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Perron Number Tiling Systems

Roger Bagula
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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.

*Mathematics > Geometry > Plane Geometry
*Mathematics > Geometry > Tiling

Tile, Tiling, fractiles, Kenyon, Perron numbers, Pisot numbers, Substitutions, von, Koch islands, fractal subsets

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