Talk:Penrose tiling

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Several images were not Penrose tilings, but were outputs from L-systems. I've moved them to L-system. Now someone needs to explain in that article what those images actually are, and how the L-system generated them.

Now I too wonder how the L-system generates the tilings. I have one guess: it might use deflation. Is this correct? —Sverdrup(talk) 15:31, 27 Dec 2003 (UTC)

A free Microsft Windows program to generate and explore rhombic Penrose tiling is available at http://www.jkssoftware.com/penrose. The software was written by Stephen Collins of JKS Software, in collaboration with the Universities of York, UK and Tsuka, Japan.

LSystems can be generated using the free Software http://jlsystem.sourceforge.net. helohe 12:10, 1 October 2005 (UTC)

Contents 1 Clark Richert 2 use of the word "uncountable" 3 Projection 4 No Matching Rules Discussed 5 Explanation? 6 More penrose tiles needed? 7 Link to a Penrose-base artistic image

[edit] Clark Richert

Yeah, I know that a reference to a random guy posting at Slashdot is exactly what Wikipedia needs. :) But his post mentions tome interesting things about the tiles, including that Clark Richert has figured at least a part of that at the same time as Penrose. Paranoid 15:05, 12 May 2005 (UTC)

[edit] use of the word "uncountable"

the article says "there are many ways (infact, uncountably many).." This is kinda vague and might lead someone to think uncountable is a synonym of infinite. In fact, countability/uncountability really has nothing to do with the size of a set. It should definitely be mentioned that the ways to form a penrose tiling is uncountable, but it should not be confused with an implication about the size of the set. 164.76.162.135 16:56, 5 December 2006 (UTC)

i just decided to go for it and made this change myself 164.76.162.135 17:05, 5 December 2006 (UTC)

[edit] Projection

Note that the Penrose tiling is a projection of a five dimensional lattice (which has cubic symmetry) down to two dimensions; thus, the readily apparent symmetry in five dimensions is rather hidden and obfuscated when seen in two.

[edit] No Matching Rules Discussed

There is a serious-- indeed critical!-- flaw in this article. The rhombs shown CAN tile periodically. (indeed, of course, any quadrilateral can). The essential aspect of the Penrose tiles is that they are marked in such a way that they can ONLY tile non-periodically. With no discussion or illustration of the matching rules that drive the construction, unfortunately, the article is nonsense.

(The illustrations do show the structure the Penrose tiles are forced to assume, but not the actual tiles themselves)

Here is a reference, chosen by Google: www2.spsu.edu/math/tile/aperiodic/penrose/penrose2.htm --—The preceding unsigned comment was added by 69.151.118.199 (talk • contribs).

The article currently reads (after describing the shapes):

The tiles are put together with one rule: no two tiles can be touching so as to form a single parallelogram. The tiles can be modified with bumps and dents around the perimeter to enforce this rule, but the tiling looks better if they have smooth sides.

Perhaps this should be more emphasized to avoid confusion by other future readers. --Chan-Ho (Talk) 03:26, 11 March 2006 (UTC)

Thank you; I did overlook this. But of course I wouldn't have been the only one. And the standard stripes that are often drawn on the rhombs are quite attractive!

True. This needs to be covered in the article, preferably with a picture. Reyk _YO! 22:08, 20 May 2006 (UTC)

[edit] Explanation?

How about a section explaining why the tiling is aperiodic, how it works, and why this is interesting? Torokun 22:05, 28 March 2006 (UTC) And also, why insist (as many others do) that ' given a bounded region of the pattern, no matter how large, that region will be repeated an infinite number of times within the tiling' which is a feature of random systems? 85.187.217.182 23:17, 13 November 2006 (UTC)

[edit] More penrose tiles needed?

See The colossal book of mathematics, Gardner M., Penrose tiles. The tiles featured there are more interesting and should be added.Doomed Rasher 18:19, 2 September 2006 (UTC)

[edit] Link to a Penrose-base artistic image

Ref: Kepler/Penrose tiling problem...i am an independent artist/designer and about 20 yrs ago i painted a picture depicting a periodic pattern using the Kepler/Penrose tiles (derived from the dissection of a pentagon)...and this image can be perused on my web-site at:

  http://www.peterhugomcclure.com/colour%20images/36.htm

Best regards pete mcclure.--81.86.8.62 13:00, 22 November 2006 (UTC)

Hi Pete. Are you willing to allow use of the image directly on the wikipedia? There's a choice of copyright tags to go with an image here; see WP:TAG.--Niels Ø 09:08, 23 November 2006 (UTC)