The self-assembly of paths and squares at temperature 1

@article{Meunier2013TheSO,
  title={The self-assembly of paths and squares at temperature 1},
  author={Pierre-Etienne Meunier},
  journal={CoRR},
  year={2013},
  volume={abs/1312.1299}
}
We prove that the number of tile types required to build squares of size n× n, in Winfree’s abstract Tile Assembly Model, when restricted to using only non-cooperative tile bindings, is at least 2n− 1, which is also the best known upper bound. Non-cooperative self-assembly, also known as “temperature 1”, is where tiles bind to each other if they match on one or more sides, whereas in cooperative binding, some tiles can bind only if they match on multiple sides. Our proof introduces a new… CONTINUE READING

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