Strict self-assembly of discrete Sierpinski triangles

Theoretical Computer Science

Volumn 410, Issue 4-5, 2009, Pages 384-405

  Lathrop, James I ^a   Lutz, Jack H ^a   Summers, Scott M ^a  

^a Iowa State University   (United States)

Author keywords

Fractals; Molecular computing; Self assembly; Sierpinski triangles

Indexed keywords

BUILDING MATERIALS; CALCULATIONS; DRUG PRODUCTS PLANTS; FRACTAL DIMENSION; FRACTALS; NUCLEIC ACIDS; ORGANIC ACIDS; SELF ASSEMBLY; TRIANGULATION; TURNING;

CHALLENGING PROBLEMS; DNA TILES; FORCE MICROSCOPIES; MOLECULAR COMPUTING; PAPER ADDRESSES; SIERPINSKI TRIANGLES; THIN FIBERS; TURNING OPERATIONS;

WAVEGUIDES;

EID: 58249142297     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2008.09.062     Document Type: Article

References (20)

1. L. Adleman, Towards a mathematical theory of self-assembly, Tech. Report, University of Southern California, 2000
2. Leonard M. Adleman, Qi Cheng, Ashish Goel, Ming-Deh A. Huang, David Kempe, Pablo Moisset de Espanés, Paul W.K. Rothemund, Combinatorial optimization problems in self-assembly, in: Proceedings of the Thirty-Fourth Annual ACM Symposium on Theory of Computing, 2002, pp. 23-32
3. Leonard M. Adleman, Jarkko Kari, Lila Kari, Dustin Reishus, On the decidability of self-assembly of infinite ribbons, in: Proceedings of the 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002, pp. 530-537
4. Apostol T.M. Modular Functions and Dirichlet Series in Number Theory. Graduate Texts in Mathematics vol. 41 (1997), Springer-Verlag
5. Qi Cheng, Ashish Goel, Pablo Moisset de Espanés, Optimal self-assembly of counters at temperature two, in: Proceedings of the First Conference on Foundations of Nanoscience: Self-assembled Architectures and Devices, 2004
6. Doty D., Gu X., Lutz J.H., Mayordomo E., and Moser P. Zeta-Dimension, Proceedings of the Thirtieth International Symposium on Mathematical Foundations of Computer Science (2005), Springer-Verlag 283-294
7. Euler L. Variae observationes circa series infinitas. Commentarii Academiae Scientiarum Imperialis Petropolitanae 9 (1737) 160-188
8. Falconer K. Fractal Geometry: Mathematical Foundations and Applications. second ed. (2003), Wiley
9. Graham R.L., Knuth D.E., and Patashnik O. Concrete Mathematics (1994), Addison-Wesley
10. Hardy G., and Wright E. An Introduction to the Theory of Numbers. 5th ed. (1979), Clarendon Press
11. John H. Reif, Molecular assembly and computation: From theory to experimental demonstrations, in: Proceedings of the Twenty-Ninth International Colloquium on Automata, Languages and Programming, 2002, pp. 1-21
12. Paul W.K. Rothemund, Theory and experiments in algorithmic self-assembly, Ph.D. Thesis, University of Southern California, December 2001
13. Paul W.K. Rothemund, Erik Winfree, The program-size complexity of self-assembled squares (extended abstract), in: Proceedings of the Thirty-Second Annual ACM Symposium on Theory of Computing, 2000, pp. 459-468
14. Rothemund P.W.K., Papadakis N., and Winfree E. Algorithmic self-assembly of DNA Sierpinski triangles. PLoS Biology 2 12 (2004)
15. Seeman N.C. Nucleic-acid junctions and lattices. Journal of Theoretical Biology 99 (1982) 237-247
16. Soloveichik D., and Winfree E. Complexity of self-assembled shapes. SIAM Journal on Computing 36 (2007) 1544-1569
17. Wang H. Proving theorems by pattern recognition - II. The Bell System Technical Journal XL 1 (1961) 1-41
18. Wang H. Dominoes and the AEA case of the decision problem. Proceedings of the Symposium on Mathematical Theory of Automata (New York, 1962) (1963), Polytechnic Press of Polytechnic Inst. of Brooklyn, Brooklyn, NY 23-55
19. Willson S.J. Growth rates and fractional dimensions in cellular automata. Physica D 10 (1984) 69-74
20. Erik Winfree, Algorithmic self-assembly of DNA, Ph.D. Thesis, California Institute of Technology, June 1998