Strict self-assembly of discrete self-similar fractals

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Strict Self-Assembly of Discrete Self-Similar Fractals

Discrete self-similar fractals are infinite aperiodic shapes that have received much interest in the domain of tile self-assembly. For instance, in [1] it was shown that the infinite Sierpinski triangle cannot strictly self-assemble in the aTAM, but a fibered approximation can be. In [2] it was shown that additional DSSFs cannot strictly self-assemble in the aTAM, but their fibered approximations can. Just a few of the additional results related to DSSFs, including more impossibility results, other approximations, and strict self-assembly in other models can be found in [3][4][5][6][7].


References

  1. ↑ James I. Lathrop, Jack H. Lutz, Scott M. Summers - Strict Self-Assembly of Discrete Sierpinski Triangles
    Theoretical Computer Science 410:384--405,2009
    Bibtex
    Author : James I. Lathrop, Jack H. Lutz, Scott M. Summers
    Title : Strict Self-Assembly of Discrete Sierpinski Triangles
    In : Theoretical Computer Science -
    Address :
    Date : 2009
  2. ↑ Matthew J. Patitz, Scott M. Summers - Self-assembly of discrete self-similar fractals
    Natural Computing 1:135--172,2010
    Bibtex
    Author : Matthew J. Patitz, Scott M. Summers
    Title : Self-assembly of discrete self-similar fractals
    In : Natural Computing -
    Address :
    Date : 2010
  3. ↑ Jack H. Lutz, Brad Shutters - Approximate self-assembly of the sierpinski triangle
    Theory Comput. Syst. 51:372--400
    Bibtex
    Author : Jack H. Lutz, Brad Shutters
    Title : Approximate self-assembly of the sierpinski triangle
    In : Theory Comput. Syst. -
    Address :
    Date :
  4. ↑ Steven M. Kautz, Brad Shutters - Self-assembling rulers for approximating generalized sierpinski carpets
    Lecture Notes in Computer Science 6842:284--296,2011
    Bibtex
    Author : Steven M. Kautz, Brad Shutters
    Title : Self-assembling rulers for approximating generalized sierpinski carpets
    In : Lecture Notes in Computer Science -
    Address :
    Date : 2011
  5. ↑ Hendricks, Jacob, Olsen, Meagan, Patitz, Matthew, Rogers, Trent, Thomas, Hadley - Hierarchical Self-Assembly of Fractals with Signal-Passing Tiles
    Natural Computing 17, 11 2017
    Bibtex
    Author : Hendricks, Jacob, Olsen, Meagan, Patitz, Matthew, Rogers, Trent, Thomas, Hadley
    Title : Hierarchical Self-Assembly of Fractals with Signal-Passing Tiles
    In : Natural Computing -
    Address :
    Date : 11 2017
  6. ↑ Chalk, Cameron T, Fernandez, Dominic A, Huerta, Alejandro, Maldonado, Mario A, Schweller, Robert T, Sweet, Leslie - Strict self-assembly of fractals using multiple hands
    Algorithmica 76(1):195--224,2016
    Bibtex
    Author : Chalk, Cameron T, Fernandez, Dominic A, Huerta, Alejandro, Maldonado, Mario A, Schweller, Robert T, Sweet, Leslie
    Title : Strict self-assembly of fractals using multiple hands
    In : Algorithmica -
    Address :
    Date : 2016
  7. ↑ Hader, Daniel, Patitz, Matthew J, Summers, Scott M - Fractal dimension of assemblies in the abstract tile assembly model
    Natural Computing pp. 1--16,2023
    Bibtex
    Author : Hader, Daniel, Patitz, Matthew J, Summers, Scott M
    Title : Fractal dimension of assemblies in the abstract tile assembly model
    In : Natural Computing -
    Address :
    Date : 2023
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