Welcome to the most awesome math art holiday project you can imagine! Make a Christmas tree out of a Sierpinski fractal triangle.
This Christmas math art project is a great STEAM activity for kids to do at home, but also in the classroom, where kids working together can construct a huge fractal tree.
For the uninitiated... a Sierpinski triangle is a mathematically generated pattern in which self-similar shapes are repeated across different scales in a never-ending feedback loop. In layman's terms, the same shape is repeated in different sizes to infinity.
The fractal is named after Wacław Sierpińsk, a Polish mathematician, who made contributions to set theory and number theory. You can read more about the math involved in the Sierpinski triangle here.
You can see my Sierpinski triangle drawing project in my book, STEAM Kids Christmas, and now I am going to encourage you to take that drawing and turn it into a 3D fractal triangle!
Here's a peek at the 2D Sierpinski Christmas tree:
Find out how to make the fractal tree drawing in STEAM Kids Christmas.
Okay, on to 3D fractal math art awesomeness.
First watch the video to experience the magic, or scroll down for written instructions and the photo how-to.
Note: although we did this project as a Christmas tree, you can do it any time of year without a holiday theme.
How to Make a 3-Dimensional Sierpinski Tree
What you need:
- The tetrahedron template. Get the printable here. You will need 4 tetrahedrons to make the small, basic tree and 16 tetrahedrons to make the larger fractal tree.
- Construction paper in any color you wish.
- Scissors
- Tape
Instructions:
Print out the template.
Cut out the tetrahedron, fold along the solid lines, fold up into the 3D shape.
Tuck in the flaps and tape edges.
Make the basic tree by taping together 4 tetrahedrons to make one large tetrahedron. Three tetrahedrons are the base and one tetrahedron sits on top, as shown in the photograph below.
Make four of these basic trees.
Tape the 4 basic trees into a large tetrahedron. Again, three basic trees will form the base, with one basic tree settled on top. This large tetrahedron will be composed of 16 of the original tetrahedrons.
Congratulations. You just made your first Sierpinski fractal!
Make as many of these large tetrahedrons as you wish in order to keep scaling up your fractal design. Follow the rule that you'll need four of each size to scale up.
If you are doing this as a holiday project you can top off the fractal tree with a star. TIP: in STEAM Kids Christmas I included instructions for making a fractal star, also known as a "Koch snowflake"! See below for a sneak peek of the math art snowflake!
Don't forget to do more awesome STEAM projects, including beautiful math art projects and designs throughout the year. My team has an amazing resource I know you will love.
Rachel says
I know people who do this with hamantaschen for Purim.
Thomas says
Have done this but on a larger scale. It's a nightmare to keep together, but very effective.
Suzie Homemaker says
Is the star a Moravian Star? I ask because our church is In Moravian Falls NC and those stars are hugh here. One tops our church tree. They were a math challenge when they first came about in the moravian church.
Nicole Irzl says
Good afternoon,
I really liked this activity and would love to try it.... however I hate wasting paper.
Wouldn't it be possible to have 2 tetrahedrons per page? : )
Enjoy all your ideas and look forward to receiving your mails. THANK YOU!!
Erica says
If you cut out the template on a piece of heavy paper then you can use it as a template to trace the tetrahedron and fit as many as possible on to one sheet. Unfortunately I don't have a fancy drawing software program (and I'm not that skilled!) and if I size it down to fit two to a page it becomes too small. But tracing the template should work well!