An aperiodic set of Wang cubes

  • Karel CulikII
  • Jarkko Kari
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1046)


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.


Cellular Automaton Sequential Machine Balance Representation Periodic Tiling Wang Tile 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Karel CulikII
    • 1
  • Jarkko Kari
    • 2
  1. 1.Department of Computer ScienceUniversity of South CarolinaColumbia
  2. 2.Iterated Systems, Inc.Atlanta

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