Substitution rules for aperiodic sequences of the cut and project type

Journal of Physics A: Mathematical and General

Volumn 33, Issue 48, 2000, Pages 8867-8886

  Masáková, Zuzana ^a   Patera, Jiří ^b   Pelantová, Edita ^a  

^a CZECH TECHNICAL UNIVERSITY IN PRAGUE   (Czech Republic)

^b UNIVERSITÉ DE MONTRÉAL   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034623744     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/33/48/319     Document Type: Article

References (16)

1. Allouche J P and Mendès France M 1995 Automata and automatic sequences Beyond Quasicrystals ed F Axel and D Gratias (Les Editions de Physique) pp 293-367
2. Baake M and Moody R V 1998 Similarity submodules and semigroups Quasicrystals and Discrete Geometry vol 10, ed J Patera (Fields Institute Monographs) (Providence, RI: American Mathematical Society) pp 1-14
3. Bombieri E and Taylor J E 1987 Quasicrystals, tilings, and algebraic number theory: some preliminary connections Contemp. Math. vol 64 (Providence, RI: American Mathematical Society) pp 241-64
4. Gähler F and Klitzing R 1996 The diffraction pattern of self-similar tilings Proc. NATO ASI: Mathematics of Long Range Aperiodic Order (Waterloo, 1996) ed R V Moody (Dordrecht: Kluwer) pp 141-74
5. Guimond L-S and Patera J 2000 Proving the deterministic period breaking of linear congruential generators using two tile quasicrystals Math. Comput. at press
6. Lamb J S W 1994 On the canonical projection method for one-dimensional quasicrystals and invertible substitution rules J. Phys. A: Math. Gen. 31 L331-6
7. Luck J M, Godrèche C, Janner A and Janssen T 1993 The nature of atomic surfaces of quasiperiodic self-similar structures J. Phys. A: Math. Gen. 26 1951-99
8. Lunnon W F and Pleasants P 1992 Characterization of two-distance sequences J. Austral. Math. Soc. (Series A) 53 198-218
9. Masáková Z, Patera J and Pelantová E 1998 Inflation center of the cut and project quasicrystals J. Phys. A: Math. Gen. 31 1443-53
10. Masáková Z, Patera J and Pelantová E 2000 Lattice-like properties of quasicrystal models with quadratic irrationalities Proc. Quantum Theory and Symmetries (Goslar, 1999) ed H D Doebner, V K Dobrev, J D Hennig and W Luecke (Singapore: World Scientific) pp 499-509
11. Moody R V and Patera J 1993 Quasicrystals and icosians J. Phys. A: Math. Gen. 26 2829-53
12. Parry W 1960 On the β-expansions of real numbers Acta Math. Acad. Sci. Hung. 11 401-16
13. Jan Patera 2000 Oral communication
14. Queffélec M 1995 Spectral study of automatic and substitutive sequences Beyond Quasicrystals ed F Axel and D Gratias (Les Editions de Physique) pp 369-414
15. Wen Z-Y, Wijnands F and Lamb J S W 1994 A natural class of generalized Fibonacci chains J. Phys. A: Math. Gen. 27 3689-706
16. Zieliński R 1990 An aperiodic pseudorandom number generator J. Comput. Appl. Math. 31 205-10