Aperiodic Tilings with One Prototile and Low Complexity Atlas Matching Rules

1. Baake, M., Schlottmann, M., Jarvis, P.D.: Quasiperiodic tilings with tenfold symmetry and equivalence with respect to local derivability. J. Phys. A 19, 4637–4654 (1991). MR1132337

   Article  MathSciNet  Google Scholar 

2. Berger, R.: The undecidability of the domino problem. Mem. Am. Math. Soc. 66 (1966)

3. Clark, A., Sadun, L.: When shape matters: deformations of tiling spaces. Ergod. Theory Dyn. Syst. 26, 69–86 (2006). doi:10.1017/S0143385705000623

   Article  MATH  MathSciNet  Google Scholar 

4. Culik, K. II: An aperiodic set of 13 Wang tiles. Discrete Math. 160(1–3), 245–251 (1996)

   Article  MATH  MathSciNet  Google Scholar 

5. Kari, J.: A small aperiodic set of Wang tiles. Discrete Math. 160(1–3), 259–264 (1996)

   Article  MATH  MathSciNet  Google Scholar 

6. Kari, J., Culik, K. II: An aperiodic set of Wang cubes. J. Univers. Comput. Sci. 1(10), 675–686 (1995)

   MATH  MathSciNet  Google Scholar 

7. Goodman-Strauss, C.: Open questions in tilings. January 10, 2000. http://comp.uark.edu/~strauss/papers/survey.pdf

8. Grünbaum, B., Shepherd, G.C.: Tilings and Patterns. W.H. Freeman, San Francisco (1987)

   MATH  Google Scholar 

9. Gummelt, P.: Penrose tilings as coverings of congruent decagons. Geom. Dedic. 62(1) (1996). doi:10.1007/BF00239998

10. Mozes, S.: Aperiodic tilings. Invent. Math. 128, 603–611 (1997)

    Article  MATH  MathSciNet  Google Scholar 

11. Myers, J.: http://www.srcf.ucam.org/~jsm28/tiling/

12. Penrose, R.: Role of aesthetics in pure and applied research. Bull. Inst. Math. Appl. 10, 266–271 (1974)

    Google Scholar 

13. Robinson, R.M.: Undecidability and nonperiodicity for tilings of the plane. Invent. Math. 12(3), 177–209 (1971)

    Article  MathSciNet  Google Scholar 

14. Sadun, L.: Topology of Tiling Spaces. University Lecture Series, vol. 46 (2008)

15. Socolar, J.E.S.: More ways to tile with only one shape polygon. Math. Intell. 29(2) (2007). doi:10.1007/BF02986203

16. Socolar, J.E.S., Taylor, J.M.: An aperiodic hexagonal tile. http://arxiv.org/abs/1003.427

17. Wang, H.: Proving theorems by pattern recognition II. Bell Syst. Tech. J. 40(1), 1–41 (1961)

    Google Scholar 

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