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Electronic Colloquium on Computational Complexity

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Reports tagged with self-assembly:
TR08-035 | 18th February 2008
James I. Lathrop, Jack H. Lutz, Scott M. Summers

Strict Self-Assembly of Discrete Sierpinski Triangles

Winfree (1998) showed that discrete Sierpinski triangles can self-assemble in the Tile Assembly Model. A striking molecular realization of this self-assembly, using DNA tiles a few nanometers long and verifying the results by atomic-force microscopy, was achieved by Rothemund, Papadakis, and Winfree (2004). Precisely speaking, the above self-assemblies tile completely ... more >>>

TR10-032 | 19th January 2010
Jack H. Lutz, Brad Shutters

Approximate Self-Assembly of the Sierpinski Triangle

The Tile Assembly Model is a Turing universal model that Winfree introduced in order to study the nanoscale self-assembly of complex (typically aperiodic) DNA crystals. Winfree exhibited a self-assembly that tiles the first quadrant of the Cartesian plane with specially labeled tiles appearing at exactly the positions of points in ... more >>>

TR10-131 | 9th July 2010
Nathaniel Bryans, Ehsan Chiniforooshan, David Doty, Lila Kari, Shinnosuke Seki

The Power of Nondeterminism in Self-Assembly

We investigate the role of nondeterminism in Winfree's abstract Tile Assembly Model (aTAM), which was conceived to model artificial molecular self-assembling systems constructed from DNA. Designing tile systems that assemble shapes, due to the algorithmic richness of the aTAM, is a form of sophisticated "molecular programming". Of particular practical importance ... more >>>

TR10-195 | 13th November 2010
Ho-Lin Chen, David Doty, Shinnosuke Seki, David Soloveichik

Parallelism, Program Size, Time, and Temperature in Self-Assembly

Revisions: 1

We settle a number of questions in variants of Winfree's abstract Tile Assembly Model (aTAM), a model of molecular algorithmic self-assembly. In the "hierarchical" aTAM, two assemblies, both consisting of multiple tiles, are allowed to aggregate together, whereas in the "seeded" aTAM, tiles attach one at a time to a ... more >>>

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