Tesselations

**NEW STUFF: ** __ [|Yesenia Aceves shows her first tessellation ever.] __ Have you done one? Try it, and show us! __ [|Pennsylvania kids tessellate] __ in school. __ [|Chess pieces tessellate] __. Who knew? For a more complete list of our newest stuff, __ [|click here.] __
 * http://www.tessellations.org/

**Tessellations ** here mean designs and patterns featuring animals, toasters, persons, etc, which can fit together in repetitive interlocking ways like simple jigsaw puzzles. These fill a surface, usually a 2D plane, without gaps or overlaps. Brick walls, tiled floors, dragonfly wings, and walls in kitchens and bathrooms, and sidewalks are all tessellated surfaces.

On these pages is information about all aspects of tessellations. We have their history, do-it-yourself tessellation lessons, and galleries of examples by school students, guest artists, the webmasters Seth and David, and of course M. C. Escher, the pioneer of the art.

This site is a dedicated //__art__// site, not requiring much math. Math teachers, don't be forlorn. We do show a smidgen of introductory geometry: polygons that tessellate. As M. C. Escher said, "Mathematicians go to the garden gate but they never venture through to appreciate the delights within." To use another metaphor, you're missing the fun if you use a microscope to enjoy a merry-go-round. We have a little simple geometry in the lessons and explanations, but nothing as fancy as the serious adults' math-oriented tessellation websites.

If, as a result of your visit, you venture through that garden gate, please __ [|send us] __ your designs for inclusion in the guest gallery.

<span style="color: #cc3300; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;">Link to us! To put a button that links to us on your website, if you're comfortable with HTML then just copy the text below, change the text to suit your feelings, and add it to your website.

<span style="color: #cc3300; font-family: Arial,sans-serif; font-size: 10pt;">|| This result...

<span style="color: #cc3300; font-family: Arial,sans-serif; font-size: 10pt;"> Click on this button to see __<span style="color: #883333; font-family: Arial,sans-serif; font-size: 10pt;"> [|a wonderful award-winning website of kid-safe Escher-style tessellation art and teachers' tutorials.] __ <span style="color: blue; font-family: Arial,sans-serif; font-size: 10pt; text-decoration: none;">

<span style="color: #cc3300; font-family: Arial,sans-serif; font-size: 10pt;">...comes from this HTML code:

<span style="color: #cc3300; font-family: Arial,sans-serif; font-size: 10pt;"> Click on this button to see <a href="http://www.tessellations.org">a wonderful award-winning website of kid-safe Escher-style tessellation art and teachers' tutorials <img src="http://www.tessellations.org/buttons/tessellations-dot-org.gif" border="2" align="middle" alt="button for tessellations.org" /> || <span style="color: black; font-family: Arial,sans-serif; font-size: 10pt;">

<span style="color: #cc3300; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;">Tessellations.org was Yahoo's 'Pick of the Week' on Feb 15 2004 and is a member of the Graphics web ring.

**<span style="color: #cc3300; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;">Latest news ** <span style="color: #cc3300; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;"> - click __<span style="color: #883333; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;"> [|here] __

**<span style="color: #cc3300; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;">Site Index ** <span style="color: #cc3300; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;"> - click __<span style="color: #883333; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;"> [|here] __

**<span style="color: #cc3300; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;">TEACHERS ** <span style="color: #cc3300; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;"> - This whole site is entirely suitable for young children.

**<span style="color: #cc3300; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;">TEACHERS, SCHOOLS, and ARTISTS ** <span style="color: #cc3300; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;"> - This site is actively seeking art, lesson plans, and tutorials from guest contributors. __<span style="color: #883333; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;"> [|Contact] __<span style="color: #cc3300; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;"> us.

**<span style="color: #cc3300; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;">SCHOOLS ** <span style="color: #cc3300; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;"> - Recently, many schools have asked to have their students' artwork put in a school gallery here. **Yes,** we'd be happy to post your class's tessellations in a "school gallery" on www.Tessellations.org.


 * <span style="color: #cc3300; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;">Our only reservation are 1) that the art be original, or cite the name of the artist whose art is being imitated together with a link to that original on the Web. 2) that the art has to actually BE tessellations. You see, in the past, some teachers have submitted art that, while symmetrical and repetitive, wasn't true tessellation. We had the unhappy chore of saying "no" or "please redraw this" to a teacher and student.
 * <span style="color: #cc3300; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;">A true tessellation covers a 2D plane with "no gaps and no overlaps". Or, at the very least, the audience's eyes should be able to see that the pattern //could// fill the entire space without gaps or overlaps. If the pattern wouldn't cover every bit of sky, floor, grass, unexplained white space... then those places where the background shows through count as gaps.
 * <span style="color: #cc3300; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;">Please check __<span style="color: #883333; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;"> [|these samples] __<span style="color: #cc3300; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;"> to see examples of what //is// a tessellation, and what is beautiful symmetry art but //not// a tessellation.
 * <span style="color: #cc3300; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;">And that's it!
 * <span style="color: #cc3300; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;">For the sake of the readers' interest, it's a good idea to have a link to the school's website, some short intro about the school, the teacher, and/or the class. So, please provide me with a short introductory paragraph and the "www...dot com" address of your school's website if you have one. If you have a lesson plan or handouts that you used and would like to share with other teachers, I'd *love* to post them as well.
 * <span style="color: #cc3300; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;">In general, the students should name their art. If they have a few words about the method or inspiration, I'd love to include that as well.
 * <span style="color: #cc3300; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;">If the artists are minors, then for the sake of their privacy we shorten the students' names. You, the school or teacher or guardian, decide whether the names are shortened to first initial + family name (J. Smith), initials only (J.S.), or just first names (John).
 * <span style="color: #cc3300; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;">Send the art by email. Scanning the art's better than photographing it. With photography, inevitably there's a shadow or fold in the paper that requires extra photoshopping. If, however, scanning represents a lot of extra work then I can work with your digital photos.
 * <span style="color: #cc3300; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;">When emailing your art to us, we prefer that you use high quality __<span style="color: #883333; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;"> JPEG (JPG) files __<span style="color: #cc3300; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;">. Other file types are perfectly acceptable, but may be awkwardly large or reduce the range of colors in your art.
 * <span style="color: #cc3300; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;">Don't try to send all the art in one email, since most emails are limited to just 3 or 5 megabytes each and art originals tend to be BIG files. The final art I'll crop down and compress myself, usually adding watermarks and copyright notices to the images, so please send me large, uncompressed scans rather than shrunken originals.

**<span style="color: #cc3300; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;">Posters, Postcards, Jigsaw Puzzles, Mugs, and Magnets ** <span style="color: #cc3300; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;"> We sell reprints of some of webmaster Seth's art online through "dA galleries". __<span style="color: #883333; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;"> Click here to visit that online art store. __<span style="color: #cc3300; font-family: 'Trebuchet MS',sans-serif; font-size: 10pt;"> We will try to post a clickable link to the store next to each tessellation available in the store. <span style="font-family: Arial,sans-serif;">