Brain Pincushion From A Hilbert Curve

A friend of mine is obsessed with brains; if there was ever a zombie apocalypse, she would ask to be in their “special-interest group”. She also likes to sew, so for me the obvious thing to do was to make her a brain pincushion.

To me, the most evident way to construct a brain was to make a Hilbert Curve and wrap it around a ball of some kind. None of my Google searches for “hilbert curve brain” came up with any relevant results, so I’m forced to conclude that I’m the first person to use a Hilbert curve to approximate the wrinkled shape of a brain.

Of course, I’m not the first person in recent memory to break out the Hilbert Curve. This XKCD map of the internet makes good use of it, and [if by this point you’re wondering what the heck a Hilbert Curve is to begin with] Vi Hart has a great instructional video on how doodling and the Hilbert Curve are related.

It all starts with a grid, like the one that I made on this piece of cloth. I made the grid spacing 3/8″, the size of the cotton filler cord (also called “piping cord”) that I bought to make the actual brain shape. I bought a bag containing 6 yards of the cord, and used most of it. The only other things you need to do this project are some thread, a needle, and a scrap of fabric that you can draw on. (I have no skill at sewing.)

After drawing the grid, I started drawing in the curve itself. The Hilbert Curve is a “space-filling curve”, but damned if it isn’t a “my-time-filling curve” too. This took a while, because I didn’t want to make a mistake. After filling up half my original grid, I realized that I had drawn much more curve than would be needed for the project.

Getting the cord to follow the line as I sewed it down was really difficult at first, because there was nothing for me to hold the cord against. I debated giving up and starting over the next day with stiffer backing, but ultimately I decided to press on and see what happened.

As I got further, it got easier. Also, if you look closely, I’m not following the line exactly… because all the corners compress the fabric of the cord, it was leaving some bare spots on the backing. So, I started putting extra zigzags in the cord where possible, and just used the Hilbert line as a general guide.

This is the completed square!

To finish the design, I balled up the leftover fabric and sewed the brain texture shut around it. I hope she likes it!