(A)/Periodic convex tilings (or near-tilings) of the plane or (3 space)
- To: mathgroup at smc.vnet.net
- Subject: [mg20907] (A)/Periodic convex tilings (or near-tilings) of the plane or (3 space)
- From: "Kai G. Gauer" <gauer at sk.sympatico.ca>
- Date: Sun, 21 Nov 1999 15:12:50 -0500 (EST)
- References: <7v3bvj$5to@smc.vnet.net> <7v6700$afl@smc.vnet.net> <7vdq5i$iii@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
I am researching the topic of either periodic or non-periodic (usually) convex tilings using congruent pieces of one or two or three shape pieces (or more, but, usually where pieces should be allowed to be used infinitely often, only sometimes necessary, or when a requirement of an additional piece set will be necessary) to do so in hopes to cover most and/or all of a plane (or a three space) that extends infinitely out in all directions. A lot of the introductory level material was apparently first brought to widespread attention in the latter portion of the 20 th century in the math columns of Scientific American magazine. I am currently studying Applied Abstract Algebra (Math 424 at U of Regina and had come across the topic of tilings in a 1998 Springer book with the title as above by Lidl & Pilz) and I am need of a research topic that relates to symmetry groups. Unfortunately, my knowledge in the vastness of symmetry groups is weak (I'd hope to improve my knowledge of them later by taking the intro level Modern Algebra class later, but, I had to take the class now, since it wouldn't be offered again in the near future) and I would hope to not be referred to post PhD level papers in which I may or may not be able to fully understand. What I am looking for however, is any source codes for Mathematica or for C (or another MODERN, popular programming language which has good graphics output capabilities) that enable a user to easily give plot sketchings and investigations to basic grouping structures that tend to give some sort of nice tiling property that is investigatable using a computer. I know of the basic 17 tilings of the plane, but I would like to come up with a slightly more nontrivial example that I could use as an example in a presentation. I would also prefer source code as opposed to a picture of somebody's fancy wallpaper pulled off their homepage. Mathematica packages that allow for undergarduate level experimentation would actually be just fine, but I would consider looking at almost anything relating to the topic. Thanks everyone for the help.