Abstract

A plane tiling is an arrangement of polygons which can be repeated to cover the plane. Squares and regular hexagons can be used to produce simple tilings, but many more interesting tiling configurations exist, most notably in the works of M. C. Escher and in parquet defomrations.

The problem of covering the plane with a repetition of polygons is an interesting example a constraint-based system. Geometrical constraints enforce symmetries necessary to produce a tiling, and our project aims to characterize these constraints and provide a software engine to allow for automatic maintenance of the symmetry constraints through deformations of tiles.

More Information

An update from Craig: Since this project was completed, I have been doing additional research in the area of computer-generated tilings. Some links to recent results can be found on my home page.

• The LaTeX source for our original project proposal
• The postscript version of the proposal
• The up-to-date project milestones
• Our Results!
• Sample artifacts
• Our current progress

Other Links of Interest

• The CSE557 WWW page
• A Gallery of Interactive On-Line Geometry
• The Geometry Junkyard Note, in particular, the page devoted to tilings
• Daniel Huson's Home page
• Xah Lee's gallery of visual symmetry
• David E. Joyce's page about Wallpaper Groups
• Yoshiaki Araki's page of Escher-like tilings
• M.C. Escher's Virtually Gone Gallery
• World of Escher
• William Chow's tesselations and periodic drawings