Wang tile (English Wikipedia)

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

refsWebsite

Global rank English rank

14doi.org

2^nd place

7ams.org

451^st place

277^th place

7semanticscholar.org

11^th place

8^th place

3harvard.edu

18^th place

17^th place

1jstor.org

26^th place

20^th place

1arxiv.org

69^th place

59^th place

1jucs.org

low place

1nih.gov

4^th place

1toronto.edu

low place

8,821^st place

1inria.fr

4,903^rd place

3,679^th place

1web.archive.org

1^st place

1microsoft.com

153^rd place

151^st place

1stanford.edu

179^th place

183^rd place

1johanneskopf.de

low place

1books.google.com

3^rd place

ams.org

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 non periodicity 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 non periodicity 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 non periodicity 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 non periodicity 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.