Perron Number Tiling Systems -- from Mathematica Information Center

*To*: mathgroup at smc.vnet.net*Subject*: [mg57107] Perron Number Tiling Systems -- from Mathematica Information Center*From*: Roger Bagula <rlbagulatftn at yahoo.com>*Date*: Mon, 16 May 2005 01:29:49 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

http://library.wolfram.com/infocenter/MathSource/5642/ Title Downloads Perron Number Tiling Systems Author Roger Bagula URL: http://www.geocities.com/rlbagulatftn/Index.html Revision date 2005-05-11 Description Four Programs for calculating Dr. Richard Kenyon's method for plane tilings from Perron numbers by substitutions. The construction of self-similar tilings , Geom. and Func. Analysis 6,(1996):417-488. Thurston showed that the expansion constant of a self-similar tiling of the plane must be a complex Perron number (algebraic integer strictly larger in modulus than its Galois conjugates except for its complex conjugate). Here we prove that, conversely, for every complex Perron number there exists a self-similar tiling. We also classify the expansion constants for self-similar tilings which have a rotational symmetry of order n. Subjects * Mathematics > Geometry > Plane Geometry * Mathematics > Geometry > Tiling Keywords Tile, Tiling, fractiles, Kenyon, Perron numbers, Pisot numbers, Substitutions, von, Koch islands, fractal subsets URL http://www.math.ubc.ca/~kenyon/papers/index.html http://www.mrlonline.org/mrl/2004-011-003/2004-011-003-001.pdf http://www.math.unt.edu/~mauldin/papers/no60.pdf Downloads Kenyon_tile_article2.nb (41.4 KB) - Mathematica Notebook [for Mathematica 5.0] -- Roger L. Bagula email: rlbagula at sbcglobal.net or rlbagulatftn at yahoo.com 11759 Waterhill Road, Lakeside, Ca. 92040 telephone: 619-561-0814