|
Symmetry of tilings of the plane
Author(s):
Charles
Radin
Journal:
Bull. Amer. Math. Soc.
29
(1993),
213-217.
MSC (2000):
Primary 28D05;
Secondary 52C20
MathSciNet review:
1215313
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
We discuss two new results on tilings of the plane. In the first, we give sufficient conditions for the tilings associated with an inflation rule to be uniquely ergodic under translations, the conditions holding for the pinwheel inflation rule. In the second result we prove there are matching rules for the pinwheel inflation rule, making the system the first known to have complete rotational symmetry.
References:
-
- [1]
- I. Cornfeld, S. Fomin, and Ya. Sinai, Ergodic theory, Springer-Verlag, New York, 1982. MR 832433 (87f:28019)
- [2]
- S. Dworkin, Spectral theory and X-ray diffraction, J. Math. Phys. (to appear). MR 1224190 (94g:82049)
- [3]
- M. Gardner, Extraordinary nonperiodic tiling that enriches the theory of tiles, Sci. Am. (USA) 236(1977), 110-119.
- [4]
- B. Grünbaum and G. C. Shephard, Tilings and patterns, Freeman, New York, 1986.
- [5]
- S. Mozes, Tilings, substitution systems and dynamical systems generated by them, J. Analyse Math. 53(1989), 139-186. MR 1014984 (91h:58038)
- [6]
- C. Radin, Global order from local sources, Bull. Amer. Math. Soc. (N.S.) 25 (1991), 335-364. MR 1094191 (92e:82007)
- [7]
- -, The pinwheel tilings of the plane, Ann. of Math. (2) (to appear). MR 1283873 (95d:52021)
- [8]
- -, Space tilings and substitutions, Univ. of Texas, preprint.
- [9]
- C. Radin and M. Wolff, Space tilings and local isomorphism, Geom. Dedicata 42 (1992), 355-360. MR 1164542 (93c:52019)
Similar Articles:
Retrieve articles in Bulletin of the American Mathematical Society
with MSC
(2000):
28D05, 52C20
Retrieve articles in all Journals with MSC
(2000):
28D05, 52C20
Additional Information:
DOI:
10.1090/S0273-0979-1993-00425-7
PII:
S 0273-0979(1993)00425-7
Copyright of article:
Copyright
1993,
American Mathematical Society
|
