I have an old fashioned webpage with these tessellation resources, and I've decided that I'm still using them enough that I should keep them up to date - which means moving them over to the blog. If I was being really retro, I'd try to find one of those old-timey "Under Construction" gifs.
I like teaching tessellations at all levels of math, and have done so from 2nd grade up through graduate level math classes. Quasiperiodic tilings (aka Penrose tilings) were even a part of my thesis. While my interests are now more in math education, tilings still hold a deep fascination for me. For younger students it is a deep application of all four Euclidean motions, and for older students the richness provides many opportunities for analysis, problem solving and pattern creation/detection. The following resources are all ones that I have found useful in one way or another. Please don't hesitate to contact me with questions, suggested resources or any mistakes or bad links.
I have a few tessellation posts on this blog and more tessellations on the tumblr. My favorite GeoGebra tessellations I've made: Pythagorean tiling, Escherized Hexagon tiling, and Rotation of base kite tiles. (More below in GeoGebra/Blogs section.) I have a separate Google doc of Islamic Tiling resources, a handout I give students when doing tile alterations a la Escher, and a memoir of making a tessellation.
- Official Website
- World of Escher (and their contest , which has lots of examples)
- Short Bio , with art and companion math lessons
- Math and the art of Escher from SLU
- Review of an Escher exhibition from Chris Watson
- Tantalizing Tessellations
- New Zealand Math , a nice tessellation activity
- Don Steward: Designing Tessellations. Neat approach using grid paper instead of tracing a tile.
High School and above:
- ArtLex includes some advanced examples.
- Glide Reflections , an Illuminations activity from the NCTM.
- Classification of Patterns , a neat grade 7-10 activity on the 17 wallpaper groups.
- Allison Chen's Book of Tessellations
- David S. Chow , not the most strongly intreractive, but a large collection with some variety.
- Hop's tiles
- Jim McNeil's Tessellation page.
- Math Munch's Tessellation posts.
- Chris Watson's tessellationart.com
- His mathart tumblr
- Pinterest (I'm linking directly to boards because his general Pinterest page has a board of nude watercolors.)
- Prof.s Bart and Clair from St. Louis University have a great Math of Escher site.
- Cut the Knot's proof of an Escher Theorem about a class of hexagons that tessellate.
- Quick overview of the wallpaper groups
- Wallpaper Groups , a college math major level unit for teaching about the wallpaper groups. Includes Mathematica and Cabri files.
- Tessellations for Wallpaper Groups and the math by David Joyce, really a master of visual display of high level mathematics.
- David Austin's two Penrose columns: ribbons and structure. Even better, his applet!
- Pythagorean Tiling (GGB, tumblr)
- Animated Rug (GGB, tumblr)
- Escherized Hexagon, 3 side to side rotations (GGB, tumblr)
- Escherized Kite, midpoint rotation (GGB, tumblr)
- Indiana Puzzle quilt (GGB, tumblr)
- Tessellating Kites (GGB, blogpost)
- Playing Math (finding the tessellation in a ceiling) (GGB, blogpost)
- Early GeoGebra tessellations (GGB, blogpost)
- Conway Pinwheel Tessellation (GGB, tumblr)
- Penrose Tiling (GGB, blogpost)
- Tiling by design (GGB, tumblr)
- Park Tessellation, a kind of generalized Pythagorean tiling (GGB, tumblr)
- jchinn1 has a number of Escher tessellations to analyze. Maybe start with the pegasi.
- ltgrau has analyses of Escher's fish, salamanders, and more fish
- Daniel Mentrard's tessellation and frieze collections. He is a GeoGebra wizard.
- Illuminations' Tessellation Creator is good for investigating regular and semiregular tilings.
- Islamic Pattern Generator (via Jennifer Silverman)
- The (sadly, closed) Geometry Center from U.Minnesota. Still some great applets, like Kali or the QuasiTiler.
- A translation tiler from Shodor.
- Hyperbolic Tessellation applet from Don Hatch, and David Joyce has the similar Poincaré.