1. Using Lateral Capillary Forces to Compute by Self-assembly Paul W. K. Rothemund PNAS, Feb. 1, 2000, vol. 97, no. 3, pp.984- 989 Summarized by Lee, In-Hee

2. © 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ Self-assembly and Computation Linked by the study of the mathematical tiling Computation by tiling is univeral.  Tiles and matching rules can be designed so that the tilings formed correspond to a simulation of computing devices(e.g. Turing machine, cellular automaton) Capillary force self-assembly may allow microfabrication of computational tilings.

3. © 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/Simulation Choose random structure(a tile or tiles) move one tile with in a random direction If collision with structure which have edges satisfying matching rules, a bond is created.

4. © 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ Simulation Results A: Unit tiles(C tiles) B: Ideal Structure C: Simulation Result  Error rate: 0.2% D: Binding Schematic

5. © 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ Simulation Results A: Unit tiles(P tiles) B: Ideal Structure C: Simulation Result  Error rate: 2.2% D: Binding Schematic  S: single bond  D: double bonds  *: mismatch  Inc: incompletable

6. © 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ Simulation Results A: Unit tiles(XOR tiles) B: Ideal Structure C: Simulation Result  Error rate: 14.7% D: Binding Schematic  S: single bond  D: double bonds  *: mismatch  Inc: incompletable

7. © 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ Physical Implementation(Wetting Codes) HydrophobicHydrophilic Total bonds L bondsF bonds

8. © 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ Physical Implementation(Wetting Codes) F L

9. © 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ Physical Self-assembly(C tiles)

10. © 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ Physical Implementation(P tiles)

11. © 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ Physical Implementation(XOR tiles)

12. © 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/Conclusions Wetting codes can be used to enforce matching rules for a simple computation Binding of tiles is reasonably cooperative Features of a tile set impact the frequency of defect formation  Compare C, P, XOR tiles