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Journal of the London Mathematical Society 1994 50(3):581-593; doi:10.1112/jlms/50.3.581
© 1994 by London Mathematical Society
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© The London Mathematical Society

Classification of Self-Affine Lattice Tilings

Christoph Bandt and Götz Gelbrich

Fachrichtungen Mathematik u. Informatik, Ernst-Moritz-Arndt-Universität Jahnstrasse 15a, 17489 Greifswald, Germany

Received 20 April 1992. Revision received 9 November 1992.

We consider tilings of the plane by a lattice of translates of some compact 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 ≥ 2 there is a finite number of equivalence classes for which A is homeomorphic to a disk. There are three affine types of tiles with two pieces, and seven types with k = 3.


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