Introduction: Kinetic Reverse Folding Tessellation

About: Hi! I like building interactive, useful things and am excited to share some of my projects with you!

💡"Simplicity is the ultimate sophistication" - Leonardo da Vinci

This project requires very few materials but produces an elegant, bold final product. You can create the tessellation design with just a single sheet of paper, but with just a few additional simple materials, you can create a neat display that appears to make it breathe and move.


Materials for the Tessellation:

  • paper (any size is fine)

Materials to make it "breathe"

  • cardboard box
  • servo
  • arduino
  • jumper wires (x3)
  • tape
  • string

Step 1: The Reverse Folded Tessellation

The technique almost feels like a magic trick requiring some advanced folding and patience, but when done right, it’s really aesthetic. I created a video tutorial embedded above, but I'll also write out the steps here as well.


  • ⬆️mountain folds (folds that go up)
  • ⬇️valley folds (folds that go down).

Step 2: Tessellation Pt 1. Fan Fold

Fan Fold:

  1. Fold about 2 inches from the bottom
  2. Flip the paper over and fold about 2 more inches from the bottom
  3. Flip the paper over again and fold 2 more inches from the bottom
  4. Flip the paper over one more time and fold 2 more inches from the bottom, ending with a long rectangle

Step 3: Tessellation Pt 2. Fold Ends and Open

Fold 1/3 of the left side of the rectangle down and 1/3 of the right side of the rectangle up creating a ┏┛shape, and then open it up.

Step 4: Tessellation Pt 3. Reverse Folding

Fold each of the horizontal end segment mountain folds into valley folds (the first two images show the before and after of this technique) and fold each of the end segment horizontal valley folds into mountain folds (the last two images show the before and after of this technique). This “reverses” the folds. This technique is portrayed in 1:30 to 2:00 of the video tutorial in step 1.

Step 5: Tessellation Pt 4. Pinch the "V" Folds

Above the folds you just reversed are a couple "V" shaped folds. Pinch the “V”s into mountain folds (see the first two images for the before and after)

Then, fold all of the mountains folds together (last two images)

Step 6: Tessellation Pt 5. Repeat on the Other Side

Repeat Tessellation parts 1-4 on the other side. Then pinch the mountain folds together, recreating the ┏┛shape. Once you open it up, you've successfully created the reverse folding tessellation!

Step 7: Hardware

The tessellation is neat by itself but a display that expands, contracts, and moves the piece around is endlessly entertaining.

Connecting the Servo and Arduino: First, connect the servo to the Arduino (either directly or using a breadboard) using the jumper wires. First, use the black (or darkest wire) to ground the Arduino. Next, connect the middle wire to the 3V and the yellow (or lightest wire) connects to the 2 on the Arduino.

For more information on Arduinos and the setup process, check it out here here.

  1. Attach any type of arm to the servo. Then connect the servo to the Arduino with the jumpwires (see the link above for comprehensive instructions).
  2. Cut out little cardboard triangles to serve as a base for the servo and glue them securely to the servo and the floor inside the box.
  3. Cut a little hole on the side of the box. Position the battery on/off switch so it is accessible from outside the box via the hole. Tape the battery and Arduino down.
  4. Tape two strings to the servo arm

Step 8: Arduino Software

First, download Arduino on your computer, here. Upload Sweep from your servo library which will move the servo arm to move in a sweeping motion. I have provided the Arduino code above (images as well as a pdf to copy and paste) which is modified from open-source code from the Adafruit website.

This sweep movement is what drives the expansion and contraction of the tessellation, and modifying the speed and time between intervals of the sweeping motions, you can change how quickly and powerfully the tessellation moves.

Once you've gotten the servo working, you're ready to start attaching the tessellation!

Step 9: Attaching the Tessellation to the Display

  1. Cut two holes on the top of the cardboard box, and pass the two strings attached to the servo arm through each hole.
  2. Cut a tiny hole on each side of the tessellation and pass the two strings through.
  3. Play around with how much slack is required for the servo to pull the tessellation into a contracted and expanded position. Once you've determined the optimal position, use tape to ensure the string won't slip out of the tessellation.

Step 10: Additional Movement (Optional)

Optionally, you can add a small stick at an angle to prop the paper up. It isn't necessary, but as the servo arms spins, if it hits the stick propping it up, it moves the tessellation around on the x and y axes as it contracts.

Step 11: 🎉🎉🎉

Turn it on and watch it expand, contract, and move around.

Hope you enjoyed making this machine as much as I had fun designing it! 😄

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