Talk:Wang tile

Materialscientist has reverted my edit to Wang tile which included an external link to a generator of infinite minimal Wang tilings. The external link contributes to the understanding of the article. The external link visually demonstrates what is discussed in the article but cannot be included within the article itself because it is a HTML5/Javascript demonstration of a Wang Tile. It is similar to the second external link which is also a HTML5/Javscript demonstration, in this case a naive demonstration of a different Wang tileset. However, the new external link which I included in my edit demonstrates a different tiling, the minimal tiling discussed in the first image on the page. And it does so non-naively, showing an actual valid infinite tiling. — Preceding unsigned comment added by Charming Computer (talk • contribs) 22:22, 12 February 2023 (UTC)[reply]

Jason.grossman: You added a reference to Mat Newman work on 8 tile aperiodic sets. Could you add or give a reference to his work?

Thank you, Sergio Demian Lerner. --Sergiolerner 03:07, 30 August 2007 (UTC)[reply]

I removed "computational model" and "Turing complete": it's not possible to compute functions with Wang tiles, and they were certainly not introduced as a computational model. They do not in any sense define the concept of "algorithm", like Turing machines, Post systems or recursive functions do. They are better described as a device that gives rise to a simple uncomputable problem. AxelBoldt 21:14 Jan 3, 2003 (UTC)

Not possible to compute functions? Can you prove that for me? >:-) --67.172.99.160 00:03, 26 August 2005 (UTC)[reply]

Maybe the definition should be generalized to mention the side-matching rules only, with aperiodic tiling as a motivating example; after all, most applications use tile sets with few constraints, that instead of forcing highly regular aperiodic tilings guarantee at least two tile choices at all or most growth sites and allow randomization.

From Sergiolerner 14:47, 5 February 2007 (UTC):[reply]
I undo the change "It can tile the plane aperiodically" to the original version "It can tile the plane, but not periodically.". The version Giftlite wrote misuses the definition of "aperiodically" and it's not mathematically correct. Many sets can tile the plane aperiodically (you can build a very simple Wang protoset of 4 tiles that do this). The problem is to find a protoset which does not allow a periodic tiling (not one that allows an aperiodic one).

It could also be expressed "It can ONLY tile the plane aperiodically", which is a bit sipler. --Sergiolerner 14:47, 5 February 2007 (UTC)[reply]