Wallpaper Functions

• Published in 2002
• Added on 2023-06-20

Instead of making wallpaper by repeating copies of a motif, we construct wallpaper functions. These are functions on \(\mathbb{R}^2\) that are invariant under the action of one of the 17 planar crystallographic groups. We also construct functions with antisymmetries, and offer a complete analysis of types. Techniques include exhibiting bases for various spaces of wallpaper functions, and an algebraic definition of equivalence of pattern type.

Links

• https://core.ac.uk/download/pdf/82036994.pdf
• https://www.sciencedirect.com/science/article/pii/S0723086902800196

Other information

BibTeX entry

@article{WallpaperFunctions,
	key = {WallpaperFunctions},
	type = {article},
	title = {Wallpaper Functions},
	author = {Frank A. Farris and Rima Lanning},
	abstract = {Instead of making wallpaper by repeating copies of a motif, we construct wallpaper functions. These are functions on \(\mathbb{\{}R{\}}^2\) that are invariant under the action of one of the 17 planar crystallographic groups. We also construct functions with antisymmetries, and offer a complete analysis of types. Techniques include exhibiting bases for various spaces of wallpaper functions, and an algebraic definition of equivalence of pattern type.},
	comment = {},
	date_added = {2023-06-20},
	date_published = {2002-12-07},
	urls = {https://core.ac.uk/download/pdf/82036994.pdf,https://www.sciencedirect.com/science/article/pii/S0723086902800196},
	collections = {art,easily-explained,fun-maths-facts,geometry,the-groups-group},
	url = {https://core.ac.uk/download/pdf/82036994.pdf https://www.sciencedirect.com/science/article/pii/S0723086902800196},
	urldate = {2023-06-20},
	year = 2002
}