Talk:Lorenz system

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)

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)

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)

Image captions

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)

Non-repeating

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)

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)

Notation for Differentiation

The differential equations were recently modified to use the Newton/dot notation (${\dot {x}}$) 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 (${\frac {dx}{dt}}$), 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)

External links modified

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Introductory Paragraph

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

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)

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)