# Labyrinth Tiling from Quasiperiodic Octonacci Chains

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This Demonstration shows two-dimensional square and labyrinth tilings based on Octonacci (Pell) and Fibonacci sequences, respectively [1, 2]. Such objects have been widely investigated in order to understand the interplay between quasiperiodicity and electronic structure in quasicrystals. Both tilings can be obtained from the grid (tensorial) product of two identical quasiperiodic chains.

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Contributed by: Jessica Alfonsi (June 2013)

(Padova, Italy)

Open content licensed under CC BY-NC-SA

## Details

Snapshot 1: periodic order for Fibonacci sequence with square tiling and ()

Snapshot 2: aperiodic order for Octonacci-Pell sequence with labyrinth tiling, and maximum available ratio ()

Snapshot 3: aperiodic order for Fibonacci sequence with square tiling, and intermediate value ratio ()

Reference

[1] U. Grimm and M. Schreiber, "Energy Spectra and Eigenstates of Quasiperiodic Tight-Binding Hamiltonians," in *Quasicrystals: Structure and Physical Properties* (H.-R. Trebin, ed.), Weinheim, Germany: Wiley-VCH, 2003 pp. 210–235. arxiv.org/abs/cond-mat/0212140.

[2] W. Steurer and S. Deloudi, "Tilings and Coverings", in *Cristallography of Quasicrystals: Concepts, Methods and Structures,* Springer-Verlag Berlin Heidelberg, Germany 2009 pp. 7-47

## Snapshots

## Permanent Citation