While I'm not sure exactly how "tiling" should be defined, it must surely involve a finite number of tile types modulo isometry. As you remark, there are an infinite number of sizes of triangle involved in your dissection; so I doubt very much whether it would qualify. Perhaps you might explain in more detail about what exactly you want to know about it? Fred Lunnon On 9/5/10, Robert Munafo <mrob27@gmail.com> wrote:
I have a recursive substitution-rule to tile the plane, which seems simple enough but nevertheless does not seem to be discussed in the normal places (like the tilings encyclopedia, http://tilings.math.uni-bielefeld.de/substitution_rules). Google searches haven't helped either (example: an Image search with the keywords: tiling regular pentagon triangle).
The rules for my tiling can be seen here:
http://mrob.com/pub/math/images/penta-tiling.jpg
I consider this a "simple" and "obvious" tiling because there are only two rules, and each rule tries to maximize the size of the pentagon(s) on the right-hand side. However, it is "non-simple" in the sense that, with repeated applications of the substitution rules, increasingly many different sizes of triangles and pentagons are produced.
- Robert
-- Robert Munafo -- mrob.com _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun