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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

569.0. "Penrose Tiling" by CACHE::MARSHALL (beware the fractal dragon) Wed Aug 20 1986 21:25

          Does anyone here know anything about Penrose Tiling?
    
    All I know is that its a way to tile a plane using irregular polygons.
    The pictures I've seen of some of these are pretty striking. Is
    there any theory to this? It can't be just trial and error.
    
    I fear I don't even know what questions to ask, just want to get
    a discussion going about something other than number theory.
    
    				sm
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569.1Try back issues of Sci AmerMODEL::YARBROUGHFri Aug 22 1986 13:0816
    There was an article on this topic in Scientific American several
    years ago, perhaps in Martin Gardner's column. As I recall there
    are two polygons involved: one, a diamond-shaped parallelogram;
    the other a concave quadrilateral whose concavity fits the obtuse
    angle of the diamond. Something like ...
	
        .
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     .     .     .
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    (Can we put ReGIS sequences in these messages?)

569.2arbitrary polygonsCACHE::MARSHALLbeware the fractal dragonFri Aug 22 1986 16:3715
    re .1:
    
    That is one tiling, but I thought there were a whole slew of tilings.
    There was an interview with Penrose in OMNI a few months back and
    they included pictures of some of the tilings. Very pretty.
    
    As for ReGIS, you *can* include them, but it'll be so much gibberish
    until the note is EXTRACT'ed and TYPE'd (on a regis terminal of
    course). Notes and Mail now suppress all <ESC> type characters.
    
    I guess one question would be: 
    
    Given "n" polygons, how do you determine if they will tile a plane?
    
    sm
569.3CLT::GILBERTeager like a childFri Aug 22 1986 20:536
I remember reading an article in Scientific American about a decade ago
about tiling the plane with copies (possibly rotated) of a single tile.
The interesting thing was that a few 'new' tilings were discovered (or
rediscovered), and it was proved that all such tilings were now identified.

I found the article fascinating.
569.4Penrose Tiling in Quasi-Crystal22537::EDDIELEUNGTue Aug 26 1986 06:007
    A recent issue of Scientific American ( July or Aug 1986 ) has an
    article about Penrose tiling in Quasi-crystals, a new kind of material
    just discovered.
    
    
    
    Eddie.
569.5Tiles for tots?VMSDEV::HALLYBThe Smart Money was on GoliathSun Sep 23 1990 20:449
    In Martin Gardner's latest book (which is mostly a compilation of his
    columns) he has a computer-generated color print of a fairly large
    Penrose tiling.  Gardner comments that Penrose had gotten patents on
    use of tiles for toys and games.
    
    Which begs the Christmas-is-coming question:  Has anybody ever seen
    commercial "Penrose Tiles" for sale?
    
      John
569.6Haven't seen them yetALLVAX::JROTHIt's a bush recording...Sun Sep 23 1990 22:1113
   Not yet - I plan to look for them next time I'm near an adult
   toy store.

   By the way, a beautifully illustrated coffee table book is

	M.C. Escher: Art and Science
	H.S.M. Coxeter, M. Emmer, R. Penrose, M.L. Teuber (eds)
	North Holland

   I for one want to write a program to generate some nice patterns
   but it's had to wait due to lack of time :-(

   - Jim
569.7certainly have been marketedHERON::BUCHANANcombinatorial bomb squadMon Sep 24 1990 08:1510
	I attended a lecture Penrose gave when he'd just come out with
these thingummies years ago.   At the time, he was selling little sets
which were green and blue critter shapes (fairly ugly), but on
the reverse side were pretty kite and dart shapes in red and yellow.

	I don't know if those things are still available.   "The Emperor's
New Mind" (which mentions the tiles) perhaps has a contact reference.

Regards,
Andrew.
569.8_The Emperor's New Mind_ has pictures, but no toys or mailing address or 800 numberCSSE::NEILSENI used to be PULSAR::WALLYFri Sep 28 1990 16:040