Hierarchical Growth Is Necessary and (Sometimes) Sufficient to Self-assemble Discrete Self-similar Fractals View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2018-09-07

AUTHORS

Jacob Hendricks , Joseph Opseth , Matthew J. Patitz , Scott M. Summers

ABSTRACT

In this paper, we prove that in the abstract Tile Assembly Model (aTAM), an accretion-based model which only allows for a single tile to attach to a growing assembly at each step, there are no tile assembly systems capable of self-assembling the discrete self-similar fractals known as the “H” and “U” fractals. We then show that in a related model which allows for hierarchical self-assembly, the 2-Handed Assembly Model (2HAM), there does exist a tile assembly systems which self-assembles the “U” fractal and conjecture that the same holds for the “H” fractal. This is the first example of discrete self similar fractals which self-assemble in the 2HAM but not in the aTAM, providing a direct comparison of the models and greater understanding of the power of hierarchical assembly. More... »

PAGES

87-104

References to SciGraph publications

  • 2014. Scaled Tree Fractals Do not Strictly Self-assemble in UNCONVENTIONAL COMPUTATION AND NATURAL COMPUTATION
  • 2016. Hierarchical Self-Assembly of Fractals with Signal-Passing Tiles in DNA COMPUTING AND MOLECULAR PROGRAMMING
  • 2012-10. Approximate Self-Assembly of the Sierpinski Triangle in THEORY OF COMPUTING SYSTEMS
  • 2013-10. Self-Assembling Rulers for Approximating Generalized Sierpinski Carpets in ALGORITHMICA
  • 2010-03. Self-assembly of discrete self-similar fractals in NATURAL COMPUTING
  • 2017. Self-Assembly of 4-Sided Fractals in the Two-Handed Tile Assembly Model in UNCONVENTIONAL COMPUTATION AND NATURAL COMPUTATION
  • 2009. Self-assembly of the Discrete Sierpinski Carpet and Related Fractals in DNA COMPUTING AND MOLECULAR PROGRAMMING
  • 2009. Polyomino-Safe DNA Self-assembly via Block Replacement in DNA COMPUTING
  • 2016. Resiliency to Multiple Nucleation in Temperature-1 Self-Assembly in DNA COMPUTING AND MOLECULAR PROGRAMMING
  • 2016-09. Strict Self-Assembly of Fractals Using Multiple Hands in ALGORITHMICA
  • Book

    TITLE

    DNA Computing and Molecular Programming

    ISBN

    978-3-030-00029-5
    978-3-030-00030-1

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-030-00030-1_6

    DOI

    http://dx.doi.org/10.1007/978-3-030-00030-1_6

    DIMENSIONS

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