Limitations of Self-Assembly at Temperature 1

@article{Doty2011LimitationsOS,
  title={Limitations of Self-Assembly at Temperature 1},
  author={David Doty and Matthew J. Patitz and Scott M. Summers},
  journal={Theor. Comput. Sci.},
  year={2011},
  volume={412},
  pages={145-158}
}
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

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