The program-size complexity of self-assembled squares (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Running time and program size for self-assembled squares
STOC '01 Proceedings of the thirty-third 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
Algorithmic self-assembly of dna
Algorithmic self-assembly of dna
Self-correcting self-assembly: growth models and the hammersley process
DNA'05 Proceedings of the 11th international conference on DNA Computing
DNA'04 Proceedings of the 10th international conference on DNA computing
Complexity of self-assembled shapes
DNA'04 Proceedings of the 10th international conference on DNA computing
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We study the times to grow structures within the tile self-assembly model proposed by Winfree, and the possible shapes that can be achieved during the self-assembly. Our earlier work was confined to the growth of rectangular structures, in which the border tiles are prefabricated. By varying the relative rates between the border-tile and rule-tile attachment, one can engineer interesting new shapes, which have been observed in the laboratory. We show that the results from an extension of our earlier stochastic models agree remarkably closely with experimental results. This is an important further demonstration of the validity and usefulness of our stochastic models, which have also been used successfully in studies of error correction in DNA self assembly.