Bob,
I believe the Penrose tiling lacks simple symetry which your math examples have.
But I thought the Alhambra had some of the very special tiling.
Regards,  Bob S.

On Thu, Apr 8, 2010 at 2:37 AM, Bob W <[email protected]> wrote:
>> On Wed, Apr 07, 2010 at 10:13:30PM +0100, Bob W scripsit:
>> > [...]
>> > He won a legal battle a few years ago against a toilet paper
>> > manufacturer who used a Penrose tiling on their paper to
>> make it less bulky when rolled.
>> > They were judged to have stolen his idea, but I can't help thinking
>> > how wonderful it would be if some junior bogroll designer
>> had come up
>> > with the same idea...
>>
>> I seem to recall that there are some medieval mosques with
>> tiling patterns that use Penrose tiling, so someone seems to
>> have managed it empirically.  (At least; if they published
>> back then, it is not known to
>> survive.)
>>
>
> These are from the Alhambra (the one in Granada, not the one in Bradford):
> <http://www2.spsu.edu/math/tile/grammar/moor.htm>
>
> I think they kept this sort of thing a closely guarded secret.
> Coincidentally I was looking at a tiling program earlier this week, just out
> of curiosity and because I like Islamic tiling. Whether or not they were
> Penrose tilings I don't know - I'm not a mathematician - but the authors of
> this software approach it from the mathematical point of view.
> <http://www.cgl.uwaterloo.ca/~csk/washington/taprats/>
>
> Bob
>
>
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