Fractal Penrose tilings. I: Construction and matching rules

DOI10.1007/BF02215977zbMath0882.52008MaRDI QIDQ1356812

Petra Gummelt, Christoph Bandt

Publication date: 3 February 1998

Published in: Aequationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/137689

zbMATH Keywords

inflationfractalsself-similar setskitesquasiperiodic tilingsaperiodic prototilesdartsPenrose tiles

Mathematics Subject Classification ID

Fractals (28A80) Tilings in (2) dimensions (aspects of discrete geometry) (52C20)

Related Items (max. 100)

On single-matrix graph-directed iterated function systems ⋮ Fractal Penrose tiles. II: Tiles with fractal boundary as duals of Penrose triangles ⋮ Algorithm for determining pure pointedness of self-affine tilings ⋮ INTERSECTIONS OF SELF-SIMILAR SETS ⋮ A fractal version of the pinwheel tiling ⋮ Fractal tilings from iterated function systems ⋮ Tilings from graph directed iterated function systems ⋮ Substitutions with vanishing rotationally invariant first cohomology ⋮ Developments in fractal geometry

Cites Work

• Self-similar sets. III: Constructions with sofic systems
• Quasicrystals: The view from Les Houches
• The pinwheel tilings of the plane
• Fractal Penrose tiles. II: Tiles with fractal boundary as duals of Penrose triangles
• Tilings, substitution systems and dynamical systems generated by them
• Hausdorff Dimension in Graph Directed Constructions
• Quasiperiodic tilings with tenfold symmetry and equivalence with respect to local derivability
• Dynamics of self-similar tilings
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