Triangle Fractal Cutout

Make a 3D cutout fractal and turn it into a pop-up card.

Ages:
3′d-6th grades

Materials:
2 pieces of 8.5″x11″ paper per student, ideally of different colors
Scissors
Glue stick

Time:
Approx 30-45 minutes

See the NM State Content Standards met by this Fractivity.

Take one piece of paper and fold it in half, so it looks like a book.

Cut through the folded edge along the dotted line above. The cut should start half way up and down the fold and go half way to the right along the folded paper. Now fold over one half and crease, as shown.

The next step is a little tricky, but critical. Open up the folded-over flap, and fold it inside itself. You should end up with your paper looking like this:

You have now completed the basic step to create the fractal cutout, and all you have to do now is keep repeating this process again and again.

Now make two cuts, half way through each of the folded edges. The cuts will be half as long, and again the cuts should be half way up and down each edge and go only half way through the piece. Be careful not to cut too far.

Once you’ve made these cuts, fold over the and crease the flaps. How do you know which ones to fold over? You want to end up with something looking like a staircase.

After you’ve folded the flaps, you must remember to open the flaps up and fold them inside themselves.

This what your paper should look like now. Repeat the same cutting, folding and inverting, but this time you need to make four cuts. After folding and flipping the flaps inside themselves, you’ll end up with this:

If you want (and if you have the patience) you can repeat this process one more time, making 8 cuts. After cutting, folding and inverting, you end up with the final stage. (After this point, there are too many layers to cut easily.)

Finally, you can turn this fractal into a pop-up card. Fold your other piece of paper in half. Apply glue to the solid parts of the fractal cutout, and sandwich it inside the solid folded paper.

Enjoy your fractal cutout pop-up card!

Many thanks to Diego Uribe for describing this activity in his book “Fractal Cuts,” and to Francesca Blueher of Montezuma Elementary for introducing us to this fun project.