This blackwork sampler is pretty much the most intricate and deeply mathematical thing I’ve stitched. It showcases all the possible symmetries that can be stitched on Aida/evenweave fabric.
The outline is the smallest simple perfect squared square, which is 112 stitches on each side and divided into 21 smaller squares. The largest square is filled by patterns representing the 7 frieze groups. The 2 smallest squares contain the empty set and a point (a French knot). The last 18 squares contain the 12 wallpaper groups and 6 rosette groups without 3-fold symmetry (because 3-fold symmetry can’t be accomplished on a square lattice). Some of the patterns are traditional but most were original. It turns out that historically people don’t tend to stitch things with very little symmetry.
This piece was originally conceived after reading Susan Goldstine’s chapter on simple perfect squared blankets in Crafting by Concepts (which is a must-own if you like fiber arts and math). It’s done on 18 count Aida using both perle cotton and embroidery floss, and the frame is a hand painted 8″ Mill Hill square frame. Before you ask: it took about 150 hours to design, chart, and stitch the whole thing...
Update: It was exhibited in the 2016 Joint Mathematics Meetings Art Gallery! Here’s the exhibit profile/gallery page. Writing the artist statement took longer than it should have taken.
Simply Symmetric Square Sampler
blackwork embroidery
112 by 112 stitches
6.25" by 6.25" on 18 count Aida