Fractal cross-stitch / counted-thread embroidery patterns

Also, staying on the topic of maths, a little while ago, I put some stitching patterns for a couple of fractals, the Sierpinski triangle and the Pythagoras tree, up on Etsy. They didn’t really sell very well, and rather than paying to keep them listed, why not host them here, for free!

I’m putting them up with a Creative Commons license (CC BY-SA 3.0), because trying to own a piece of maths seems pretty daft, and these designs were made to be remixed anyway. Just link back to this post if you take them and do anything with them.

Click for full size

(Click here for a PDF version)

Originally invented by Wacław Sierpiński in 1915, the Sierpiński Triangle is one of the best known fractals. This pattern creates a frame based on the triangle, which can be adapted to fit almost any design. The corner pieces are 16 x 16 stitches, the middle pieces are 32 x 16, and the smaller triangles that fill in the rest of the border are 8 x 4. The border can be increased to any size by adding more triangles. For a more compact border, the large middle pieces can be removed.

This pattern is 112 x 64 and unmodified fits a design roughly 96 x 32 (3 or 4 lines of text).

Click for full size

(Click here for a PDF version)

The Pythagoras Tree is a compact fractal. The blackwork patterns used to create the bark can be swapped with any other pattern, or simply replaced with cross stitch if desired.

This pattern is 42 x 29. The pattern could be continued to double its size, but further iterations would mean a lot of branches in the middle would start crossing.

Enjoy! And if you use them, send us a picture! I’d love to see these in the wild.