Fractal Penrose tilings. I: Construction and matching rules
type: Item
instance of: scholarly article
title: Fractal Penrose tilings. I: Construction and matching rules
zbMATH Open document ID: 0882.52008
DOI: 10.1007/BF02215977
published in: Aequationes Mathematicae
publication date: 1998-02-03T00:00:00Z
full work available at URL: https://eudml.org/doc/137689
review text: The authors describe two aperiodic pairs of fractal prototiles, new versions of the famous Penrose tiles which are derived from the `kites and darts', and the pair of rhombs. They are interesting because they are strictly self-similar, and their matching conditions are defined by the shape of the tiles, only.
Mathematics Subject Classification ID: 52C20
Mathematics Subject Classification ID: 28A80
zbMATH DE Number: 1019199
zbMATH Keywords: Penrose tiles
zbMATH Keywords: kites
zbMATH Keywords: darts
zbMATH Keywords: quasiperiodic tilings
zbMATH Keywords: aperiodic prototiles
zbMATH Keywords: fractals
zbMATH Keywords: self-similar sets
zbMATH Keywords: inflation
author: Christoph Bandt
author: Petra Gummelt
MaRDI profile type: Publication
cites work: Quasiperiodic tilings with tenfold symmetry and equivalence with respect to local derivability
cites work: Self-similar sets. III: Constructions with sofic systems
cites work: Fractal Penrose tiles. II: Tiles with fractal boundary as duals of Penrose triangles
cites work: Q3735714
cites work: Q4027593
cites work: Hausdorff Dimension in Graph Directed Constructions
cites work: Tilings, substitution systems and dynamical systems generated by them
cites work: The pinwheel tilings of the plane
cites work: Q4837266
cites work: Quasicrystals: The view from Les Houches
cites work: Dynamics of self-similar tilings
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description: scientific article; zbMATH DE number 1019199