Perron Number Tiling Systems -- from Mathematica Information Center

Roger Bagula · science forum addict Joined: 03 May 2005 Posts: 59

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

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.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]

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