Matching rules and substitution tilings

Annals of Mathematics

Volumn 147, Issue 1, 1998, Pages 181-223

  Goodman Strauss, Chaim ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032399384     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.2307/120988     Document Type: Article

References (25)

1. R. BERGER, The Undecidability of the Domino Problem, Memoirs A. M. S. 66 (1966).
2. J. H. CONWAY and C. RADIN, Quaquaversal tilings and rotation, to appear in Inventiones.
3. N. G. DE BRUIJN, Algebraic theory of Penrose's non-periodic tilings, Nederl. Akad. Wentensch Proc. Ser. A 84 (1981), 39-66.
4. L. DANZER, A family of 3D-spacefillers not permitting any periodic or quasiperiodic tiling, preprint.
5. L. DANZER, personal communication.
6. C. GOODMAN-STRAUSS, Addressing in substitution tilings, in preparation.
7. _, Aperiodic hierarchical tilings, to appear in Foams, NATO-ASI (1998).
8. n for all n > 1, in preparation.
9. _, Matching rules and markings, in preparation.
10. _, A small set of aperiodic tiles, preprint.
11. B. GRUNBAUM and G. C. SHEPHERD, Tilings and Patterns, W.H. Freeman and Co. (1989).
12. J. KARI, A small aperiodic set of Wang tiles, Discrete Math. 160 (1996), 259-264.
13. R. KENYON, Self similar tilings, thesis, Princeton University, 1990.
14. T. T. Q. LE, Local rules for quasiperiodic tilings, Proc. of NATO Advanced Studies Inst., The Mathematics of Long Range Aperiodic Order (ed. R. Moody), pp. 331-366.
15. S. MOZES, Tilings, substitution systems and dynamical systems generated by them, J. D'Analyse Math. 53 (1989), 139-186.
16. R. PENROSE, The role of aesthetics in pure and applied mathematical research, Bull. Inst. of Math. and its Appl. 10 (1974), 266-271.
17. C. RADIN, The pinwheel tilings of the plane, Ann. of Math. 139 (1994), 661-702.
18. R. ROBINSON, Undecidability and nonperiodicity of tilings in the plane, Inv. Math. 12 (1971), 177.
19. L. SADUN, Some generalizations of the pinwheel tiling, preprint.
20. M. SENECHAL, Quasicrystals and Geometry, Cambridge University Press (1995).
21. P. STEINHARDT and S. OSTLUND, The Physics of Quasicrystals, World Scientific (1987).
22. J. SOCOLAR, personal communication.
23. B. SOLOMYAK, Non-periodicity implies unique composition for self-similar translationally-finite tilings, to appear in J. Disc. and Comp. Geometry.
24. W. THURSTON, Groups, tilings and finite state automata: Summer 1989 AMS Coll. Lect., GCG 1, Geometry Center.
25. P. WALTERS, editor, Symbolic Dynamics and its Applications, Contemporary Mathematics 135 (1992).