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Perron Number Tiling Systems
Author

Roger Bagula
URL: http://www.geocities.com/rlbagulatftn/Index.html
Revision date

2005-05-11
Description

Dragon Tile 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.mrlonline.org/mrl/2004-011-003/2004-011-003-001.pdf
http://www.math.unt.edu/~mauldin/papers/no60.pdf

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