Math Mondays: Fractal Fun for Time-Fillers

I love to merge math with other subject areas.  Often the easiest link is between math and science, but the intersection between art and math can be fascinating. 

This week, my students made some discoveries about fractals.  Fractals are a never-ending pattern.  Fractal numbers repeat a pattern and never end.  It could be 3.33333 or  ... 5.162162162 or ... 242424242424 or...

Fractals occur throughout nature.  To introduce students to fractals, we began with a series of examples of fractals in nature such as those in the pictures below:

You might also share pine cones, which if you collect at the right time of year can provide a hands-on exploration.  

When I first was planning fractal activities, I had thought we would construct  Koch snowflakes.  I tried them myself.  They are not easy.  Knowing my students, I decided that fractals could be much more fun and engaging.  So, I introduced some examples of visual fractals such as the Sierpinski Triangle

 and the Pythagorean Fractal.

Then, students decided whether they wanted to try an existing fractal or wanted to make their own.  My talkative class turned silent as they focused their attention on the creation of the complex fractals.  A large variety of fractals were created such as the box fractals.
I challenged the students to explore the algorithms used to create their designs or the other ones, such as Sierpinski's triangle .  For a complete guide and lesson with student handouts, you might like the Art of Fractals.  Enjoy!

Math Mondays is a bi-weekly blog post (2nd and 4th Monday of each month) sharing tips, ideas, resources, and products for teaching math.  If you have questions or think there is something I should include, you can leave me a message in the comments section below or at the store in the question and answer section.



  1. Very interesting connections here! Love the differentiation used to allow students to make up their own or create an existing fractal.

  2. A great way to engage students - and you are right; math and art are a natural pair!