Fractal Paper Sculpture

This activity is adapted from "Using Algorithms to Generate Objects of Mathematical Interest" by Elaine Simmt.* It will work best if the template is printed on heavy paper.

Fractals are mathematical objects that repeat a pattern over and over in a smaller and sometimes rotated fashion. Some famous fractals are the Mandelbrot and Julia Sets.

We can create paper sculptures that form fractals. Fractals are formed by selecting a starting point and repeating a procedure over and over. We will fold and cut, then fold and cut, and fold and cut again to make our fractal sculptures. You can repeat the pattern until you run out of paper or the folds get too thick to cut.

Print out the template and follow these instructions:

DIRECTIONS:

1. Fold your template on the large dotted line across the middle of the paper.
2. Cut along the largest, darkest solid lines.
3. Fold the center cut section upwards along the dotted line, revealing the next set of solid lines.
4. Cut on the solid lines now showing.
5. Fold the center cut section upwards along the dotted line, revealing the next set of solid lines.
6. Cut on the solid lines now showing.
7. Now open your paper up and refold to make the cut portions bend out and form your sculpture.

What are fractals?
Cantor middle thirds set

Sierpinski triangle set
Another fractal card
More fractal cards

 

 

 

 

 

 

 

 

 

 

 

 

 

* Morrow, L. J., & Kenney, M. J. (Eds.). (1998). The Teaching and Learning of
Algorithms in School Mathematics: NCTM Yearbook. Reston: VA: NCTM.