# Labyrinth Tiling from Quasiperiodic Octonacci Chains

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This Demonstration shows a two-dimensional labyrinth tiling [1]. Such objects have been widely investigated in order to understand the interplay between quasiperiodicity and electronic structure in quasicrystals. The labyrinth can be obtained from the grid (tensorial) product of two identical octonacci chains.

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Contributed by: Jessica Alfonsi (June 2013)

(Padova, Italy)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Snapshot 1: periodic order for tiling with ()

Snapshot 2: aperiodic order for tiling with and maximum available ratio ()

Snapshot 3: aperiodic order for tiling with 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.

## Permanent Citation

"Labyrinth Tiling from Quasiperiodic Octonacci Chains"

http://demonstrations.wolfram.com/LabyrinthTilingFromQuasiperiodicOctonacciChains/

Wolfram Demonstrations Project

Published: June 21 2013