JUCS - Journal of Universal Computer Science 1(10): 675-686, doi: 10.3217/jucs-001-10-0675
An Aperiodic Set of Wang Cubes
expand article infoKarel Culik Ii.‡, Jarkko Kari§
‡ Department of Computer Science, University of South Carolina, Columbia, SC, United States of America§ Iterated Systems, Inc., Atlanta, GA, United States of America

Corresponding author: Karel Ii.

© Karel Ii., Jarkko Kari.
This article is freely available under the J.UCS Open Content License.
Citation: Ii. KC, Kari J (1995) An Aperiodic Set of Wang Cubes. JUCS - Journal of Universal Computer Science 1(10): 675-686. https://doi.org/10.3217/jucs-001-10-0675
Open Access
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
discrete mathematics, automata theory, aperiodic tilings, Wang tiles, Wang cubes, sequential machines