By George Hart for the Museum of Mathematics

Continuing our fiber arts theme of past weeks, today’s Math Monday offers an excellent example of mathematical needlepoint. This piece illustrates a Hilbert curve, taken to the sixth approximation. The continuously changing color of the thread makes it easy for your eye not to lose its place as you follow the long path that starts at the top-left and ends at the top-right.

If you want to embroider your own Hilbert curve, you can work up to this level starting with any of the simpler patterns below. Each level consists of four copies of the next simpler approximation plus three connecting stitches, highlighted below in red. The nth version has 4n-1 visible stitches, so the sixth order approximation above shows 4095 stitches, and that doesn’t include what’s on the back. The maker, Gio, must be very patient.

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## 4 thoughts on “Math Monday: Mathematical needlepoint”

1. blktauna says:

You obviously haven’t done much blackwork if you thing this was something. Still it’s beautifully made and congrats to Gio!

2. lunkwill says:

You can also think of the hilbert curve as a recursive function, as you “zoom in” to smaller and smaller pixels.

If you show the sub-squares as solid blocks instead of drawing a line along the path you take to reach them, and color each of the 4 sub-squares a different color, you get a beautiful and instructive pattern.

I liked it so much that I had a few yards of fabric printed with it:

http://credentiality2.blogspot.com/2010/06/space-filling-fabric.html