{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T11:09:27Z","timestamp":1740136167249,"version":"3.37.3"},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2018,10,30]],"date-time":"2018-10-30T00:00:00Z","timestamp":1540857600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Nat Comput"],"published-print":{"date-parts":[[2019,3]]},"DOI":"10.1007\/s11047-018-9718-6","type":"journal-article","created":{"date-parts":[[2018,10,30]],"date-time":"2018-10-30T08:31:37Z","timestamp":1540888297000},"page":"75-92","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Self-assembly of 4-sided fractals in the Two-Handed Tile Assembly Model"],"prefix":"10.1007","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6738-4449","authenticated-orcid":false,"given":"Jacob","family":"Hendricks","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Joseph","family":"Opseth","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,10,30]]},"reference":[{"key":"9718_CR1","doi-asserted-by":"crossref","unstructured":"Abel Z, Benbernou N, Damian M, Demaine E, Demaine M, Flatland R, Kominers S, Schweller R (2010) Shape replication through self-assembly and RNase enzymes. In: SODA 2010: proceedings of the twenty-first annual ACM-SIAM symposium on discrete algorithms, Austin, Texas. Society for Industrial and Applied Mathematics","DOI":"10.1137\/1.9781611973075.85"},{"key":"9718_CR2","doi-asserted-by":"crossref","unstructured":"Barth K, Furcy D, Summers SM, Totzke P (2014) Scaled tree fractals do not strictly self-assemble. In: Unconventional computation and natural computation (UCNC) 2014, University of Western Ontario, London, Ontario, Canada, 14\u201318 July 2014, pp 27\u201339","DOI":"10.1007\/978-3-319-08123-6_3"},{"key":"9718_CR3","unstructured":"Cannon S, Demaine ED, Demaine ML, Eisenstat S, Patitz MJ, Schweller RT, Summers SM, Winslow A (2013) Two hands are better than one (up to constant factors): self-assembly in the 2HAM vs. aTAM. In: Portier N, Wilke T (eds) STACS, volume\u00a020 of LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, pp 172\u2013184"},{"key":"9718_CR4","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1007\/s00453-015-0022-x","volume":"76","author":"CT Chalk","year":"2015","unstructured":"Chalk CT, Fernandez DA, Huerta A, Maldonado MA, Schweller RT, Sweet L (2015) Strict self-assembly of fractals using multiple hands. Algorithmica 76:195\u2013224","journal-title":"Algorithmica"},{"key":"9718_CR5","doi-asserted-by":"crossref","unstructured":"Chalk C, Demaine ED, Demaine ML, Martinez E, Schweller R, Vega L, Wylie T (2017) Universal shape replicators via self-assembly with attractive and repulsive forces. In: Proceedings of the twenty-eighth annual ACM-SIAM symposium on discrete algorithms, SODA\u201917, Philadelphia, PA, USA. Society for Industrial and Applied Mathematics, pp 225\u2013238","DOI":"10.1137\/1.9781611974782.15"},{"key":"9718_CR6","doi-asserted-by":"publisher","first-page":"1493","DOI":"10.1137\/S0097539704446037","volume":"34","author":"Q Cheng","year":"2005","unstructured":"Cheng Q, Aggarwal G, Goldwasser MH, Kao M-Y, Schweller RT, de Espan\u00e9s PM (2005) Complexities for generalized models of self-assembly. SIAM J Comput 34:1493\u20131515","journal-title":"SIAM J Comput"},{"key":"9718_CR7","doi-asserted-by":"crossref","unstructured":"Cook M, Fu Y, Schweller RT (2011) Temperature 1 self-assembly: deterministic assembly in 3D and probabilistic assembly in 2D. In: SODA 2011: proceedings of the 22nd annual ACM-SIAM symposium on discrete algorithms. SIAM","DOI":"10.1137\/1.9781611973082.45"},{"key":"9718_CR9","unstructured":"Demaine ED, Patitz MJ, Schweller RT, Summers SM (2011) Self-assembly of arbitrary shapes using RNAse enzymes: meeting the Kolmogorov bound with small scale factor (extended abstract). In: Schwentick T, D\u00fcrr C (eds) 28th international symposium on theoretical aspects of computer science (STACS 2011), vol 9. Leibniz International Proceedings in Informatics (LIPIcs). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Dagstuhl, pp 201\u2013212"},{"key":"9718_CR10","doi-asserted-by":"crossref","unstructured":"Demaine ED, Demaine ML, Fekete SP, Patitz MJ, Schweller RT, Winslow A, Woods D (2014) One tile to rule them all: simulating any tile assembly system with a single universal tile. In: Proceedings of the 41st international colloquium on automata, languages, and programming (ICALP 2014), IT University of Copenhagen, Denmark, 8\u201311 July 2014, volume 857 of LNCS, pp 368\u2013379","DOI":"10.1007\/978-3-662-43948-7_31"},{"issue":"2","key":"9718_CR11","doi-asserted-by":"publisher","first-page":"812","DOI":"10.1007\/s00453-015-9976-y","volume":"74","author":"ED Demaine","year":"2016","unstructured":"Demaine ED, Patitz MJ, Rogers TA, Schweller RT, Summers SM, Woods D (2016) The Two-Handed Tile Assembly Model is not intrinsically universal. Algorithmica 74(2):812\u2013850","journal-title":"Algorithmica"},{"key":"9718_CR12","unstructured":"Doty D, Patitz MJ, Summers SM (2009) Limitations of self-assembly at temperature 1. In: Proceedings of the fifteenth international meeting on dna computing and molecular programming (Fayetteville, Arkansas, USA, 8\u201311 June 2009), pp 283\u2013294"},{"key":"9718_CR13","doi-asserted-by":"crossref","unstructured":"Doty D, Patitz MJ, Reishus D, Schweller RT, Summers SM (2010a) Strong fault-tolerance for self-assembly with fuzzy temperature. In: Proceedings of the 51st annual IEEE symposium on foundations of computer science (FOCS 2010), pp 417\u2013426","DOI":"10.1109\/FOCS.2010.47"},{"key":"9718_CR14","doi-asserted-by":"crossref","unstructured":"Doty D, Kari L, Masson B (2010b) Negative interactions in irreversible self-assembly. In: DNA 16: proceedings of the sixteenth international meeting on DNA computing and molecular programming, lecture notes in computer science. Springer, pp 37\u201348","DOI":"10.1007\/978-3-642-18305-8_4"},{"key":"9718_CR15","doi-asserted-by":"crossref","unstructured":"Doty D, Lutz JH, Patitz MJ, Schweller RT, Summers SM, Woods D (2012) The Tile Assembly Model is intrinsically universal. In: Proceedings of the 53rd annual IEEE symposium on foundations of computer science, FOCS 2012, pp 302\u2013310","DOI":"10.1109\/FOCS.2012.76"},{"key":"9718_CR16","doi-asserted-by":"crossref","unstructured":"Fekete SP, Hendricks J, Patitz MJ, Rogers TA, Schweller RT (2015) Universal computation with arbitrary polyomino tiles in non-cooperative self-assembly. In: Proceedings of the twenty-sixth annual ACM-SIAM symposium on discrete algorithms (SODA 2015), San Diego, CA, USA, 4\u20136 Jan 2015, pp 148\u2013167","DOI":"10.1137\/1.9781611973730.12"},{"issue":"7","key":"9718_CR17","doi-asserted-by":"publisher","first-page":"1791","DOI":"10.1021\/nl0722830","volume":"8","author":"K Fujibayashi","year":"2007","unstructured":"Fujibayashi K, Hariadi R, Park SH, Winfree E, Murata S (2007) Toward reliable algorithmic self-assembly of DNA tiles: a fixed-width cellular automaton pattern. Nano Lett 8(7):1791\u20131797","journal-title":"Nano Lett"},{"key":"9718_CR18","unstructured":"Gilber O, Hendricks J, Patitz MJ, Rogers TA (2016) Computing in continuous space with self-assembling polygonal tiles. In: Proceedings of the twenty-seventh annual ACM-SIAM symposium on discrete algorithms (SODA 2016), Arlington, VA, USA, 10\u201312 Jan 2016, pp 937\u2013956"},{"key":"9718_CR20","doi-asserted-by":"crossref","unstructured":"Hendricks J, Olsen M, Patitz MJ, Rogers TA, Thomas H (2016a) Hierarchical self-assembly of fractals with signal-passing tiles (extended abstract). In: Proceedings of the 22nd international conference on DNA computing and molecular programming (DNA 22), Ludwig-Maximilians-Universitt, Munich, Germany, 4\u20138 Sept, pp 82\u201397","DOI":"10.1007\/978-3-319-43994-5_6"},{"key":"9718_CR21","doi-asserted-by":"crossref","unstructured":"Hendricks J, Patitz MJ, Rogers TA (2016b) Universal simulation of directed systems in the abstract tile assembly model requires undirectedness. In: Proceedings of the 57th annual IEEE symposium on foundations of computer science (FOCS 2016), New Brunswick, New Jersey, USA, 9\u201311 Oct, pp 800\u2013809","DOI":"10.1109\/FOCS.2016.90"},{"issue":"2","key":"9718_CR19","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1007\/s11047-017-9617-2","volume":"16","author":"J Hendricks","year":"2017","unstructured":"Hendricks J, Patitz MJ, Rogers TA (2017a) Reflections on tiles (in self-assembly). Natural Computing 16(2):295\u2013316","journal-title":"Natural Computing"},{"issue":"1\u20132","key":"9718_CR22","doi-asserted-by":"publisher","first-page":"131","DOI":"10.3233\/FI-2017-1579","volume":"155","author":"J Hendricks","year":"2017","unstructured":"Hendricks J, Patitz MJ, Rogers TA (2017b) The simulation powers and limitations of higher temperature hierarchical self-assembly systems. Fundam Inform 155(1\u20132):131\u2013162","journal-title":"Fundam Inform"},{"key":"9718_CR23","doi-asserted-by":"crossref","unstructured":"Hendricks J, Opseth J, Patitz MJ, Summers SM (2018) Hierarchical growth is necessary and (sometimes) sufficient to self-assemble discrete self-similar fractals. In: International conference on DNA computing and molecular programming, pp 87\u2013104. Springer","DOI":"10.1007\/978-3-030-00030-1_6"},{"issue":"02","key":"9718_CR24","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1142\/S0129054114500087","volume":"25","author":"N Jonoska","year":"2014","unstructured":"Jonoska N, Karpenko D (2014a) Active tile self-assembly, part 1: universality at temperature 1. Int J Found Comput Sci 25(02):141\u2013163","journal-title":"Int J Found Comput Sci"},{"issue":"02","key":"9718_CR25","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1142\/S0129054114500099","volume":"25","author":"N Jonoska","year":"2014","unstructured":"Jonoska N, Karpenko D (2014b) Active tile self-assembly, part 2: self-similar structures and structural recursion. Int J Found Comput Sci 25(02):165\u2013194","journal-title":"Int J Found Comput Sci"},{"key":"9718_CR26","unstructured":"Jonoska N, Karpenko D (2012) Active tile self-assembly, self-similar structures and recursion. Technical report 1211.3085, Computing Research Repository"},{"key":"9718_CR27","unstructured":"Kao M-Y, Schweller RT (2007) Reducing tile complexity for self-assembly through temperature programming. In: Proceedings of the 17th annual ACM-SIAM symposium on discrete algorithms (SODA 2006), Miami, Florida, Jan 2006, pp 571\u2013580"},{"key":"9718_CR28","unstructured":"Kautz SM, Lathrop JI (2009) Self-assembly of the Sierpinski carpet and related fractals. In: Proceedings of the fifteenth international meeting on DNA computing and molecular programming (Fayetteville, Arkansas, USA, 8\u201311 June 2009), pp 78\u201387"},{"issue":"2","key":"9718_CR29","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1007\/s00453-012-9691-x","volume":"67","author":"S Kautz","year":"2013","unstructured":"Kautz S, Shutters B (2013) Self-assembling rulers for approximating generalized Sierpinski carpets. Algorithmica 67(2):207\u2013233","journal-title":"Algorithmica"},{"key":"9718_CR30","doi-asserted-by":"publisher","first-page":"384","DOI":"10.1016\/j.tcs.2008.09.062","volume":"410","author":"JI Lathrop","year":"2009","unstructured":"Lathrop JI, Lutz JH, Summers SM (2009) Strict self-assembly of discrete Sierpinski triangles. Theor Comput Sci 410:384\u2013405","journal-title":"Theor Comput Sci"},{"key":"9718_CR31","doi-asserted-by":"crossref","unstructured":"Luchsinger A, Schweller R, Wylie T (2017) Self-assembly of shapes at constant scale using repulsive forces. In: Patitz M, Stannett M (eds) Unconventional computation and natural computation - 16th international conference, UCNC 2017, Fayetteville, AR, USA, June 5\u20139, 2017, Proceedings, pp 82\u201397","DOI":"10.1007\/978-3-319-58187-3_7"},{"issue":"3","key":"9718_CR32","doi-asserted-by":"publisher","first-page":"372","DOI":"10.1007\/s00224-011-9345-4","volume":"51","author":"JH Lutz","year":"2012","unstructured":"Lutz JH, Shutters B (2012) Approximate self-assembly of the Sierpinski triangle. Theory Comput Syst 51(3):372\u2013400","journal-title":"Theory Comput Syst"},{"key":"9718_CR33","doi-asserted-by":"crossref","unstructured":"Meunier P, Woods D (2017) The non-cooperative tile assembly model is not intrinsically universal or capable of bounded Turing machine simulation. In: Proceedings of the 49th annual ACM SIGACT symposium on theory of computing, STOC 2017, Montreal, QC, Canada, 19\u201323 June 2017, pp 328\u2013341","DOI":"10.1145\/3055399.3055446"},{"key":"9718_CR34","unstructured":"Meunier P-E, Patitz MJ, Summers SM, Theyssier G, Winslow A, Woods D (2014) Intrinsic universality in tile self-assembly requires cooperation. In: Proceedings of the ACM-SIAM symposium on discrete algorithms (SODA 2014) (Portland, OR, USA, 5\u20137 Jan 2014), pp 752\u2013771"},{"issue":"4","key":"9718_CR35","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1142\/S0129054114400061","volume":"25","author":"JE Padilla","year":"2014","unstructured":"Padilla JE, Patitz MJ, Schweller RT, Seeman NC, Summers SM, Zhong X (2014) Asynchronous signal passing for tile self-assembly: fuel efficient computation and efficient assembly of shapes. Int J Found Comput Sci 25(4):459\u2013488","journal-title":"Int J Found Comput Sci"},{"issue":"2","key":"9718_CR36","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1007\/s11047-013-9379-4","volume":"13","author":"MJ Patitz","year":"2014","unstructured":"Patitz MJ (2014) An introduction to tile-based self-assembly and a survey of recent results. Nat Comput 13(2):195\u2013224","journal-title":"Nat Comput"},{"key":"9718_CR37","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1007\/s11047-009-9147-7","volume":"1","author":"MJ Patitz","year":"2010","unstructured":"Patitz MJ, Summers SM (2010) Self-assembly of discrete self-similar fractals. Nat Comput 1:135\u2013172","journal-title":"Nat Comput"},{"key":"9718_CR38","doi-asserted-by":"crossref","unstructured":"Patitz MJ, Schweller RT, Summers SM (2011) Exact shapes and Turing universality at temperature 1 with a single negative glue. In: Proceedings of the 17th international conference on DNA computing and molecular programming, DNA\u201911, pp 175\u2013189","DOI":"10.1007\/978-3-642-23638-9_15"},{"issue":"12","key":"9718_CR39","doi-asserted-by":"publisher","first-page":"2041","DOI":"10.1371\/journal.pbio.0020424","volume":"2","author":"PW Rothemund","year":"2004","unstructured":"Rothemund PW, Papadakis N, Winfree E (2004) Algorithmic self-assembly of DNA Sierpinski triangles. PLoS Biol 2(12):2041\u20132053","journal-title":"PLoS Biol"},{"issue":"12","key":"9718_CR40","doi-asserted-by":"publisher","first-page":"e424","DOI":"10.1371\/journal.pbio.0020424","volume":"2","author":"PWK Rothemund","year":"2004","unstructured":"Rothemund PWK, Papadakis N, Winfree E (2004) Algorithmic self-assembly of DNA Sierpinski triangles. PLoS Biol 2(12):e424","journal-title":"PLoS Biol"},{"key":"9718_CR41","unstructured":"Rothemund PWK, Winfree E (2000) The program-size complexity of self-assembled squares (extended abstract). In: STOC\u201900: proceedings of the thirty-second annual ACM symposium on theory of computing, Portland, Oregon, United States. ACM, pp 459\u2013468"},{"issue":"1\u20132","key":"9718_CR42","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1007\/s00453-011-9522-5","volume":"63","author":"SM Summers","year":"2012","unstructured":"Summers SM (2012) Reducing tile complexity for the self-assembly of scaled shapes through temperature programming. Algorithmica 63(1\u20132):117\u2013136","journal-title":"Algorithmica"},{"key":"9718_CR43","unstructured":"Winfree E (1998) Algorithmic self-assembly of DNA. PhD thesis, California Institute of Technology"}],"container-title":["Natural Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11047-018-9718-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11047-018-9718-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11047-018-9718-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,30]],"date-time":"2019-10-30T18:51:09Z","timestamp":1572461469000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11047-018-9718-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,30]]},"references-count":42,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,3]]}},"alternative-id":["9718"],"URL":"https:\/\/doi.org\/10.1007\/s11047-018-9718-6","relation":{},"ISSN":["1567-7818","1572-9796"],"issn-type":[{"type":"print","value":"1567-7818"},{"type":"electronic","value":"1572-9796"}],"subject":[],"published":{"date-parts":[[2018,10,30]]},"assertion":[{"value":"30 October 2018","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}