Talk:Wang tile

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I removed "computational model" and "Turing complete": it's not possible to compute functions with Want 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)

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):
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)