Teaching Fractals

Fractal Heart Tree

With printable activity

Reading my children the book Swirl by Swirl: Spiral in Nature yesterday sparked my interest in fractals.  I watched the PBS program Nova: Hunting the Hidden Dimension last night and honestly, fractals might be the hardest concept I have tried to understand!  The video does a great job of explaining in layman’s terms. Even so, throughout the program, I vacillated between glimpses of understanding and wonder and confusion bordering on terror!  If you are interested in learning about fractals, I highly recommend you watch this program.  I found it to be a very fascinating way to spend an hour and a great introduction to fractals!


There is no definitive definition for fractals.  Fractals are characterized by repeating patterns within an object at a smaller and smaller scale.  Fractal characteristics had been know about and utilized for centuries.  I can remember learning about the Fibonacci spiral and its application in classical architecture from art history class.  However, fractals were named and really brought to light by Benoit Mandelbrot, an IBM mathematician in the 1970’s with the publication of his book – Fractals: Form, Change, and Dimension.


As fractals are themselves infinite, they also seem to have infinite potential for applications even though this potential is not fully accepted in the traditional mathematical community.  The Nova program gives some current examples of how fractals are being used today: creating realistic looking natural elements like mountains for special effects and games, miniaturizing cell-phone antennas, and as an analytically tool for scientists.  By taking measurements from one tree and measuring the CO2 from one leaf of that tree, the CO2 absorption potential for the entire surrounding forest can be extrapolated!  It also gave some examples of potential future uses like detecting cancers using ultrasound.  Cancers have different fractal structures to their blood supply networks than that of healthy tissue.

I love this part…  You might look at the natural world you see chaos but if you zoom in you will begin to see repeating patterns.  Trees look complicated but if you break them down into smaller and smaller forking elements they are actually pretty simple and their growth relies on a identifiable fractal equation!


Here is my simple version of a Sierpinski’s Triangle being built.  If you would like to see an infinite ZOOMING version click on this link!

You can bring fractals to life for children with this simple activity.  Print out the following PDF in multiples (3, 9, or 27 will create another full triangle): Sierpinski’s Triangle

Then you can color (if you like), cut out, and try to repeat the pattern you see in the triangle at an increasingly larger scale!  


I'm a practical mom inspired by nature & I enjoy sharing ideas that encourage kids' innate curiosity & creativity. Interested in subscribing? Check out the blue box at the top of my sidebar. I'm also a wannabe author/illustrator & product designer by day. Let's connect! doodlesandjots@hotmail.com. If you purchase through my Amazon links I get a small commission at no additional cost to you (thanks for supporting Doodles and Jots)! And remember to always credit your source here & elsewhere on the internet.


  1. Thanks for sharing these resources. A long, long time ago, I took a workshop on fractals, and about all I remember from it is my brain hurting afterwards! I guess it would be good to tackle it again with my kids.

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