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Vibrating Wallpaper

Table of Contents

Constructing Wallpaper Functions
 - Wallpaper drums
- Example in a rectangular lattice
- Lattice waves -- translational invariance
- Eigenfunctions with 3-fold rotations
- Experiment on line with wallpaper design
Negating Isometries
 - A motivating example
- Classification and naming
- Recipes for negation
The general lattice
The rectangular lattice
The rhombic lattice
The square lattice
The hexagonal lattice
- Telling the types apart
The Algebra of Wallpaper
 - Informal discussion of anti-symmetries
- Combining negating isometries
- Group homomorphisms
- Type equivalence
- Why there are 63 types
Ways to Visualize Wallpaper Functions
 - Real-valued wallpaper functions
- Complex-valued wallpaper functions
- Completeness of eigenfunctions of the Laplacian
- Color-turning wallpaper
The Wallpaper Vibrates
 - A pmg example
- Gallery of movies
Directions for Further Work
Appendices
 - Introduction to wallpaper groups
- History and notation
- Index of images


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Communications in Visual Mathematics, vol 1, no 1, July 1998.
Copyright © 1998, The Mathematical Association of America. All rights reserved.
Created: 8 Jul 1998 --- Last modified: Sep 30, 2003 4:38:14 PM
Comments to: CVM@maa.org