{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T18:35:39Z","timestamp":1768070139301,"version":"3.49.0"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2011,7,1]],"date-time":"2011-07-01T00:00:00Z","timestamp":1309478400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Theory Comput Syst"],"published-print":{"date-parts":[[2012,10]]},"DOI":"10.1007\/s00224-011-9345-4","type":"journal-article","created":{"date-parts":[[2011,6,30]],"date-time":"2011-06-30T11:49:50Z","timestamp":1309434590000},"page":"372-400","source":"Crossref","is-referenced-by-count":20,"title":["Approximate Self-Assembly of the Sierpinski Triangle"],"prefix":"10.1007","volume":"51","author":[{"given":"Jack H.","family":"Lutz","sequence":"first","affiliation":[]},{"given":"Brad","family":"Shutters","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2011,7,1]]},"reference":[{"key":"9345_CR1","first-page":"125","volume-title":"Proc. London Math. Soc.","author":"M.T. Barlow","year":"1992","unstructured":"Barlow, M.T., Taylor, S.J.: Defining fractal subsets of \u2124 d . In: Proc. London Math. Soc., vol. 64, pp. 125\u2013152 (1992)"},{"key":"9345_CR2","doi-asserted-by":"crossref","unstructured":"Bondarenko, B.A.: Generalized Pascal Triangles and Pyramids, Their Fractals, Graphs and Applications. The Fibonacci Association (1993)","DOI":"10.1080\/00150517.1993.12429322"},{"issue":"3","key":"9345_CR3","doi-asserted-by":"crossref","first-page":"75","DOI":"10.24033\/asens.401","volume":"11","author":"E. Cahen","year":"1894","unstructured":"Cahen, E.: Sur la fonction \u03b6(s) de Riemann et sur des fonctions analogues. Annales Scientifiques de L\u2019\u00c9cole Normale Sup\u00e9rieure 11(3), 75\u2013164 (1894)","journal-title":"Annales Scientifiques de L\u2019\u00c9cole Normale Sup\u00e9rieure"},{"key":"9345_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1007\/11549345_25","volume-title":"Proc. of the Thirtieth International Symposium on Mathematical Foundations of Computer Science","author":"D. Doty","year":"2005","unstructured":"Doty, D., Gu, X., Lutz, J.H., Mayordomo, E., Moser, P.: Zeta-dimension. In: Proc. of the Thirtieth International Symposium on Mathematical Foundations of Computer Science. Lecture Notes in Computer Science, vol.\u00a03618, pp. 283\u2013294. Springer, Berlin (2005)"},{"key":"9345_CR5","first-page":"160","volume":"9","author":"L. Euler","year":"1737","unstructured":"Euler, L.: Variae observationes circa series infinitas. Comment. Acad. Sci. Imp. Petropolitanae 9, 160\u2013188 (1737)","journal-title":"Comment. Acad. Sci. Imp. Petropolitanae"},{"key":"9345_CR6","volume-title":"Concrete Mathematics","author":"R.L. Graham","year":"1994","unstructured":"Graham, R.L., Knuth, D.E., Patashnik, O.: Concrete Mathematics. Addison-Wesley, Reading (1994)"},{"key":"9345_CR7","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1017\/S0963548397002940","volume":"6","author":"I. Hueter","year":"1997","unstructured":"Hueter, I., Peres, Y.: Self-affine carpets on the square lattice. Comb. Probab. Comput. 6, 197\u2013204 (1997)","journal-title":"Comb. Probab. Comput."},{"key":"9345_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1007\/978-3-642-10604-0_8","volume-title":"Proc. of the Fifteenth International Meeting on DNA Computing and Molecular Programming","author":"S.M. Kautz","year":"2009","unstructured":"Kautz, S.M., Lathrop, J.I.: Self-assembly of the Sierpinski carpet and related fractals. In: Proc. of the Fifteenth International Meeting on DNA Computing and Molecular Programming. Lecture Notes in Computer Science, vol.\u00a05877, pp. 78\u201387. Springer, Berlin (2009)"},{"key":"9345_CR9","doi-asserted-by":"crossref","first-page":"384","DOI":"10.1016\/j.tcs.2008.09.062","volume":"410","author":"J.I. Lathrop","year":"2009","unstructured":"Lathrop, J.I., Lutz, J.H., Summers, S.M.: Strict self-assembly of discrete Sierpinski triangles. Theor. Comput. Sci. 410, 384\u2013405 (2009)","journal-title":"Theor. Comput. Sci."},{"issue":"3","key":"9345_CR10","doi-asserted-by":"crossref","first-page":"253","DOI":"10.4064\/aa105-3-4","volume":"105","author":"L. Olsen","year":"2002","unstructured":"Olsen, L.: Distribution of digits in integers: fractal dimension and zeta functions. Acta Arith. 105(3), 253\u2013277 (2002)","journal-title":"Acta Arith."},{"key":"9345_CR11","volume-title":"Proc. of the Sixth Annual Conference on Foundations of Nanoscience: Self-Assembled Architectures and Devices","author":"M.J. Patitz","year":"2009","unstructured":"Patitz, M.J.: Simulation of self-assembly in the abstract tile assembly model with ISU TAS. In: Proc. of the Sixth Annual Conference on Foundations of Nanoscience: Self-Assembled Architectures and Devices (2009)"},{"issue":"1","key":"9345_CR12","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1007\/s11047-009-9147-7","volume":"9","author":"M.J. Patitz","year":"2010","unstructured":"Patitz, M.J., Summers, S.M.: Self-assembly of discrete self-similar fractals. Nat. Comput. 9(1), 135\u2013172 (2010)","journal-title":"Nat. Comput."},{"key":"9345_CR13","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-007-1168-6","volume-title":"Nanotechnology research directions for societal needs in 2020, NSF\/WTEC report","author":"M.C. Roco","year":"2011","unstructured":"Roco, M.C., Mirkin, C.A., Hersam, M.C.: Nanotechnology research directions for societal needs in 2020, NSF\/WTEC report. Springer, Berlin (2011)"},{"key":"9345_CR14","unstructured":"Rothemund, P.W.: Theory and experiments in algorithmic self-assembly. Ph.D. thesis, University of Southern California, Los Angeles, California (2001)"},{"key":"9345_CR15","doi-asserted-by":"crossref","unstructured":"Rothemund, P.W.K., Papadakis, N., Winfree, E.: Algorithmic self-assembly of DNA Sierpinski triangles. PLoS Biol. 2(12) (2004)","DOI":"10.1371\/journal.pbio.0020424"},{"key":"9345_CR16","volume-title":"Proc. of the Thirty Second Annual ACM Symposium on Theory of Computing","author":"P.W.K. Rothemund","year":"2000","unstructured":"Rothemund, P.W.K., Winfree, E.: The program-size complexity of self-assembled squares. In: Proc. of the Thirty Second Annual ACM Symposium on Theory of Computing (2000)"},{"key":"9345_CR17","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/0022-5193(82)90002-9","volume":"99","author":"N.C. Seeman","year":"1982","unstructured":"Seeman, N.C.: Nucleic-acid junctions and lattices. J. Theor. Biol. 99, 237\u2013247 (1982)","journal-title":"J. Theor. Biol."},{"key":"9345_CR18","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1038\/nature01406","volume":"421","author":"N.C. Seeman","year":"2003","unstructured":"Seeman, N.C.: DNA in a material world. Nature 421, 427\u2013431 (2003)","journal-title":"Nature"},{"key":"9345_CR19","first-page":"302","volume":"160","author":"W. Sierpi\u0144ski","year":"1915","unstructured":"Sierpi\u0144ski, W.: Sur une courbe dont tout point est un point de ramification. C. R. Math. 160, 302\u2013305 (1915)","journal-title":"C. R. Math."},{"key":"9345_CR20","doi-asserted-by":"crossref","first-page":"1544","DOI":"10.1137\/S0097539704446712","volume":"36","author":"D. Soloveichik","year":"2007","unstructured":"Soloveichik, D., Winfree, E.: Complexity of self-assembled shapes. SIAM J. Comput. 36, 1544\u20131569 (2007)","journal-title":"SIAM J. Comput."},{"issue":"1","key":"9345_CR21","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1007\/BF03024718","volume":"17","author":"I. Stewart","year":"1995","unstructured":"Stewart, I.: Four encounters with Sierpinski\u2019s gasket. Math. Intell. 17(1), 52\u201364 (1995)","journal-title":"Math. Intell."},{"key":"9345_CR22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/j.1538-7305.1961.tb03975.x","volume":"40","author":"H. Wang","year":"1961","unstructured":"Wang, H.: Proving theorems by pattern recognition, ii. Bell Syst. Tech. J. 40, 1\u201341 (1961)","journal-title":"Bell Syst. Tech. J."},{"key":"9345_CR23","volume-title":"Proc. of the Symposium on Mathematical Theory of Automata","author":"H. Wang","year":"1962","unstructured":"Wang, H.: Dominoes and the AEA case of the decision problem. In: Proc. of the Symposium on Mathematical Theory of Automata (1962)"},{"key":"9345_CR24","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1016\/0167-2789(87)90073-X","volume":"24","author":"S.J. Willson","year":"1987","unstructured":"Willson, S.J.: The equality of fractional dimensions for certain cellular automata. Physica D 24, 179\u2013189 (1987)","journal-title":"Physica D"},{"key":"9345_CR25","unstructured":"Winfree, E.: Algorithmic self-assembly of DNA. Ph.D. thesis, California Institute of Technology, Pasadena, California (1998)"}],"container-title":["Theory of Computing Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00224-011-9345-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00224-011-9345-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00224-011-9345-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,6]],"date-time":"2025-03-06T20:57:52Z","timestamp":1741294672000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00224-011-9345-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,7,1]]},"references-count":25,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2012,10]]}},"alternative-id":["9345"],"URL":"https:\/\/doi.org\/10.1007\/s00224-011-9345-4","relation":{},"ISSN":["1432-4350","1433-0490"],"issn-type":[{"value":"1432-4350","type":"print"},{"value":"1433-0490","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,7,1]]}}}