Triangular and Hexagonal Tile Self-assembly Systems

Abstract. 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.

• Type: Journal
• Year: 2012
• Where: BIRTHDAY
• Authors: Lila Kari, Shinnosuke Seki, Zhi Xu
• Keywords: Applied Computing, BIRTHDAY 2012, Hexagonal Tile, Hexagonal Tiles, Square Tile