Limitations of Self-Assembly at Temperature 1

  title={Limitations of Self-Assembly at Temperature 1},
  author={David Doty and Matthew J. Patitz and Scott M. Summers},
  journal={Theor. Comput. Sci.},
We prove that if a set X ⊆ Z weakly self-assembles at temperature 1 in a deterministic (Winfree) tile assembly system satisfying a natural condition known as pumpability, then X is a finite union of semi-doubly periodic sets. This shows that only the most simple of infinite shapes and patterns can be constructed using pumpable temperature 1 tile assembly systems, and gives evidence for the thesis that temperature 2 or higher is required to carry out general-purpose computation in a tile… CONTINUE READING


Publications citing this paper.


Publications referenced by this paper.
Showing 1-10 of 17 references

Schweller , Temperature 1 self - assembly : Deterministic assembly in 3 D and probabilistic assembly in 2 D , Tech

  • Matthew Cook, Yunhui Fu, T. Robert
  • 2009

Summers , Strict self - assembly of discrete Sierpinski triangles

  • James I. Lathrop, Jack H. Lutz, M. Scott
  • Theoretical Computer Science
  • 2009

K . Rothemund , Nick Papadakis , and Erik Winfree , Algorithmic self - assembly of DNA Sierpinski triangles

  • W. Paul
  • PLoS Biology
  • 2004

Adleman , Jarkko Kari , Lila Kari , and Dustin Reishus , On the decidability of self - assembly of infinite ribbons

  • M Leonard
  • 2002

Rothemund, Theory and experiments in algorithmic self-assembly

  • W K.Paul
  • Ph.D. thesis,
  • 2001
2 Excerpts

Similar Papers

Loading similar papers…