Triangular and Hexagonal Tile Self-assembly Systems

  • Lila Kari
  • Shinnosuke Seki
  • Zhi Xu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7160)


We discuss theoretical aspects of the self-assembly of triangular tiles, in particular, right triangular tiles and equilateral triangular tiles, and the self-assembly of hexagonal tiles. We show that triangular tile assembly systems and square tile assembly systems cannot be simulated by each other in a non-trivial way. More precisely, there exists a deterministic square (hexagonal) tile assembly system S such that no deterministic triangular tile assembly system that is a division of S produces an equivalent supertile (of the same shape and same border glues). There also exists a deterministic triangular tile assembly system T such that no deterministic square (hexagonal) tile assembly system produces the same final supertile while preserving border glues.


Equilateral Triangle Tile System Adjacent Edge Tile Type Grid Graph 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Lila Kari
    • 1
  • Shinnosuke Seki
    • 1
  • Zhi Xu
    • 1
  1. 1.Department of Computer ScienceUniversity of Western OntarioLondonCanada

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