Self-Assembly of Patterns in the abstract Tile Assembly Model
<|reference_start|>Self-Assembly of Patterns in the abstract Tile Assembly Model: In the abstract Tile Assembly Model, self-assembling systems consisting of tiles of different colors can form structures on which colored patterns are ``painted.'' We explore the complexity, in terms of the numbers of unique tile types required, of assembling various patterns. We first demonstrate how to efficiently self-assemble a set of simple patterns, then show tight bounds on the tile type complexity of self-assembling 2-colored patterns on the surfaces of square assemblies. Finally, we demonstrate an exponential gap in tile type complexity of self-assembling an infinite series of patterns between systems restricted to one plane versus those allowed two planes.<|reference_end|>
@article{drake2024self-assembly,
    title={Self-Assembly of Patterns in the abstract Tile Assembly Model},
    author={Phillip Drake and Matthew J. Patitz and Scott M. Summers and Tyler
  Tracy},
    journal={arXiv preprint arXiv:2402.16284},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.16284},
    primaryClass={cs.ET cs.CC cs.CG}
}