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MathGroup Archive 2005

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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


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