The program-size complexity of self-assembled squares (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Combinatorial optimization problems in self-assembly
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Concrete Mathematics: A Foundation for Computer Science
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On the Decidability of Self-Assembly of Infinite Ribbons
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Algorithmic self-assembly of dna
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Theory and experiments in algorithmic self-assembly
Theory and experiments in algorithmic self-assembly
Complexities for generalized models of self-assembly
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Reducing tile complexity for self-assembly through temperature programming
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Complexity of Self-Assembled Shapes
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Randomized Self-assembly for Approximate Shapes
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MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Approximate self-assembly of the Sierpinski triangle
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
Self-assembly of infinite structures: A survey
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COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
An introduction to tile-based self-assembly
UCNC'12 Proceedings of the 11th international conference on Unconventional Computation and Natural Computation
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In this paper, we search for theoretical limitations of the Tile Assembly Model (TAM), along with techniques to work around such limitations. Specifically, we investigate the self-assembly of fractal shapes in the TAM. We prove that no self-similar fractal weakly self-assembles at temperature 1 in a locally deterministic tile assembly system, and that certain kinds of discrete self-similar fractals do not strictly self-assemble at any temperature. Additionally, we extend the fiber construction of Lathrop et al. (2009) to show that any discrete self-similar fractal belonging to a particular class of "nice" discrete self-similar fractals has a fibered version that strictly self-assembles in the TAM.