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.

May the 4th be with You - Star Wars Day Earrings

 

I may have too many earrings, but they are so quick and fun to make, that I can't stop making them!

For Star Wars Day - aka May 4th (because May the 4th... sort of sounds like May the Force... so people called it Star Wars Day) - I decided to add some Star Wars themed earrings. I made three pairs, and haven't decided which ones I'll actually wear on the day. I have considered randomly swapping out the earrings throughout the day so that every hour I have a different combination of symbols. 

The symbols for various factions are easy to obtain from the internet. I visited StarWars.com and found an article called, "5 symbols in the Star Wars Universe," which not only showed 5 of the most common symbols in Star Wars, but included very nice images of each. 

I downloaded the images and imported them into Silhouette Studio.  I expanded the first image to about 12" wide. I have found that if the image is expanded before tracing, then it comes out slightly better after tracing. 

Select Trace to open the trace window, then click on "Select Trace Area" and highlight the image.

These images traced nicely. If the image is very small, or it's in many colors, adjusting the "threshold" to a higher number has worked to include more of the details. Click "Trace" to create a cut shape. 

Select the palette and choose a color to fill the symbol. I like to use colors close to the colors I will be cutting the design from. Double click on the symbol after filling in the color to see the edit points. 

Because the Jedi symbol was originally much smaller, the lines are pixellated. These extra points can cause the machine to do a lot of extra work when it's cutting because it's turning and making a lot of small cuts that we can't see and don't want. To fix, from the menu select Object > Simplify.

This function removes most of the excess points to simplify the design.

Since there are still a bunch of excess points, click on a point to select it then delete it. Repeat until you have cleaned it up as much as is logical for the design.

Above is my cleaned up version. This will cut very smoothly. Repeat a similar process for additional Star Wars symbols, depending upon how many you want to create. 

I wanted to make 3 pairs of earrings, so I created two copies of each of the three symbols I selected. I resized the circles to about 1.5" tall. 

Use the shapes tool to create circles to go behind the symbols. After you've chosen your colors, move the symbols off of the mat and line up your circles in matched color pairs. You can use the markings on the grid to determine the size to cut the faux leather pieces. I usually back my faux leather with a piece of HTV before sending it to cut to ensure that the backing HTV completely covers the back side of the earring. 

After the faux leather pieces are cut, bring the pairs of symbols onto the mat and remove the circles. You can mirror the symbols if you wish, however, these particular ones are symmetrical so mirroring won't change anything. Cut the HTV symbols, then press the HTV on the faux leather using a heat press. 

To finish the earrings, punch holes in the top of each circle using a small hole punch. Finally, add jump rings and earring hoops and enjoy your Star Wars Day jewelry!

 The hardest part of the whole project is deciding which pair to wear. I've decided to mix and match throughout the day so sometimes I'll have matching earrings and sometimes not. 

HAPPY CRAFTING!!