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2012
Springer

Triangular and Hexagonal Tile Self-assembly Systems

10 years 7 months ago
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.
Lila Kari, Shinnosuke Seki, Zhi Xu
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Added 20 Apr 2012
Updated 20 Apr 2012
Type Journal
Year 2012
Where BIRTHDAY
Authors Lila Kari, Shinnosuke Seki, Zhi Xu
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