Wang tile (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Wang tile" in English language version.

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14doi.org

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mathscinet.ams.org

Berger, Robert (1966), "The undecidability of the domino problem", Memoirs of the American Mathematical Society, 66: 72, MR 0216954. Berger coins the term "Wang tiles", and demonstrates the first aperiodic set of them.
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, MR 0297572, S2CID 14259496.
Culik, Karel II (1996), "An aperiodic set of 13 Wang tiles", Discrete Mathematics, 160 (1–3): 245–251, doi:10.1016/S0012-365X(96)00118-5, MR 1417576. (Showed an aperiodic set of 13 tiles with 5 colors.)
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, MR 1417578.
Jeandel, Emmanuel; Rao, Michaël (2021), "An aperiodic set of 11 Wang tiles", Advances in Combinatorics: 1:1–1:37, arXiv:1506.06492, doi:10.19086/aic.18614, MR 4210631, S2CID 13261182. (Showed an aperiodic set of 11 tiles with 4 colors, and proved that fewer tiles or fewer colors cannot be aperiodic.)
Culik, Karel II; Kari, Jarkko (1995), "An aperiodic set of Wang cubes", Journal of Universal Computer Science, 1 (10): 675–686, doi:10.1007/978-3-642-80350-5_57, MR 1392428.
Kari, Jarkko (1990), "Reversibility of 2D cellular automata is undecidable", Cellular automata: theory and experiment (Los Alamos, NM, 1989), Physica D: Nonlinear Phenomena, vol. 45, pp. 379–385, Bibcode:1990PhyD...45..379K, doi:10.1016/0167-2789(90)90195-U, MR 1094882.

arxiv.org

Jeandel, Emmanuel; Rao, Michaël (2021), "An aperiodic set of 11 Wang tiles", Advances in Combinatorics: 1:1–1:37, arXiv:1506.06492, doi:10.19086/aic.18614, MR 4210631, S2CID 13261182. (Showed an aperiodic set of 11 tiles with 4 colors, and proved that fewer tiles or fewer colors cannot be aperiodic.)

books.google.com

Burnham, Karen (2014), Greg Egan, Modern Masters of Science Fiction, University of Illinois Press, pp. 72–73, ISBN 978-0-252-09629-7.

doi.org

Wang, Hao (1961), "Proving theorems by pattern recognition—II", Bell System Technical Journal, 40 (1): 1–41, doi:10.1002/j.1538-7305.1961.tb03975.x. Wang proposes his tiles, and conjectures that there are no aperiodic sets.
Wang, Hao (November 1965), "Games, logic and computers", Scientific American, 213 (5): 98–106, doi:10.1038/scientificamerican1165-98. Presents the domino problem for a popular audience.
Renz, Peter (1981), "Mathematical proof: What it is and what it ought to be", The Two-Year College Mathematics Journal, 12 (2): 83–103, doi:10.2307/3027370, JSTOR 3027370.
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, MR 0297572, S2CID 14259496.
Culik, Karel II (1996), "An aperiodic set of 13 Wang tiles", Discrete Mathematics, 160 (1–3): 245–251, doi:10.1016/S0012-365X(96)00118-5, MR 1417576. (Showed an aperiodic set of 13 tiles with 5 colors.)
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, MR 1417578.
Jeandel, Emmanuel; Rao, Michaël (2021), "An aperiodic set of 11 Wang tiles", Advances in Combinatorics: 1:1–1:37, arXiv:1506.06492, doi:10.19086/aic.18614, MR 4210631, S2CID 13261182. (Showed an aperiodic set of 11 tiles with 4 colors, and proved that fewer tiles or fewer colors cannot be aperiodic.)
Culik, Karel II; Kari, Jarkko (1995), "An aperiodic set of Wang cubes", Journal of Universal Computer Science, 1 (10): 675–686, doi:10.1007/978-3-642-80350-5_57, MR 1392428.
Winfree, E.; Liu, F.; Wenzler, L.A.; Seeman, N.C. (1998), "Design and self-assembly of two-dimensional DNA crystals", Nature, 394 (6693): 539–544, Bibcode:1998Natur.394..539W, doi:10.1038/28998, PMID 9707114, S2CID 4385579.
Neyret, Fabrice; Cani, Marie-Paule (1999), "Pattern-Based Texturing Revisited", Proceedings of the 26th annual conference on Computer graphics and interactive techniques - SIGGRAPH '99 (PDF), Los Angeles, United States: ACM, pp. 235–242, doi:10.1145/311535.311561, ISBN 0-201-48560-5, S2CID 11247905. Introduces stochastic tiling.
Cohen, Michael F.; Shade, Jonathan; Hiller, Stefan; Deussen, Oliver (2003), "Wang tiles for image and texture generation", ACM SIGGRAPH 2003 Papers on - SIGGRAPH '03 (PDF), New York, NY, USA: ACM, pp. 287–294, doi:10.1145/1201775.882265, ISBN 1-58113-709-5, S2CID 207162102, archived from the original (PDF) on 2006-03-18.
Wei, Li-Yi (2004), "Tile-based texture mapping on graphics hardware", Proceedings of the ACM SIGGRAPH/EUROGRAPHICS Conference on Graphics Hardware (HWWS '04), New York, NY, USA: ACM, pp. 55–63, doi:10.1145/1058129.1058138, ISBN 3-905673-15-0, S2CID 53224612. Applies Wang Tiles for real-time texturing on a GPU.
. Kopf, Johannes; Cohen-Or, Daniel; Deussen, Oliver; Lischinski, Dani (2006), "Recursive Wang tiles for real-time blue noise", ACM SIGGRAPH 2006 Papers on - SIGGRAPH '06, New York, NY, USA: ACM, pp. 509–518, doi:10.1145/1179352.1141916, ISBN 1-59593-364-6, S2CID 11007853. Shows advanced applications.
Kari, Jarkko (1990), "Reversibility of 2D cellular automata is undecidable", Cellular automata: theory and experiment (Los Alamos, NM, 1989), Physica D: Nonlinear Phenomena, vol. 45, pp. 379–385, Bibcode:1990PhyD...45..379K, doi:10.1016/0167-2789(90)90195-U, MR 1094882.

harvard.edu

ui.adsabs.harvard.edu

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, MR 0297572, S2CID 14259496.
Winfree, E.; Liu, F.; Wenzler, L.A.; Seeman, N.C. (1998), "Design and self-assembly of two-dimensional DNA crystals", Nature, 394 (6693): 539–544, Bibcode:1998Natur.394..539W, doi:10.1038/28998, PMID 9707114, S2CID 4385579.
Kari, Jarkko (1990), "Reversibility of 2D cellular automata is undecidable", Cellular automata: theory and experiment (Los Alamos, NM, 1989), Physica D: Nonlinear Phenomena, vol. 45, pp. 379–385, Bibcode:1990PhyD...45..379K, doi:10.1016/0167-2789(90)90195-U, MR 1094882.

inria.fr

hal.inria.fr

Neyret, Fabrice; Cani, Marie-Paule (1999), "Pattern-Based Texturing Revisited", Proceedings of the 26th annual conference on Computer graphics and interactive techniques - SIGGRAPH '99 (PDF), Los Angeles, United States: ACM, pp. 235–242, doi:10.1145/311535.311561, ISBN 0-201-48560-5, S2CID 11247905. Introduces stochastic tiling.

johanneskopf.de

. Kopf, Johannes; Cohen-Or, Daniel; Deussen, Oliver; Lischinski, Dani (2006), "Recursive Wang tiles for real-time blue noise", ACM SIGGRAPH 2006 Papers on - SIGGRAPH '06, New York, NY, USA: ACM, pp. 509–518, doi:10.1145/1179352.1141916, ISBN 1-59593-364-6, S2CID 11007853. Shows advanced applications.

jstor.org

Renz, Peter (1981), "Mathematical proof: What it is and what it ought to be", The Two-Year College Mathematics Journal, 12 (2): 83–103, doi:10.2307/3027370, JSTOR 3027370.

jucs.org

Culik, Karel II; Kari, Jarkko (1995), "An aperiodic set of Wang cubes", Journal of Universal Computer Science, 1 (10): 675–686, doi:10.1007/978-3-642-80350-5_57, MR 1392428.

microsoft.com

research.microsoft.com

Cohen, Michael F.; Shade, Jonathan; Hiller, Stefan; Deussen, Oliver (2003), "Wang tiles for image and texture generation", ACM SIGGRAPH 2003 Papers on - SIGGRAPH '03 (PDF), New York, NY, USA: ACM, pp. 287–294, doi:10.1145/1201775.882265, ISBN 1-58113-709-5, S2CID 207162102, archived from the original (PDF) on 2006-03-18.

nih.gov

pubmed.ncbi.nlm.nih.gov

Winfree, E.; Liu, F.; Wenzler, L.A.; Seeman, N.C. (1998), "Design and self-assembly of two-dimensional DNA crystals", Nature, 394 (6693): 539–544, Bibcode:1998Natur.394..539W, doi:10.1038/28998, PMID 9707114, S2CID 4385579.

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, MR 0297572, S2CID 14259496.
Jeandel, Emmanuel; Rao, Michaël (2021), "An aperiodic set of 11 Wang tiles", Advances in Combinatorics: 1:1–1:37, arXiv:1506.06492, doi:10.19086/aic.18614, MR 4210631, S2CID 13261182. (Showed an aperiodic set of 11 tiles with 4 colors, and proved that fewer tiles or fewer colors cannot be aperiodic.)
Winfree, E.; Liu, F.; Wenzler, L.A.; Seeman, N.C. (1998), "Design and self-assembly of two-dimensional DNA crystals", Nature, 394 (6693): 539–544, Bibcode:1998Natur.394..539W, doi:10.1038/28998, PMID 9707114, S2CID 4385579.
Neyret, Fabrice; Cani, Marie-Paule (1999), "Pattern-Based Texturing Revisited", Proceedings of the 26th annual conference on Computer graphics and interactive techniques - SIGGRAPH '99 (PDF), Los Angeles, United States: ACM, pp. 235–242, doi:10.1145/311535.311561, ISBN 0-201-48560-5, S2CID 11247905. Introduces stochastic tiling.
Cohen, Michael F.; Shade, Jonathan; Hiller, Stefan; Deussen, Oliver (2003), "Wang tiles for image and texture generation", ACM SIGGRAPH 2003 Papers on - SIGGRAPH '03 (PDF), New York, NY, USA: ACM, pp. 287–294, doi:10.1145/1201775.882265, ISBN 1-58113-709-5, S2CID 207162102, archived from the original (PDF) on 2006-03-18.
Wei, Li-Yi (2004), "Tile-based texture mapping on graphics hardware", Proceedings of the ACM SIGGRAPH/EUROGRAPHICS Conference on Graphics Hardware (HWWS '04), New York, NY, USA: ACM, pp. 55–63, doi:10.1145/1058129.1058138, ISBN 3-905673-15-0, S2CID 53224612. Applies Wang Tiles for real-time texturing on a GPU.
. Kopf, Johannes; Cohen-Or, Daniel; Deussen, Oliver; Lischinski, Dani (2006), "Recursive Wang tiles for real-time blue noise", ACM SIGGRAPH 2006 Papers on - SIGGRAPH '06, New York, NY, USA: ACM, pp. 509–518, doi:10.1145/1179352.1141916, ISBN 1-59593-364-6, S2CID 11007853. Shows advanced applications.

stanford.edu

graphics.stanford.edu

Wei, Li-Yi (2004), "Tile-based texture mapping on graphics hardware", Proceedings of the ACM SIGGRAPH/EUROGRAPHICS Conference on Graphics Hardware (HWWS '04), New York, NY, USA: ACM, pp. 55–63, doi:10.1145/1058129.1058138, ISBN 3-905673-15-0, S2CID 53224612. Applies Wang Tiles for real-time texturing on a GPU.

toronto.edu

dgp.toronto.edu

Stam, Jos (1997), Aperiodic Texture Mapping (PDF). Introduces the idea of using Wang tiles for texture variation, with a deterministic substitution system.

web.archive.org

Cohen, Michael F.; Shade, Jonathan; Hiller, Stefan; Deussen, Oliver (2003), "Wang tiles for image and texture generation", ACM SIGGRAPH 2003 Papers on - SIGGRAPH '03 (PDF), New York, NY, USA: ACM, pp. 287–294, doi:10.1145/1201775.882265, ISBN 1-58113-709-5, S2CID 207162102, archived from the original (PDF) on 2006-03-18.