Since I sometimes like to just browse the text files, instead of going to
the trouble of saving, unziping, reading, etc. I'll attach the macros to
this message, and follow up with the demonstrator file.  I wish I could get
something to work that would allow attaching multiple things to a single
message... <sigh>

This include file not only has the macros to generate Rhomb and Kite/Dart
Tilings, like the images I put in p.b.i, but it has lots of patterns in it
already.  Different vetrex groups, and their empires, and all the Decagons
for the centers of cartwheels, etc.

Jon

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Attachments:
Download 'penrose.inc.txt' (43 KB)

This message has the Scene description file for all the images in the thread
of the same name in p.b.i...

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Attachments:
Download 'penrose.pov.txt' (13 KB)

"Jon Buller" <jon### [at] bullersnet> wrote:
> Since I sometimes like to just browse the text files, instead of going to
> the trouble of saving, unziping, reading, etc. I'll attach the macros to
> this message, and follow up with the demonstrator file.  I wish I could get
> something to work that would allow attaching multiple things to a single
> message... <sigh>
>
> This include file not only has the macros to generate Rhomb and Kite/Dart
> Tilings, like the images I put in p.b.i, but it has lots of patterns in it
> already.  Different vetrex groups, and their empires, and all the Decagons
> for the centers of cartwheels, etc.
>
> Jon

Thank you Jon. I am amazed. I will play with it and try to understand it
all.

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"Janet" <par### [at] attnet> wrote:

> Thank you Jon. I am amazed. I will play with it and try to understand it
> all.

If you (or anyone else) have any questions, just ask here (or in p.b.i) for
the next week or two, or send me an email.  Any comments on the code or its
output will help me tweak and tune to make it better.

As you may have noticed, I have this in version control on my system so I
can break it, and still get working copies back, etc.  It's already gone
through a bunch of revisions, so a few more won't hurt it. 8^)

I should say that all those decagons are due to a whim I had about 20 years
ago when I first read about Penrose Tiling.  Martin Gardner wrote that
there are 62 distinct decagons, only one of which can be filled.  I always
thought it might be interesting to have a complete set.  But if you count
them, you will see that there are only 56, although there are multiple
versions of some of them.

A short computer program I wrote told me that there were only 56, so I
wonder if there are 6 more that I missed, or if people have been quoting a
mistake for years and years.  I guess the way to verify it would be to
generate all 1024 decagons, and see which are reflections or rotations of
the others.  That's a bit too much for me, though, and it should be what my
little program did to get its answer of 56.

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