Fractals are SMART: Science, Math and Art!

Fractal Cutout Card

Cut out a 3-dimensional fractal and turn it into a pop-up card


Students make a 3-dimensional fractal cutout card by repeating a simple process of cutting and folding. They can turn their cutout into a fractal popup greeting card, decorate it artistically and share the lessons of fractals with others. Although it is formed by a very different process, the resulting fractal shares much in common with the Sierpinski triangle.

3rd – 8th grades

8.5″ x 11″ white paper
8.5″ x 11″ card stock in contrasting color
Glue stick
Ruler in centimeters
Cutout Card worksheet

Approx 30-45 minutes





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Teachers – if you have comments or suggestions about this or any of our other fractivities, please email us at JenFFEmailImage

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

cutout1Cut 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:

cutout3You 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.

cutout4Once 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.

cutout5After you’ve folded the flaps, you must remember to open the flaps up and fold them inside themselves.

cutout6This 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:

cutout7If you want, you can repeat this process one more time, making eight 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.


  1. shira shira
    October 10, 2015    

    Thanks for sharing, this is amazing!

  2. Catherine Gilpin Catherine Gilpin
    September 22, 2015    

    I used this activity and the Sierpinski Triangle (sorry I didn’t get this sent to you!) and am hoping that I may introduce these during a break-out session at the Gifted Association of Missouri Conference in October. Do I have your permission? I will, of course, cite you as the source and give this site information.

  3. Marala Copeland Marala Copeland
    February 15, 2015    

    For several years, I studied energy AND ENTROPY. I was enthralled with the fact that 1) energy is only a concept UNTIL it is acted upon, and 2) that no action ever occurs without some entropy attached!(Energy is not perfect,in other words.) Fusing that knowledge with fractals is unbelievably fascinating…even entertaining! Science was never more fun! I am deeply involved in utilizing this data to help people create order out of chaos in their emotional biosystems, as well as in their external, personal ecosystems. Fractally yours, Marala

  4. Clarissa Clarissa
    March 16, 2014    

    Thank you for posting this online with such great instructions!

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