Geometric String Art in Cubes

For a long time, I've been interested in geometric patterns in mathematical surfaces. I think they look beautiful as sculptures.

This project was partially inspired by my previous project on a transforming hyperbolic sculpture. In that project, I arranged wooden skewers into a hyperbolic shape.

I wanted to create more complex surfaces in this project, so I decided to use string art and anchor the strings on a cube-shaped frame.

Material

1. Frame-3Dprinted: PLA filament
2. Frame-Wood: Balsa wood sticks 1/2"x1/2"x12", 4 for each frame; sewing pins; Wood glue
3. Polyester embroidery machine thread of various colors
4. Craft Glue/B7000 Glue
5. Black marker
6. Spray paint, Acrylic paint

Equipment

1. Frame-3Dprinted: 3D printer
2. Frame-Wood: Craft knife/saw and Precision Pin Vise Hand Drill
3. Needle for hand sewing
4. Electric Foam Cutting Machine Pen

The easiest way to create the frame is to 3D print it.

Using an Elder3 3D printer, print out the attached STL files:

1. cube-topbottom.stl
2. cube-sidebars.stl

Notice that each beam only has one row of holes. We initially designed the frame so that every beam had two rows of holes perpendicular to each other. However, our 3D printer struggled to print this accurately, so we have simplified it to one row of holes into our latest templates.

Use the connection pieces to put together the top frame, bottom frame, and side bars by inserting them into the holes as shown. Apply glue to secure. If any holes get blocked, you can use an electric foam cutter to open the holes again.

If you don't have a 3D printer, you may use 1/2"x1/2"x12" wooden sticks instead. Cut 4 beams of length 6.25" and 8 beams of length 5.25".

Drill evenly spaced holes with a precision hand drill. You don't have to drill holes close to either end of the 6.25" beams, as the ends of the 6.25" beams will become the corners of the cubes. Each edge should have an equal number of holes.

Glue together as shown. Secure with sewing pins.

Wait until the g dry to remove pins.

This is the first design we came up with. In this design, we separate the 12 beams into 6 pairs, then for each pair, we connect the two beams with string.

The first image shows how to connect two beams. The second image shows how we separate the beams into pairs.

We decided to use a warm color spectrum, with each pair having a gradient of colors.

1. Y1 & Y2: cream/yellow/orange.
2. O1 & O2: tangerine/vermillion/red.
3. P1 & P2: deep rose/dark fuchsia/magenta/purple

The thread we used was for machine sewing, so it was relatively thin. We therefore decided to fold each piece of thread into a U shape to give it twice the thickness.

Start with the Y1 pair and Y2 pair. Cut a long length of string and fold the ends to each other to create a U shape. Make a loop knot at the end of one edge (the loop knot is illustrated using a binder clip and a rubber band in the second image).

The open end of the string should now have 2 threads. Thread the string through the holes as shown. When you're ready to switch to the next color, cut most of the string off (leaving about a half-inch of string), then tie the two threads together in a loop. Start the next color by tying a string of the next color to the previous string using a loop knot.

Repeat for the Y2 pair.

Similarly thread the O1 pair and O2 pair. Note that you might have to weave a string between two existing strings. Some trial and error may be required to get each string from its origin to its destination without distorting any existing strings.

Finally, thread P1 and P2. These are the hardest pairs to thread, so be careful!

Once you're done with all the threading, secure the thread onto the beams with glue.

When the glue is dry, use a black Sharpie to color all the exposed threads.

There are so many possibilities--have fun and explore!

Each of the 4 diagrams showcases a pattern that can be repeated to fill the whole cube. We repeated the pattern in the first diagram 2 times, using a black/white/gold color scheme, to create our sculpture "Day and Night". We used a purple/pink/gold color scheme and the pattern in the second diagram to create "Cyber Sunset." Finally, we used a rainbow color scheme and the pattern in the fourth diagram to create "Prism." Note that the pattern in the fourth diagram requires you to use some holes more than once.

You can also using different materials, for example, string lights and fiber optic cables as in the last one.

I hope you enjoyed this Instructable! If you find your own interesting patterns, please share them in the comments below!