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.
Love this site. I just discovered fractals the other day and now I am addicted. We have a fundraising event coming up with dinner and dancing. As I am on the committee, perhaps having a fractal card at each place setting would be impressive and show how much we value our patrons.
great idea dave.i bet patrons would love it.good thinking.
I thank you for having this online. I have been looking for a project in fractals for my art classes!This is very important in our time!
AWESOME! Thank you sooooo much! the paper that my teacher gave me was cofuzzling…. This made MUCH more sense!!!!! I LOVE YOU!!!!!!!
Exactly what I was looking for…a simple explanation of doing this for my students…plus more! Love the site…Math and Art is a curriculem I am developing for middle school kids!
AWESOME..!!!!!!!!!!!
THANKS!!!
This website was great! Without it I would have failed my math assignment. Thanks so much!!!
I will certainly use this as an activity for a fractal presentation I will be giving to middle school students. Thank you for sharing.
I modified this activity for my high school students. We folded the paper in half hamburger, then in half again, and in half again. Doing the activity by thirds was difficult, even for me, so we did it in fourths… After folding the paper in half, we cut out a medium size shape in the middle. We then folded that half in half, and cut out two small shapes in the middle of the two bigger shapes. Lastly, we cut out four tiny shapes in the middle of the medium size shapes. I’m not sure how well my explanation is here in writing, but it worked great, and the students loved this activity! It takes 7 cuts, and three folds. I have triangles, hearts, stars, vases, and all sorts of other fun shapes iterated! Thanks for the idea!
As I am re reading my explanation it is terrible!
Fold a paper in half (hamburger)
Cut out a medium size heart (shape, I will use a heart)
Fold that half, in half again, so the paper is still long and skinny
Cut out one small heart, on the top half, in the middle
Cut out another small heart, on the bottom half, in the middle
Fold that paper in half again, the paper should still be long and skinny
Find the top small heart
Cut out a tiny heart above the small heart
Cut out a tiny heart below the small heart
Find the bottom small heart
Cut out a tiny heart above the small heart
Cut out a tiny heart below the small heart
Open up your paper, paste to another colour of paper
Hang on the wall for all your classes and students to enjoy!
Yes, my high schoolers loved this, and this mini project helped them understand fractals!