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1994•Philosophical Magazine LettersRequires access

Two-colour Penrose tiling

X. Z. Li, J- M. Dusois, K. H. Kuo

Open publisher page 18 citations

Abstract

Penrose tiling is a two-dimensional quasiperiodic pattern, which is composed of two tiles, namely thick and thin rhombi. In this letter, white and black colours are given to the tiles to distinguish their top and bottom surfaces. Then, a two-colour Penrose tiling is yielded by the white black rhombi. The new pattern is a three-dimensional array and its projection is considered as a two-dimensional grey Penrose tiling. These new concepts can be applied to analyse the structure of the decagonal quasicrystal.

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What this paper is about

Penrose tiling is a two-dimensional quasiperiodic pattern, which is composed of two tiles, namely thick and thin rhombi. In this letter, white and black colours are given to the tiles to distinguish their top and bottom surfaces. Then, a two-colour Penrose tiling is yielded by the white black rhombi. The new pattern is a three-dimensional array and its projection is considered as a two-dimensional grey Penrose tiling. These new concepts can be applied to analyse the structure of the decagonal quasicrystal.

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Available abstract

Penrose tiling is a two-dimensional quasiperiodic pattern, which is composed of two tiles, namely thick and thin rhombi. In this letter, white and black colours are given to the tiles to distinguish their top and bottom surfaces. Then, a two-colour Penrose tiling is yielded by the white black rhombi. The new pattern is a three-dimensional array and its projection is considered as a two-dimensional grey Penrose tiling. These new concepts can be applied to analyse the structure of the decagonal quasicrystal.

Key concepts: Penrose tiling, Quasicrystal, Substitution tiling, Square tiling, Quasiperiodic function, Hexagonal tiling, Mathematics, Projection (relational algebra)

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