Talk:Paul Lévy (mathematician)

	Biography portal This article is within the scope of WikiProject Biography, a collaborative effort to create, develop and organize Wikipedia's articles about people. All interested editors are invited to join the project and contribute to the discussion. For instructions on how to use this banner, please refer to the documentation.BiographyWikipedia:WikiProject BiographyTemplate:WikiProject Biographybiography articles
	This article is supported by the science and academia work group.

Mathematics Mid‑priority

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles
Mid	This article has been rated as Mid-priority on the project's priority scale.

France Low‑importance

	France portal This article is within the scope of WikiProject France, a collaborative effort to improve the coverage of France on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.FranceWikipedia:WikiProject FranceTemplate:WikiProject FranceFrance articles
Low	This article has been rated as Low-importance on the project's importance scale.

Lévy dragon curve

(Discussion copied from User talk:Solkoll and User talk:Gandalf61)

Saw your changes to Lévy C curve and Paul Pierre Lévy. Can you explain what your definition of the Lévy dragon curve is, and how it differs from the Lévy C curve ? The only references I can find to the Lévy dragon curve are actually about the Lévy C curve (see here for example). When people refer to a dragon curve without qualification, they always seem to mean the Harter-Heighway dragon curve, which I think has nothing to do with Paul Lévy. I don't mind removing the phrase "also known as the Lévy dragon curve" from the C curve article, but, as far as I know, there is not a separate curve called the Lévy dragon curve. Gandalf61 11:01, Feb 15, 2005 (UTC)

Hello Gandalf! About the Lévy curves: I'm not really sure where I read about the curves, (and maybe the source was wrong), it was some years ago now. But as far as I know there are three diffrent, closly related curves. At the moment I'm uploading images of IFS fractals I'm creating to "Commons". There I uploaded these three images the recent day or so, (doing this I also made some changes to the wikipedia articles about the curves, as you know =)

Here you can see the diffrence between the "Harter-Heighways dragon curve" and the "Lévy dragon curve". Using IFS (random game), the construction of these curves are almost the same.

Lévy C curve:

two points in a plane, (two "rules")
scale factor; 1:sqrt(2) for both rules
rotation angles; rule [0] = 45º, rule[1] = -45º

Lévy dragon curve:

two points in a plane
scale factor; 1:sqrt(2) for both rules
rotation angle; 45º for both rules

Harter-Heighways dragon curve:

two points in a plane
scale factors; rule [0] = 1:sqrt(2), rule [1] = -1:sqrt(2)
rotation angles; rule [0] = 45º, rule[1] = -45º

I'm not 100% sure I got it all correct, but it's close =)

I hope this helped you a bit? If I can find some kind of source for this information, then I get back to you. // Solkoll 17:09, 15 Feb 2005 (UTC)

Thank you for your response on my talk page, and for the illustrations. I have re-read Lévy's original paper "Plane or Space Curves and Surfaces Consisting of Parts Similar to the Whole", and I cannot find any mention of the curve that you are calling the Lévy dragon curve. Lévy presents various general results that apply to any self-similar curve, but the only two 2-D curves that he discusses in detail are the Koch curve and the curve that he refers to as

C_{0}

, which we call the Lévy C curve. All his figures show the Lévy C curve. In the copy I have, which is in Gerald Edgar's anthology "Classics on Fractals", Edgar adds commentary in which he refers to Lévy's

C_{0}

curve as the Lévy dragon curve, which is another reason why I thought this was just another name for the Lévy C curve. Can you provide any reference that links your Lévy dragon curve to Lévy, or that calls it the Lévy dragon curve ? Gandalf61 11:07, Feb 16, 2005 (UTC)

In the absence of any evidence that Solkoll's Lévy dragon curve has any link to Paul Lévy, I have removed the reference to it from the article. Gandalf61 11:09, Feb 21, 2005 (UTC)