JG qwerty (talk) 08:40, 10 November 2025 (UTC)[reply]

Oppose The current article it not too big; the attractor is a subtopic. Plus Lorenz system is a mess and one mess is better than two. Johnjbarton (talk) 23:23, 11 November 2025 (UTC)[reply]

i am saying there is alot to be explored in the topic of the lorenz attractor but it is not talked about enough inside of the Lorenz system article. JG qwerty (talk) 00:31, 12 November 2025 (UTC)[reply]

Great, add it! Johnjbarton (talk) 03:13, 12 November 2025 (UTC)[reply]

I would tend to agree with @Johnjbarton. I think the Lorenz system and the Lorenz attractor are best discussed together. I also agree that the page is a mess. Adding a new section on further details of the attractor would probably be the least intrusive solution. Duncanpark (talk) 01:05, 13 November 2025 (UTC)[reply]

hence why i would like to make a new clean page away from the mess of this page

JG qwerty (talk) 02:33, 13 November 2025 (UTC)[reply]