Mathematics + Crafting = Hilbert Curve on Sweatshirt

 

Every morning we take a walk around the neighborhood. Of course, there are various paths to choose from and for the most part, the walk lasts from 30 minutes to an hour depending upon the chosen route. Since we walk so early, we are often out before the sun decides to peek out above the mountains so it's either dark enough to need flashlights or not quite bright enough for people without lights to be seen. This means we need to find a way to be seen. Reflective clothing works, but is usually totally boring. Therefore, I sought a good solution to the dilemma.

I majored in mathematics and physics for my bachelor's degree, so I naturally leaned toward finding a solution that would be at least somewhat related to mathematics or physics. I found the Hilbert Curve. This is a continuous fractal space-filling curve in which the length of the th curve is , i.e., the length grows exponentially with , even though each curve is contained in a square with area .

What that means is it's a way to make a continuous path that looks really cool and weeds out in a single piece. This will glow nicely on my back and will guarantee that I'll be seen if I'm wearing it while walking when it's dark. The HTV I used is some reflective HTV I found on sale at Hobby Lobby. Reflective HTV is the best stuff to use for designs you want to wear on your exercise garments when walking when it's dark or the sun is still thinking about rising. 

I found the image of the Hilbert curve on the Wikipedia site about the Hilbert Curve. The site explains the mathematics behind the construction of the curve and has images of multiple iterations of it. Choose the version that suits your design interests. I snagged an image of the 4th iteration and downloaded it. 

Import the Hilbert Curve image into Silhouette Studio and select Trace. 

The Default trace settings won't correctly capture the shape as shown above. This is because the image has several colors and SS isn't certain which lines are important. Thankfully, there's an easy way to "fix" the issue. 

When I adjusted the Threshold from the default value up to 74%, the image was fully highlighted in yellow. This means that it found the complete curve. Hit "Trace" to trace the curve. 

The original image may be deleted after tracing, or at least moved aside off of the mat. Once the original image has been moved off the mat or deleted, click on the color palette, select the image and choose a color to fill it with. 

The fill doesn't do much other than allow you to see the completed curve easier than viewing just the cut lines. 

If you double-click on the image to show the points, you will see that there are some extra dots that we don't need to create the design. We want to remove them. To do so, from the main menu, select Object > Simplify

You can also zoom in and delete the extra points as you wish: 

Reducing the number of points makes the machine run more quietly because each point is an indicator to move or turn the blade, so removing points keeps the blade oriented in the same direction. Clean up the design as much as you desire to do so (without changing the shape of course!). 

Once it has been cleaned up, send it to cut. I sized the design to about 11.5" x 11.5" and cut a piece of reflective HTV to 12" x 12". I found that I had to use a new extra sticky mat to get the Reflective HTV to adhere to the mat. I also used a brayer to firmly adhere the HTV to the mat. 

Since it's HTV, Silhouette Studio will ask if you wish to mirror the design before cutting. You could choose to do so, but because this is a fractal, it's symmetrical and doesn't need to be mirrored.

After cutting, weed out the negative bits. Those who are especially interested in conserving material may find a way to lay the weeded out bits onto another shirt and neatly iron those on to make a positive and negative version of the Hilbert Curve. I tossed my weeded piece in the trash because I didn't have the time or patience to convince the curling mess to lay out flat on another garment. 

You can easily see the difference between no flash photo (above) and flash photo (below). 

My dress form does a pretty good job of modeling the hoodie with its back design. With flash (above) and without (below).

I think you can see how having an image this large on my backside will be a good safety feature when we return to the time of year when we need to wear a hoodie to take walks and it's dark enough that I want to ensure that cars can see me. And, of course, the best part is that the design is a geeky design that's very subtle in its geekiness.

HAPPY CRAFTING.