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Penrose tiling

A. Glassner
1998 IEEE Computer Graphics and Applications  
Penrose tiling.  ...  A popular account of Penrose tiles appears in Martin Gardner's book Penrose Tilings to Trapdoor Ciphers (W.H. Freeman, New York, 1989) .  ... 
doi:10.1109/38.689670 fatcat:oql7qdpddfaujdwo5dfoirh5uq

Penrose tiling approximants

O. Entin-Wohlman, M. Kléman, A. Pavlovitch
1988 Journal de Physique  
Abstract. 2014 The modification of the Penrose tiling into a periodic structure is considered.  ...  2014 Nous considérons les structures obtenues en modifiant un pavage de Penrose en un pavage périodique.  ...  Penrose tiling approximants. 3.1 THE PERFECT TILING. -The detailed geometrical description of the Penrose tiling was given by de Bruijn [17] .  ... 
doi:10.1051/jphys:01988004904058700 fatcat:kqfcnfisongclfppgkoq5x3hne

Deformed Penrose tilings

T.R. Welberry, B. Sing
2007 Philosophical Magazine  
Monte Carlo (MC) simulation of a model quasicrystal (2D Penrose rhomb tiling) shows that the kinds of local distortions that result from size-effect-like relaxations are in fact very similar to mathematical  ...  The resulting model sets are all topologically equivalent to the Penrose tiling (same connectedness), are perfectly quasicrystalline but show an enormous variation in the Bragg peak intensities.  ...  The 2D Penrose rhomb tiling is an example of such a model set.  ... 
doi:10.1080/14786430701364978 fatcat:3zdkrbnmxvgm3avh53vu2af6fy

Deformed Penrose tilings

T. R. Welberry, A. G. Beasley, B. Sing
2006 Acta Crystallographica Section A Foundations of Crystallography  
The resulting model sets are all topologically equivalent to the Penrose tiling (same connectedness), are perfectly quasicrystalline but show an enormous variation in the Bragg peak intensities.  ...  In this paper we demonstrate that simple deformed model sets can be constructed, based on the simple Penrose rhomb tiling, by using deformations which are defined in terms of the local (nearest neighbour  ... 
doi:10.1107/s0108767306099090 fatcat:hbeuci7wm5fw5ghhhns5yiy7ly

Stripes on Penrose tilings

A Hizume, Y Yamagishi
2010 Journal of Physics A: Mathematical and Theoretical  
Introduction One dimensional quasicrystal structure on the Penrose tiling ( [1] ) was first recognized as the musical sequence of Ammann bars [3] .  ...  Theorem Let Λ P ⊂ C be a Penrose set. Let w ∈ C, w = 0. If wR ∩ Z[ζ] = 0, ζ = e 2π √ −1/5 , then the quotient (Λ P + wR)/(wR) is a one-dimensional cut-and-project set.  ... 
doi:10.1088/1751-8113/44/1/015202 fatcat:4isfpfatcfa6rbbs2nd3jxdhme

Homogenization of Penrose tilings

Andrea Braides, Giuseppe Riey, Margherita Solci
2009 Comptes rendus. Mathematique  
Remark 1 (characterization of Penrose tilings). The tiling obtained by joining p and p in P by an edge if and only if |p − p | = 1 is a Penrose tiling.  ...  Theorem 2.1 (homogenization of Penrose tilings). Let f be as above.  ... 
doi:10.1016/j.crma.2009.03.019 fatcat:h22hw73kbjhcdb2xlplkh222gi

Penrose Tilings as Jammed Solids

Olaf Stenull, T. C. Lubensky
2014 Physical Review Letters  
Penrose tilings form lattices, exhibiting 5-fold symmetry and isotropic elasticity, with inhomogeneous coordination much like that of the force networks in jammed systems.  ...  To model this property in Penrose tilings, we follow Ref.  ...  unit cells of increasing size, that approach the 5-fold Penrose tiling as n → ∞.  ... 
doi:10.1103/physrevlett.113.158301 pmid:25375746 fatcat:kdhni7jyfzau3o4eqqlm2xfuhu

-algebras of Penrose hyperbolic tilings

Hervé Oyono-Oyono, Samuel Petite
2011 Journal of Geometry and Physics  
Penrose hyperbolic tilings are tilings of the hyperbolic plane which admit, up to affine transformations a finite number of prototiles.  ...  In this paper, we give a complete description of the C * -algebras and of the K-theory for such tilings.  ...  Besides its famous Euclidean tiling, Penrose in [15] constructs a finite affine type tiling made with a single prototile which is not stable for any Fuchsian group.  ... 
doi:10.1016/j.geomphys.2010.09.019 fatcat:v2nrz26vmfdwjempgkxib4iqi4

Inflationary character of Penrose tilings

Yuval Gefen, Maurice Kléman, Andrdi Pavlovitch, Jacques Peyrière
1988 Journal de Physique  
We also study a special type of inflated defects in a deterministic Penrose tiling.  ...  Abstract. 2014 The inflation of Penrose tilings is described by means of Transfer Matrices of Fractals (TMFs) which emphasize the self-similar nature of these aperiodic tilings.  ...  In the appendix we discuss a relation between the 6 shape tiling and the 9 shape tiling presented earlier. A Penrose tiling with six tiles.  ... 
doi:10.1051/jphys:019880049070111100 fatcat:malenf7uxnem7jff5z5v5jzxvy

Classical Dimers on Penrose Tilings [article]

Felix Flicker, Steven H. Simon, S. A. Parameswaran
2019 arXiv   pre-print
We find that Penrose tilings do not admit perfect matchings (defect-free dimer coverings).  ...  We study the classical dimer model on rhombic Penrose tilings, whose edges and vertices may be identified with those of a bipartite graph.  ...  The Penrose Dart-Kite (P2) Tiling The Penrose P2 tiling consists of two tiles, referred to by Penrose as the dart and kite.  ... 
arXiv:1902.02799v2 fatcat:6shlilzqing3tl33roowzvesve

Classical Dimers on Penrose Tilings

Felix Flicker, Steven H. Simon, S. A. Parameswaran
2020 Physical Review X  
We find that Penrose tilings do not admit perfect matchings (defectfree dimer coverings).  ...  We study the classical dimer model on rhombic Penrose tilings, whose edges and vertices may be identified as those of a bipartite graph.  ...  The Penrose dart-kite (P2) tiling The Penrose P2 tiling consists of two tiles referred to by Penrose as the dart and kite.  ... 
doi:10.1103/physrevx.10.011005 fatcat:ys2wofyc4rc3lit5n2us5lir6a

Symmetry properties of Penrose type tilings

N. Cotfas
2008 Philosophical Magazine  
., where τ =(1+√(5))/2, are scaling factors of the Penrose tiling.  ...  The Penrose tiling is directly related to the atomic structure of certain decagonal quasicrystals and, despite its aperiodicity, is highly symmetric.  ...  The best known and by far most studied aperiodic tiling of plane is the Penrose tiling [1, 2] .  ... 
doi:10.1080/14786430802035691 fatcat:dfujardwizb6zj4apb4vjkv5ka

A noncommutative theory of Penrose tilings [article]

Christopher J. Mulvey, Pedro Resende
2005 arXiv   pre-print
Considering quantales as generalised noncommutative spaces, we address as an example a quantale Pen based on the Penrose tilings of the plane.  ...  tilings from which its representation as a quotient of Cantor space is recovered.  ...  the Penrose tilings of the plane.  ... 
arXiv:math/0306361v2 fatcat:l5v3xaatlffejdkr6x4of3eqcm

Energy landscape in a Penrose tiling

Patrizia Vignolo, Matthieu Bellec, Julian Böhm, Abdoulaye Camara, Jean-Marc Gambaudo, Ulrich Kuhl, Fabrice Mortessagne
2016 Physical review B  
Here, we report on measurements and energy-scaling analysis of the gap labelling and the spatial intensity distribution of the eigenstates for a microwave Penrose-tiled quasicrystal.  ...  (a) Diamond-vertex Penrose-tiled quasicrystal, where the tiling is superposed to guide the eye (thin diamonds in green).  ...  A typical example is given by the Penrose tiling [14] . Here, we implement a microwave realisation of a Penrose-tiled lattice using a set of coupled dielectric resonators [see Fig. 1 (a) ].  ... 
doi:10.1103/physrevb.93.075141 fatcat:i6ilazccl5dz5n6seb5wif6ivm

Diffusive Limits on the Penrose Tiling

A. Telcs
2010 Journal of statistical physics  
In this paper random walks on the Penrose lattice are investigated. Heat kernel estimates and the invariance principle are shown.  ...  This applies to generalized Penrose tilings (produced by p-grids), higher dimensional Penrose tilings and stochastic tilings. Remark 18 1.  ...  Let us consider the original Penrose tiling and pentagrid.  ... 
doi:10.1007/s10955-010-0072-z fatcat:p4aqlpqrv5aglc7mbkyputk7xy
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