Quasiperiodicity and randomness in tilings of the plane

Journal Article · Sat Apr 01 04:00:00 EST 1989 · Journal of Statistical Physics; (USA)

DOI:https://doi.org/10.1007/BF01042590· OSTI ID:5551645

Godreche, C; Luck, J M ^[1]

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1. CEN Saclay, Gif-sur-Yvette (France)

The authors define new tilings of the plane with Robinson triangles, by means of generalized inflation rules, and study their Fourier spectrum. Penrose's matching rules are not obeyed; hence the tilings exhibit new local environments, such as three different bond lengths, as well as new patterns at all length scales. Several kinds of such generalized tilings are considered. A large class of deterministic tilings, including chiral tilings, is strictly quasiperiodic, with a tenfold rotationally symmetric Fourier spectrum. Random tilings, either locally (with extensive entropy) or globally random (without extensive entropy), exhibit a mixed (discrete + continuous) diffraction spectrum, implying a partial perfect long-range order.

• OSTI ID: 5551645
• Journal Information: Journal of Statistical Physics; (USA), Journal Name: Journal of Statistical Physics; (USA) Vol. 55:1-2; ISSN 0022-4715; ISSN JSTPB
• Country of Publication: United States
• Language: English

Related Subjects

656002* -- Condensed Matter Physics-- General Techniques in Condensed Matter-- (1987-)
657002 -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
CHIRAL SYMMETRY
COHERENT SCATTERING
CRYSTAL MODELS
DIFFRACTION
ENTROPY
FOURIER TRANSFORMATION
GEOMETRY
INTEGRAL TRANSFORMATIONS
ITERATIVE METHODS
MATHEMATICAL MANIFOLDS
MATHEMATICAL MODELS
MATHEMATICS
MATRICES
MECHANICS
MESH GENERATION
ONE-DIMENSIONAL CALCULATIONS
ORDER PARAMETERS
PHYSICAL PROPERTIES
RANDOMNESS
RECURSION RELATIONS
SCATTERING
SPECTRA
STATISTICAL MECHANICS
SYMMETRY
THERMODYNAMIC PROPERTIES
TRANSFORMATIONS
VARIATIONS