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Self-Assembly with General Shaped Tiles

  • Reference work entry
  • First Online:
Encyclopedia of Algorithms

  • 124 Accesses

Years and Authors of Summarized Original Work

  • 2012; Fu, Patitz, Schweller, Sheline

  • 2014; Demaine, Demaine, Fekete, Patitz, Schweller, Winslow, Woods

Problem Definition

Self-assembly is an asynchronous, decentralized process in which particles aggregate to form superstructures according to localized interactions. The most well-studied models of these particle systems, e.g., the abstract Tile Assembly Model of Winfree [11], utilize square-shaped particles arranged on a lattice by attaching edgewise. Particles attach to form larger assemblies, and a pair of assemblies or tiles can attach if they can translate to a nonoverlapping configuration with a set of k coincident edges, where k ≥ τ, a parameter of the system called the temperature.

In seeded assembly, individual particles attach to a growing seed assembly. This assembly may begin as a single-tile or a multi-tile assembly. In unseeded assembly (also called hierarchical [3], two-handed [2], or polyomino [7] assembly), there is no...

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Recommended Reading

  1. Adleman L, Cheng Q, Goel A, Huang MD (2001) Running time and program size for self-assembled squares. In: Proceedings of symposium on theory of computing (STOC), Heraklion

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  7. Luhrs C (2010) Polyomino-safe DNA self-assembly via block replacement. Nat Comput 9(1):97–109

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Author information

Authors and Affiliations

  1. Department of Computer Science, Tufts University, Medford, MA, USA

    Andrew Winslow

Authors
  1. Andrew Winslow
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Correspondence to Andrew Winslow .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Winslow, A. (2016). Self-Assembly with General Shaped Tiles. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_673

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