Triangular tile self-assembly systems

Authors:
Lila Kari;Shinnosuke Seki;Zhi Xu
Affiliations:
The University of Western Ontario, Department of Computer Science, London, Ontario, Canada;The University of Western Ontario, Department of Computer Science, London, Ontario, Canada;The University of Western Ontario, Department of Computer Science, London, Ontario, Canada
Venue:
DNA'10 Proceedings of the 16th international conference on DNA computing and molecular programming
Year:
2010

Citing 3
Cited 0

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Running time and program size for self-assembled squares

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Reducing tile complexity for self-assembly through temperature programming

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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. Contrary to intuition, we show that triangular tile assembly systems and square tile assembly systems are not comparable in general. More precisely, there exists a square tile assembly system S such that no triangular tile assembly system that is a division of S produces the same final supertile. There also exists a deterministic triangular tile assembly system T such that no square tile assembly system produces the same final supertiles while preserving border glues. We discuss the assembly of triangles by triangular tiles and show triangular systems with Θ(log N/log logN) tiles that can self-assemble into a triangular super-tile of size Θ(N2). Lastly, we show that triangular tile assembly systems, either right-triangular or equilateral, are Turing universal.