Triangular and hexagonal tile self-assembly systems

Authors:
Lila Kari;Shinnosuke Seki;Zhi Xu
Affiliations:
Department of Computer Science, University of Western Ontario, London, Ontario, Canada;Department of Computer Science, University of Western Ontario, London, Ontario, Canada;Department of Computer Science, University of Western Ontario, London, Ontario, Canada
Venue:
WTCS'12 Proceedings of the 2012 international conference on Theoretical Computer Science: computation, physics and beyond
Year:
2012

Citing 3
Cited 0

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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.