CLASSIFICATION OF SELF-AFFINE LATTICE TILINGS

Authors
BANDT C GELBRITCH G
Citation
C. Bandt et G. Gelbritch, CLASSIFICATION OF SELF-AFFINE LATTICE TILINGS, Journal of the London Mathematical Society, 50, 1994, pp. 581-593
Citations number
21
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Journal of the London Mathematical Society → ACNP
ISSN journal
00246107
Volume
50
Year of publication
1994
Part
3
Pages
581 - 593
Database
ISI
SICI code
0024-6107(1994)50:<581:COSLT>2.0.ZU;2-C
Abstract
We consider tilings of the plane by a lattice of translates of some co mpact set A such that the union of k suitably chosen tiles is similar to A. Affine and metric equivalence of such 'k-reptiles' are defined. We show that for every k greater than or equal to 2 there is a finite number of equivalence classes for which A is homeomorphic to a disk. T here are three affine types of tiles with two pieces, and seven types with k = 3.