Characterization Of Planar Pseudo-Self-Similar Tilings

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Characterization Of Planar Pseudo-Self-Similar Tilings (2001) (Make Corrections) (1 citation)
Natalie Priebe, Boris SolomyakDiscrete & Computational Geometry

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Abstract: . A pseudo-self-similar tiling is a hierarchical tiling of Euclidean space which obeys a non-exact substitution rule: the substitution for a tile is not geometrically similar to itself. An example is the Penrose tiling drawn with rhombi. We prove that a non-periodic repetitive tiling of the plane is pseudoself -similar if and only if it has a nite number of derived Vorono tilings up to similarity. To establish this characterization, we settle (in the planar case) a conjecture of E. A.... (Update)

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BibTeX entry: (Update)

N. Priebe and B. Solomyak, Characterization of planar pseudo-self-similar tilings. Discrete Comput. Geom. 26 (2001), 289--306. http://citeseer.ist.psu.edu/priebe01characterization.html More

@article{ priebe01characterization,
    author = "N. Priebe and B. Solomyak",
    title = "Characterization of Planar Pseudo-Self-Similar Tilings",
    journal = "Discrete & Computational Geometry",
    volume = "26",
    number = "3",
    pages = "289-306",
    year = "2001",
    url = "citeseer.ist.psu.edu/priebe01characterization.html" }

Citations (may not include all citations):
91 Tilings and Patterns (context) - Gr, Shephard - 1986
26 Space tilings and substitutions - Radin - 1995
21 A characterization of substitutive sequences using return wo.. (context) - Durand - 1998
19 Recurrent sets (context) - Dekking - 1982
16 Geometric aspects of tilings and equivalence concepts (context) - Baake, Schlottmann - 1995
13 The construction of self-similar tilings (context) - Kenyon - 1996
12 Non-periodicity implies unique composition for self-similar .. - Solomyak - 1998
11 Quasiperiodic tilings with tenfold symmetry and equivalence .. (context) - Baake, Schlottmann et al. - 1991
10 On Rauzy fractal (context) - Ito, Kimura - 1991
9 The dynamical properties of Penrose tilings (context) - Robinson - 1997
6 Isomorphism of hierarchical structures - Radin, Sadun
6 Descendants of primitive substitutions - Holton, Zamboni - 1999
5 Generating special Markov partitions for hyperbolic toral au.. (context) - Bedford - 1986
3 Factor maps between tiling dynamical systems - Petersen - 1999
2 Towards a characterization of self-similar tilings in terms .. (context) - Priebe - 2000

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