Geodesic
Inductive rotation tilings
Informatics and Automation, Geometry, topology, and applications, Tome 288 (2015), pp. 269-280.

Voir la notice de l'article provenant de la source Math-Net.Ru

A new method for constructing aperiodic tilings is presented. The method is illustrated by constructing a particular tiling and its hull. The properties of this tiling and the hull are studied. In particular, it is shown that these tilings have a substitution rule and that they are nonperiodic, aperiodic, limit-periodic and pure point diffractive. 
@article{TRSPY_2015_288_a18,
     author = {Dirk Frettl\"oh and Kurt Hofstetter},
     title = {Inductive rotation tilings},
     journal = {Informatics and Automation},
     pages = {269--280},
     publisher = {mathdoc},
     volume = {288},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2015_288_a18/}
}
TY  - JOUR
AU  - Dirk Frettlöh
AU  - Kurt Hofstetter
TI  - Inductive rotation tilings
JO  - Informatics and Automation
PY  - 2015
SP  - 269
EP  - 280
VL  - 288
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2015_288_a18/
LA  - en
ID  - TRSPY_2015_288_a18
ER  - 
%0 Journal Article
%A Dirk Frettlöh
%A Kurt Hofstetter
%T Inductive rotation tilings
%J Informatics and Automation
%D 2015
%P 269-280
%V 288
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2015_288_a18/
%G en
%F TRSPY_2015_288_a18
Dirk Frettlöh; Kurt Hofstetter. Inductive rotation tilings. Informatics and Automation, Geometry, topology, and applications, Tome 288 (2015), pp. 269-280. http://geodesic.mathdoc.fr/item/TRSPY_2015_288_a18/

[1] Baake M., Grimm U., Aperiodic order. V. 1: A mathematical invitation, Cambridge Univ. Press, Cambridge, 2013 | MR

[2] Dolbilin N.P., Lagarias J.C., Senechal M., “Multiregular point systems”, Discrete Comput. Geom., 20:4 (1998), 477–498 | DOI | MR | Zbl

[3] Frettlöh D., Richard C., “Dynamical properties of almost repetitive Delone sets”, Discrete Contin. Dyn. Syst., 34:2 (2014), 531–556 | MR | Zbl

[4] Frettlöh D., Sing B., “Computing modular coincidences for substitution tilings and point sets”, Discrete Comput. Geom., 37:3 (2007), 381–407 | DOI | MR | Zbl

[5] Grünbaum B., Shephard G.C., Tilings and patterns, W.H. Freeman, New York, 1987 | MR | Zbl

[6] Harriss E., Frettlöh D., Tilings encyclopedia http://tilings.math.uni-bielefeld.de/

[7] Hof A., “On diffraction by aperiodic structures”, Commun. Math. Phys., 169:1 (1995), 25–43 | DOI | MR | Zbl

[8] Hofstetter K., New irrational patterns http://hofstetterkurt.net/ip

[9] Lagarias J.C., Pleasants P.A.B., “Repetitive Delone sets and quasicrystals”, Ergodic Theory Dyn. Syst., 23:3 (2003), 831–867 | DOI | MR | Zbl

[10] Lee J.-Y., Moody R.V., Solomyak B., “Pure point dynamical and diffraction spectra”, Ann. Henri Poincaré, 3:5 (2002), 1003–1018 | DOI | MR | Zbl

[11] Lee J.-Y., Moody R.V., Solomyak B., “Consequences of pure point diffraction spectra for multiset substitution systems”, Discrete Comput. Geom., 29:4 (2003), 525–560 | DOI | MR | Zbl

[12] Parzer S., Irrational image generator, Diploma thesis, Vienna Univ. Technol., Vienna, 2013

[13] Penrose R., “The rôle of aesthetics in pure and applied mathematical research”, Bull. Inst. Math. Appl., 10 (1974), 266–271

[14] Radin C., Wolff M., “Space tilings and local isomorphism”, Geom. dedicata, 42:3 (1992), 355–360 | DOI | MR | Zbl

[15] Schlottmann M., “Generalized model sets and dynamical systems”, Directions in mathematical quasicrystals, CRM Monogr. Ser., 13, eds. M. Baake, R.V. Moody, Amer. Math. Soc., Providence, RI, 2000, 143–159 | MR | Zbl

[16] Shechtman D., Blech I., Gratias D., Cahn J.W., “Metallic phase with long-range orientational order and no translational symmetry”, Phys. Rev. Lett., 53:20 (1984), 1951–1954 | DOI

[17] Solomyak B., “Nonperiodicity implies unique composition for self-similar translationally finite tilings”, Discrete Comput. Geom., 20:2 (1998), 265–279 | DOI | MR | Zbl

[18] Wikipedia contributors, Substitution tiling, Wikipedia: The free encyclopedia. Sept. 16, 2014. http://en.wikipedia.org/wiki/Substitution_tiling