Aperiodic tiling (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Aperiodic tiling" in English language version.

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19doi.org

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9harvard.edu

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1archive.org

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1bromleytilers.co.uk

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ams.org

Treviño, Rodrigo (2023). "Aperiodic Tilings, Order, and Randomness" (PDF). Notices of the American Mathematical Society. 70 (8): 1183. doi:10.1090/noti2759. S2CID 260818304.

archive.org

Gardner, Martin (1988). Penrose Tiles to Trapdoor Ciphers. W H Freeman & Co. ISBN 978-0-7167-1987-8.

arxiv.org

Smith, David; Myers, Joseph Samuel; Kaplan, Craig S.; Goodman-Strauss, Chaim (2023-03-19). "An aperiodic monotile". arXiv:2303.10798 [math.CO].
Smith, David; Myers, Joseph Samuel; Kaplan, Craig S.; Goodman-Strauss, Chaim (2023-05-28). "A chiral aperiodic monotile". arXiv:2305.17743 [math.CO].

books.google.com

Grünbaum, Branko; Shephard, Geoffrey Colin (1987). Tilings and Patterns. New York: W. H. Freeman. p. 584f. ISBN 0-7167-1193-1.
Grünbaum, Branko; Shephard, Geoffrey Colin (1987). Tilings and Patterns. New York: W. H. Freeman. p. 528f. ISBN 0-7167-1193-1.

bromleytilers.co.uk

"Bromley Tilers". Retrieved 26 July 2023.

brown.edu

math.brown.edu

N. G. de Bruijn, Nederl. Akad. Wetensch. Indag. Math. 43, 39–52, 53–66 (1981). Algebraic theory of Penrose's nonperiodic tilings of the plane, I, II

doi.org

Gardner, Martin (January 1977). "Mathematical Games". Scientific American. 236 (1): 111–119. Bibcode:1977SciAm.236a.110G. doi:10.1038/scientificamerican0177-110.
Schechtman, D.; Blech, I.; Gratias, D.; Cahn, J.W. (1984). "Metallic Phase with long-range orientational order and no translational symmetry". Physical Review Letters. 53 (20): 1951–1953. Bibcode:1984PhRvL..53.1951S. doi:10.1103/PhysRevLett.53.1951.
Robinson, Raphael M. (1971). "Undecidability and Nonperiodicity for Tilings of the Plane". Inventiones Mathematicae. 12 (3): 177–209. Bibcode:1971InMat..12..177R. doi:10.1007/BF01418780. S2CID 14259496.
Lagarias, J.C. (1996). "Meyer's concept of quasicrystal and quasiregular sets". Communications in Mathematical Physics. 179 (2): 356–376. Bibcode:1996CMaPh.179..365L. doi:10.1007/BF02102593. S2CID 122753893.
Moody, R.V. (1997). "Meyer Sets and Their Duals". In Moody, R.V. (ed.). The Mathematics of Long-Range Aperiodic Order. NATO ASI Series C. pp. 403–441. doi:10.1007/978-94-015-8784-6_16. ISBN 978-90-481-4832-5.
Goodman-Strauss, Chaim (1998). "Matching rules and substitution tilings". Annals of Mathematics. 147 (1): 181–223. CiteSeerX 10.1.1.173.8436. doi:10.2307/120988. JSTOR 120988.
Mozes, Shahar (1989). "Tilings, substitution systems and dynamical systems generated by them". Journal d'Analyse Mathématique. 53 (1): 139–186. doi:10.1007/BF02793412. S2CID 121775031.
Treviño, Rodrigo (2023). "Aperiodic Tilings, Order, and Randomness" (PDF). Notices of the American Mathematical Society. 70 (8): 1183. doi:10.1090/noti2759. S2CID 260818304.
Goodman-Strauss, Chaim (1999). "A small aperiodic set of planar tiles". European Journal of Combinatorics. 20 (5): 375–384. doi:10.1006/eujc.1998.0281.
Socolar, J.E.S. (1989). "Simple octagonal and dodecagonal quasicrystals". Phys. Rev. B. 39 (15): 10519–51. Bibcode:1989PhRvB..3910519S. doi:10.1103/PhysRevB.39.10519. PMID 9947860.
Nischke, K.-P.; Danzer, L. (1996). "A construction of inflation rules based on n-fold symmetry". Discrete & Computational Geometry. 15 (2): 221–236. doi:10.1007/BF02717732.
Radin, Charles (1994). "The pinwheel tilings of the plane". Annals of Mathematics. 139 (3): 661–702. doi:10.2307/2118575. JSTOR 2118575.
See, for example, the survey by Le, T.T.Q. (1997). "Local Rules for Quasiperiodic Tilings". In Moody, R.V. (ed.). The Mathematics of Long-Range Aperiodic Order. NATO Adv. Sci. Inst. Ser. C. Math. Phys. Sci. Vol. 489. pp. 331–366. doi:10.1007/978-94-015-8784-6_13. ISBN 978-90-481-4832-5.
Kari, Jarkko (1996). "A small aperiodic set of Wang tiles". Discrete Mathematics. 160 (1–3): 259–264. doi:10.1016/0012-365X(95)00120-L.
Goodman-Strauss, Chaim (2005). "A strongly aperiodic set of tiles in the hyperbolic plane". Inventiones Mathematicae. 159 (1): 119–132. Bibcode:2004InMat.159..119G. CiteSeerX 10.1.1.477.1974. doi:10.1007/s00222-004-0384-1. S2CID 5348203.
Mozes, Shahar (1997). "Aperiodic tilings". Inventiones Mathematicae. 128 (3): 603–611. Bibcode:1997InMat.128..603M. doi:10.1007/s002220050153. S2CID 189819776.
Block, J.; Weinberger, S. (1992). "Aperiodic tilings, positive scalar curvature and amenability of spaces". Journal of the American Mathematical Society. 5 (4): 907–918. doi:10.1090/s0894-0347-1992-1145337-x.
Socolar, Joshua (1990). "Weak matching rules for quasicrystals". Communications in Mathematical Physics. 129 (3): 599–619. Bibcode:1990CMaPh.129..599S. doi:10.1007/BF02097107. S2CID 123629334.
Edwards, W.; Fauve, S. (1993). "Parametrically excited quasicrystalline surface waves". Physical Review E. 47 (2): R788 – R791. Bibcode:1993PhRvE..47..788E. doi:10.1103/PhysRevE.47.R788. PMID 9960162.

harvard.edu

ui.adsabs.harvard.edu

Gardner, Martin (January 1977). "Mathematical Games". Scientific American. 236 (1): 111–119. Bibcode:1977SciAm.236a.110G. doi:10.1038/scientificamerican0177-110.
Schechtman, D.; Blech, I.; Gratias, D.; Cahn, J.W. (1984). "Metallic Phase with long-range orientational order and no translational symmetry". Physical Review Letters. 53 (20): 1951–1953. Bibcode:1984PhRvL..53.1951S. doi:10.1103/PhysRevLett.53.1951.
Robinson, Raphael M. (1971). "Undecidability and Nonperiodicity for Tilings of the Plane". Inventiones Mathematicae. 12 (3): 177–209. Bibcode:1971InMat..12..177R. doi:10.1007/BF01418780. S2CID 14259496.
Lagarias, J.C. (1996). "Meyer's concept of quasicrystal and quasiregular sets". Communications in Mathematical Physics. 179 (2): 356–376. Bibcode:1996CMaPh.179..365L. doi:10.1007/BF02102593. S2CID 122753893.
Socolar, J.E.S. (1989). "Simple octagonal and dodecagonal quasicrystals". Phys. Rev. B. 39 (15): 10519–51. Bibcode:1989PhRvB..3910519S. doi:10.1103/PhysRevB.39.10519. PMID 9947860.
Goodman-Strauss, Chaim (2005). "A strongly aperiodic set of tiles in the hyperbolic plane". Inventiones Mathematicae. 159 (1): 119–132. Bibcode:2004InMat.159..119G. CiteSeerX 10.1.1.477.1974. doi:10.1007/s00222-004-0384-1. S2CID 5348203.
Mozes, Shahar (1997). "Aperiodic tilings". Inventiones Mathematicae. 128 (3): 603–611. Bibcode:1997InMat.128..603M. doi:10.1007/s002220050153. S2CID 189819776.
Socolar, Joshua (1990). "Weak matching rules for quasicrystals". Communications in Mathematical Physics. 129 (3): 599–619. Bibcode:1990CMaPh.129..599S. doi:10.1007/BF02097107. S2CID 123629334.
Edwards, W.; Fauve, S. (1993). "Parametrically excited quasicrystalline surface waves". Physical Review E. 47 (2): R788 – R791. Bibcode:1993PhRvE..47..788E. doi:10.1103/PhysRevE.47.R788. PMID 9960162.

jstor.org

Goodman-Strauss, Chaim (1998). "Matching rules and substitution tilings". Annals of Mathematics. 147 (1): 181–223. CiteSeerX 10.1.1.173.8436. doi:10.2307/120988. JSTOR 120988.
Radin, Charles (1994). "The pinwheel tilings of the plane". Annals of Mathematics. 139 (3): 661–702. doi:10.2307/2118575. JSTOR 2118575.

mathgenealogy.org

Robert Berger at the Mathematics Genealogy Project.

nih.gov

pubmed.ncbi.nlm.nih.gov

Socolar, J.E.S. (1989). "Simple octagonal and dodecagonal quasicrystals". Phys. Rev. B. 39 (15): 10519–51. Bibcode:1989PhRvB..3910519S. doi:10.1103/PhysRevB.39.10519. PMID 9947860.
Edwards, W.; Fauve, S. (1993). "Parametrically excited quasicrystalline surface waves". Physical Review E. 47 (2): R788 – R791. Bibcode:1993PhRvE..47..788E. doi:10.1103/PhysRevE.47.R788. PMID 9960162.

nobelprize.org

"The Nobel Prize in Chemistry 2011". Nobelprize.org. Retrieved 2011-10-06.

princeton.edu

wwwphy.princeton.edu

Steinhardt, Paul J. "A New Paradigm for the Structure of Quasicrystals". Archived from the original on 23 February 2007. Retrieved 2007-03-26.

psu.edu

citeseerx.ist.psu.edu

Goodman-Strauss, Chaim (1998). "Matching rules and substitution tilings". Annals of Mathematics. 147 (1): 181–223. CiteSeerX 10.1.1.173.8436. doi:10.2307/120988. JSTOR 120988.
Goodman-Strauss, Chaim (2005). "A strongly aperiodic set of tiles in the hyperbolic plane". Inventiones Mathematicae. 159 (1): 119–132. Bibcode:2004InMat.159..119G. CiteSeerX 10.1.1.477.1974. doi:10.1007/s00222-004-0384-1. S2CID 5348203.

researchgate.net

Lagarias, J.C. (1996). "Meyer's concept of quasicrystal and quasiregular sets". Communications in Mathematical Physics. 179 (2): 356–376. Bibcode:1996CMaPh.179..365L. doi:10.1007/BF02102593. S2CID 122753893.

sciencenews.org

Conover, Emily (2023-03-24). "Mathematicians have finally discovered an elusive 'einstein' tile". Science News. Retrieved 2023-03-25.

semanticscholar.org

api.semanticscholar.org

Robinson, Raphael M. (1971). "Undecidability and Nonperiodicity for Tilings of the Plane". Inventiones Mathematicae. 12 (3): 177–209. Bibcode:1971InMat..12..177R. doi:10.1007/BF01418780. S2CID 14259496.
Lagarias, J.C. (1996). "Meyer's concept of quasicrystal and quasiregular sets". Communications in Mathematical Physics. 179 (2): 356–376. Bibcode:1996CMaPh.179..365L. doi:10.1007/BF02102593. S2CID 122753893.
Mozes, Shahar (1989). "Tilings, substitution systems and dynamical systems generated by them". Journal d'Analyse Mathématique. 53 (1): 139–186. doi:10.1007/BF02793412. S2CID 121775031.
Treviño, Rodrigo (2023). "Aperiodic Tilings, Order, and Randomness" (PDF). Notices of the American Mathematical Society. 70 (8): 1183. doi:10.1090/noti2759. S2CID 260818304.
Goodman-Strauss, Chaim (2005). "A strongly aperiodic set of tiles in the hyperbolic plane". Inventiones Mathematicae. 159 (1): 119–132. Bibcode:2004InMat.159..119G. CiteSeerX 10.1.1.477.1974. doi:10.1007/s00222-004-0384-1. S2CID 5348203.
Mozes, Shahar (1997). "Aperiodic tilings". Inventiones Mathematicae. 128 (3): 603–611. Bibcode:1997InMat.128..603M. doi:10.1007/s002220050153. S2CID 189819776.
Socolar, Joshua (1990). "Weak matching rules for quasicrystals". Communications in Mathematical Physics. 129 (3): 599–619. Bibcode:1990CMaPh.129..599S. doi:10.1007/BF02097107. S2CID 123629334.

uark.edu

comp.uark.edu

Goodman-Strauss, Chaim (1998). "Matching rules and substitution tilings". Annals of Mathematics. 147 (1): 181–223. CiteSeerX 10.1.1.173.8436. doi:10.2307/120988. JSTOR 120988.

web.archive.org

Steinhardt, Paul J. "A New Paradigm for the Structure of Quasicrystals". Archived from the original on 23 February 2007. Retrieved 2007-03-26.