Go home now Header Background Image
Submission Procedure
share: |
Follow us
Volume 1 / Issue 10

available in:   PDF (193 kB) PS (53 kB)
Similar Docs BibTeX   Write a comment
Links into Future
DOI:   10.3217/jucs-001-10-0675


An Aperiodic Set of Wang Cubes

Karel Culik II. (Department of Computer Science, University of South Carolina, USA)

Jarkko Kari (Iterated Systems, Inc., USA)

Abstract: We introduce Wang cubes with colored faces that are a generalization of Wang tiles with colored edges. We show that there exists an aperiodic set of 21 Wang cubes, that is, a set for which there exists a tiling of the whole space with matching unit cubes but there exists no periodic tiling. We use the aperiodic set of 13 Wang tiles recently obtained by the first author using the new method developed by the second. Our method can be used to construct an aperiodic set of n-dimensional cubes for any n 3.

Keywords: Wang cubes, Wang tiles, aperiodic tilings, automata theory, discrete mathematics, sequential machines

Categories: F.1.1, G.2