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MathGroup Archive 2005

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Perron Number Tiling Systems -- from Mathematica Information Center

  • To: mathgroup at
  • Subject: [mg57107] Perron Number Tiling Systems -- from Mathematica Information Center
  • From: Roger Bagula <rlbagulatftn at>
  • Date: Mon, 16 May 2005 01:29:49 -0400 (EDT)
  • Sender: owner-wri-mathgroup at
Title 	Downloads 	
Perron Number Tiling Systems
Roger Bagula
	Revision date 		
   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.
* 	Mathematics > Geometry > Plane Geometry
* 	Mathematics > Geometry > Tiling
Tile, Tiling, fractiles, Kenyon, Perron numbers, Pisot numbers, 
Substitutions, von, Koch islands, fractal subsets

	Kenyon_tile_article2.nb (41.4 KB) - Mathematica Notebook [for 
Mathematica 5.0]

Roger L. Bagula       email: rlbagula at  or 
rlbagulatftn at
11759 Waterhill Road,
Lakeside, Ca. 92040    telephone: 619-561-0814

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