Embroidered Tesselations Part 1

It all began with a phone call from my aunt, the very talented quilter.  A mathematical artist was looking for an embroiderer to collaborate on a project.   Was I interested?   Life can take you done some interesting paths when you say yes at the right moment.

This was the image that my collaborator, Doug Dunham of Duluth, MN created.

You might recognize it as very similar to some images by the artist M.C. Escher, famous for images with mathematical foundations.  This is a tessellation, also sometimes called a tiling.  The fish shapes, all identical, completely cover the surface.   Wait...  all identical?  This can't be!  Some are large, many are small and they aren't all the same shape.

In fact, they are all the same shape if you see this not as a regular two dimensional circle, but rather the Poincare disk, a hyperbolic geometry, where the distance between two points depends on how close to the edge they are.  In fact, it's an infinite distance from the center to the edge.

The question asked whether this image could be rendered in embroidery in some pleasing way.  Making this work would require many days with Floriani Total Control, my embroidery design software.  It was also obvious from the beginning that with an image this detailed, the larger the embroidery could be made, the more details could be included.  I knew from the beginning that the Husqvarna Majestic Hoop, at 350mm x360mm was going to produce the best results.

Here's a version of the image in embroidery at 4"x4".  Not much detail is included.  As the fish get small towards the edge, there's no way to render them.  However, as a first crack at the problem, it wasn't bad.

Come back next week and see what can be done with a 260mm x 360 mm hoop.