|WikiProject Mathematics||(Rated C-class, Low-importance)|
|WikiProject Systems||(Rated B-class, Mid-importance)|
Unfolding the Dragon
This article, especially the section mentioned above, seems very unencyclopediac to say the least. I've searched google briefly to try and find any copyright violations, but was unsuccessful. Either way, it needs to be editted.
- I have re-written (and shortened) the paper folding section. Gandalf61 11:21, 24 January 2006 (UTC)
Supposing you were reading this artcile out of casual interest - like I was - and that you have no particular knowledge of mathematics, then do you really think that there is anything here that is remotely helpful? I came to this page from, predictably, the Jurassic Park page, and I have no idea what on earth these semi-fractal things are used for other than generating pretty pictures. Perhaps a little more consideration should be given to the lay man here? Lots of the science articles are like this - you'd only be able to read them if you already knew all about the subject. --Corinthian 16:27, 24 January 2006 (UTC)
Why is my dragon curve live demonstration deleted?
I added a live demonstration to the article in the external link. Why is it deleted? I don't see anything wrong with it. http://jsonchiu.prophp.org/flash/fractal.swf 188.8.131.52 15:06, 18 April 2007 (UTC)
perhaps because the link is broken? I'll delete it now, but be happy to see a working link again. If you need working webspace to put it up feel free to send me a mail. I'll host anything dragon-related :) Zefiro 20:17, 25 May 2007 (UTC)
that dimension again?
"The fractal dimension of [the Heighway dragon's] boundary has been calculated ...: 1.5238"
Presumably it's something of the form log(m)/log(n), but what are m,n? —184.108.40.206 00:10, 12 June 2007 (UTC)
Added information and reorganized a bit.
Added : reference for the fractal dimension of the boundary, image showing the standard construction, various properties, and a gallery dedicated to the many ways of tiling the plane. And clarified the table of contents. A question : Does that chapter about the Levy C curve has its place here ? Prokofiev2. 10 december 2007.
- The article already has several illustrations of dragon tilings. I don't think this image would add anything. Gandalf61 (talk) 09:31, 21 November 2008 (UTC)
Right - Left Code
I have written a little piece of C++ code using the formula to determine the turn at a certain step:
for(int i = 1; i < 10; ++i)
const bool turnRight = ((((i & -i) << 1) & i) != 0);
cout << i << ": " << (turnRight ? 'R' : 'L') << endl;
The output shows 'L' and 'R' the opposite way you would expect:
1: L 2: L 3: R 4: L 5: L 6: R 7: R 8: L 9: L
Doesn't that prove that the formula in the article is not correct as the comment for the (undone) change of 6 December 2008 suggests?
- Yes, I think you are right; (((n & -n) << 1) & n) != 0 is TRUE if n = k2m and k = 3 mod 4, in which case the nth turn is Left. There was an error in the previous line of the explanation of the algorithm; I have fixed it now. Gandalf61 (talk) 01:32, 8 March 2009 (UTC)
Are dragon curves tileable after any nuber of iterations or only after they're "complete" (after infinite iterations)? Are curves after 10 or 20 iterations tileable? I made a 6th iteration curve which seems to be, if this is the case maybe it should be mentioned in the article. 220.127.116.11 (talk) 07:30, 7 March 2011 (UTC)
- The "tileability" is a result of the self-similarity properties of the Heighway dragon curve - it is made out of two smaller copies of itself. But this self-similarity is only exact in the limit (i.e. after "infinite iterations) - each finite iteration is made out of two copies of the previous iteration, not of itself. So tiling will only be exact for the "complete" fractal dragon curve. Any finite iteration will only have approximate tileability, although it may be close enough to fool the naked eye. Gandalf61 (talk) 09:02, 7 March 2011 (UTC)
Issues with 2011-06 article version
While I am not a member of the lay audience, I agree with the opening comment that this article in its current form needs improvement. We cann't just keep discarding everybodies changes when they try to improve it. "Anchoring" is a well-known method for retarding progress. Here's a list of specific problems I think need addressing.
- The 1-sentence introduction is not accessible to lay audiences. For one of the most famous examples of mathematical art, we are losing a great educational opportunity.
- The introduction sentence talks about the "dragon curve" as a genus, but only one species, the "Heighway dragon", is discussed subsequently. We need to either explain the classification system in general, or stop speaking in unnecessary generalities.
- The "Construction" section for string-rewriting is not implementable, as described. "angle 90" means nothing in the context of the subsequent bullet points. For the actual symbol rewritting in the next bullet points, no interpretations for the symbols are given, and there is no suggestion of how to handle any ambiguities which arrise from "+-" and "--" symbols.
- The connection with complex function iteration is similiarly not explained adequately to be useful. These are simple linear functions, so their compositions will also be linear. Transformation to matrix arithmetic just transforms the functions from one specialized language to another, and every mathematician can do this transformation for themselves if needed. It's much more important to describe how these functions relate to the construction of the dragon curve, or if they are merely symmetries under which the curve is invariant. The random software references seems unnecessary and unhelpful.
- The folding section is by far the most important of the explanations so far presented. It was the piece of the page I was able to use to construct a dragon curve of my own, and highlights the non-local aspects of this rule that distinguish it from more common Lindenmayer systems. It is also a highly accessible explanation for lay audiences, and as such should be emphasized first, before the more inaccessible explanations for those with mathematical and computational training. — Preceding unsigned comment added by 18.104.22.168 (talk) 18:48, 25 June 2011 (UTC)
- The twindragon, terdragon and Lévy C curve are also called draogn curves - each curve has its own section in the article. The linked articles L-system and iterated function system contain more details of these construction methods. The folding construction is not more important or more fundamental than the other construction methods. Gandalf61 (talk) 21:28, 25 June 2011 (UTC)
Does anyone know a sequential algorithm to calculate the next turn with just a finite amount of memory and a constant amount of time?