Tile Self-Assembly Simulations
Cannon, Sarah M.
- Tile self-assembly models describe both mathematically and computationally the ways in which small square tiles can attach to each other to form larger assemblies. Two such models are the abstract tile assembly model, in which all tiles attach to one main assembly containing a "seed tile," and the two-handed assembly model, in which there is no seed tile and tiles can attach at any time. This thesis ... read morepresents results showing that the seed-based assembly process of any tile set that assembles under the conditions of the abstract tile assembly model can be simulated by the assembly process of another tile set in the two-handed model. The simulation is only a constant scale factor larger than the original system and actually requires a lower temperature, a characteristic that describes how easily tiles attach to each other. This result is surprising and interesting, and provides insight into the relative fundamental computational power of both models. This work has direct applications in DNA computing, where biologists are using these models to self-assemble pieces of DNA (represented abstractly by tiles) into structures at the nanoscale level.read less