-algebras, Ergodic
Theory Dynam. Systems 18 (1998), no. 3, 509–537, DOI 10.1017/S0143385798100457.
MR1631708[AA20]
Shigeki Akiyama and Pierre Arnoux (eds.), Substitution
and tiling dynamics: introduction to self-inducing structures, Lecture
Notes in Mathematics, vol. 2273, Springer, Cham,
2020. CIRM Jean-Morlet Chair, Fall 2017; Lecture notes
from the Tiling Dynamical Systems research school held
as part of Tilings and Discrete Geometry program, DOI 10.1007/978-3-030-57666-0. MR4200104
[AS99]
Jean-Paul Allouche and Jeffrey Shallit, The
ubiquitous Prouhet-Thue-Morse sequence,
Sequences and their applications (Singapore, 1998), Springer Ser. Discrete Math. Theor.
Comput. Sci., Springer, London, 1999, pp. 1–16. MR1843077
[AP98]
Jared E. Anderson and Ian F. Putnam, Topological
invariants for substitution tilings and their associated -algebras, Ergodic
Theory Dynam. Systems 18 (1998), no. 3, 509–537, DOI 10.1017/S0143385798100457.
MR1631708
[BGM19]
Michael Baake, Franz Gähler, and Neil Mañibo, Renormalisation of pair correlation measures for
primitive inflation rules
and absence of absolutely continuous diffraction, Comm. Math. Phys. 370 (2019),
no. 2, 591–635, DOI 10.1007/s00220-019-03500-w.
MR3994581
[BG13]
Michael Baake and Uwe Grimm, Aperiodic order. Vol. 1,
Encyclopedia of Mathematics and its Applications, vol.
149, Cambridge University Press, Cambridge, 2013. A mathematical
invitation; With a foreword by Roger Penrose, DOI
10.1017/CBO9781139025256. MR3136260
[CS06]
Alex Clark and Lorenzo Sadun, When shape matters: deformations of tiling spaces,
Ergodic Theory Dynam. Systems 26 (2006),
no. 1, 69–86, DOI 10.1017/S0143385705000623. MR2201938
[CN16]
María Isabel Cortez and Andrés Navas, Some
examples of repetitive, nonrectifiable Delone sets,
Geom. Topol. 20 (2016), no. 4, 1909–1939, DOI 10.2140/gt.2016.20.1909. MR3548461
[dB81]
N. G. de Bruijn, Algebraic theory of Penrose’s nonperiodic tilings of the
plane. I, II, Nederl. Akad. Wetensch. Indag. Math.
43 (1981),
no. 1, 39–52, 53–66. MR609465
[GKM15]
Franz Gähler, Eugene E. Kwan, and Gregory R. Maloney, A computer search for planar substitution tilings with 𝑛-fold
rotational symmetry, Discrete Comput. Geom. 53 (2015), no. 2, 445–465. MR3316232
[GL89]
C. Godrèche and J. M. Luck, Quasiperiodicity and randomness in tilings of the plane, J.
Statist. Phys. 55 (1989), no. 1-2, 1–28. MR1003500
[GMRS23]
P. Gohlke, A. Mitchell, D. Rust, and T. Samuel, Measure Theoretic Entropy of Random Substitution
Subshifts, Ann.
Henri Poincaré 24 (2023), no. 1, 277–323. MR4533524
[GT22]
Rachel Greenfeld and Terence Tao, A counterexample to the periodic tiling conjecture,
Preprint, arXiv:arXiv:2209.08451,
2022.
[GS16]
B. Grünbaum and G.C. Shephard, Tilings and patterns, Second Edition, Dover Books on Mathematics Series, Dover Publications, Incorporated, 2016.
[JS18]
Antoine Julien and Lorenzo Sadun, Tiling deformations, cohomology, and orbit equivalence of
tiling spaces, Ann. Henri Poincaré 19 (2018),
no. 10, 3053–3088, DOI 10.1007/s00023-018-0713-3. MR3851781
[KLS15]
Johannes Kellendonk, Daniel Lenz, and Jean Savinien (eds.), Mathematics
of aperiodic order, Progress in Mathematics,
vol. 309, Birkhäuser/Springer, Basel, 2015, DOI 10.1007/978-3-0348-0903-0. MR3380566
[Lan40]
C. Dudley Langford, 1464. uses of a geometric puzzle, The Mathematical Gazette 24 (1940),
no. 260, 209–211.
[MRST22]
Eden Miro, Dan Rust, Lorenzo Sadun, and Gwendolyn Tadeo, Topological mixing of random substitutions,
Israel J.
Math. (2022).
[Sad08]
Lorenzo Sadun, Topology of tiling spaces,
University Lecture
Series, vol. 46, American Mathematical Society,
Providence, RI, 2008, DOI 10.1090/ulect/046. MR2446623
[Sol97]
Boris Solomyak, Dynamics of self-similar tilings,
Ergodic Theory
Dynam. Systems 17 (1997), no. 3, 695–738, DOI 10.1017/S0143385797084988. MR1452190