Penrose Tilings

Francesco D’Andrea ()
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Francesco D’Andrea: University of Naples Federico II, Department of Mathematics and Applications “Renato Caccioppoli”

Chapter Chapter 4 in A Guide to Penrose Tilings, 2023, pp 85-120 from Springer

Abstract: Abstract In this chapter, we study two of the aperiodic protosets discovered by Penrose: one formed by a kite and a dart, and the other formed by golden rhombi. We use the preliminary study of Robinson triangles in Chap. 3 to prove several local and global properties of Penrose tilings. We discuss Conway worms and their relation to some one-dimensional non-periodic tilings called Fibonacci tilings. We discuss ribbons and their properties and prove, using ribbons, that tiles in a Penrose tiling can have only finitely many orientations. We discuss non-local properties of Penrose tilings and empires, and finally talk about the 3-coloring problem for a Penrose tiling.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-28428-1_4

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DOI: 10.1007/978-3-031-28428-1_4

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