On Disk-like Self-affine Tiles Arising from Polyominoes
Gmainer, Johannes ; Thuswaldner, Jörg M.
Methods Appl. Anal., Tome 13 (2006) no. 1, p. 351-372 / Harvested from Project Euclid
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In this paper we study a class of plane self-affine lattice tiles that are defined using polyominoes. In particular, we characterize which of these tiles are homeomorphic to a closed disk. It turns out that their topological structure depends very sensitively on their defining parameters. ¶ In order to achieve our results we use an algorithm of Scheicher and the second author which allows to determine neighbors of tiles in a systematic way as well as a criterion of Bandt and Wang, with that we can check disk-likeness of a self-affine tile by analyzing the set of its neighbors.
Publié le : 2006-12-15
Classification:  polyomino,  self-affine tile,  topological disk,  28A80,  05B50,  54F65 
@article{1202219968,
     author = {Gmainer, Johannes and Thuswaldner, J\"org M.},
     title = {On Disk-like Self-affine Tiles Arising from Polyominoes},
     journal = {Methods Appl. Anal.},
     volume = {13},
     number = {1},
     year = {2006},
     pages = { 351-372},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1202219968}
}

Gmainer, Johannes; Thuswaldner, Jörg M. On Disk-like Self-affine Tiles Arising from Polyominoes. Methods Appl. Anal., Tome 13 (2006) no. 1, pp.  351-372. http://gdmltest.u-ga.fr/item/1202219968/