Self-assembly of Discrete Self-similar Fractals

(Extended Abstract)
  • Matthew J. Patitz
  • Scott M. Summers
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5347)


In this paper, we search for absolute limitations of the Tile Assembly Model (TAM), along with techniques to work around such limitations. Specifically, we investigate the self-assembly of fractal shapes in the TAM. We prove that no self-similar fractal fully weakly self-assembles at temperature 1, and that certain kinds of self-similar fractals do not strictly self-assemble at any temperature. Additionally, we extend the fiber construction from Lathrop et. al. (2007) to show that any self-similar fractal belonging to a particular class of “nice” self-similar fractals has a fibered version that strictly self-assembles in the TAM.


Assembly Sequence Impossibility Result Tile Type Grid Graph Fractal Shape 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Matthew J. Patitz
    • 1
  • Scott M. Summers
    • 1
  1. 1.Department of Computer ScienceIowa State UniversityAmesUSA

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