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Related Experiment Video

Updated: Sep 6, 2025

Applying Hyperspectral Reflectance Imaging to Investigate the Palettes and the Techniques of Painters

Applying Hyperspectral Reflectance Imaging to Investigate the Palettes and the Techniques of Painters

Published on: June 18, 2021

Multidimensional color codes for chair tilings.

Shelomo Izhaq Ben-Abraham¹, Dvir Flom²

¹Department of Physics, Ben-Gurion University of the Negev, Beersheba, Israel.

Acta Crystallographica. Section A, Foundations and Advances

|July 5, 2022

Summary

This summary is machine-generated.

This study introduces a novel color coding method for chair tilings in any dimension. This digital coding translates into visual colors, aiding the study of complex aperiodic structures.

Keywords:

aperiodic structures chair tilings color codes digital codes letter codes quasicrystals

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Area of Science:

Crystallography
Mathematical Physics
Geometry

Background:

Ordered aperiodic structures and lattice substitution systems have been studied for decades.
Chair tilings are a specific type of aperiodic structure with complex geometric properties.

Purpose of the Study:

To present a novel color coding system for chair tilings applicable in arbitrary dimensions.
To visualize and analyze complex aperiodic structures more effectively.

Main Methods:

Development of a digital color code for chair tilings.
Explicit construction of a 3D color coding for one octant.
Extension of the tiling and coding to full 3D space and arbitrary dimensions.

Main Results:

A systematic color code for chair tilings in arbitrary dimensions is established.
A concrete 3D example of color-coded chair tiling is demonstrated.
The methodology is shown to be extendable to higher dimensions and other complex tilings.

Conclusions:

The developed color coding provides a powerful tool for understanding and visualizing complex aperiodic structures.
This method can be applied to various complex tilings, including brick tiling.
The approach facilitates further research in crystallography and related fields.