Explore the geometry of nature
Fractals here, fractals there, fractals everywhere…but what are they?
In mathematics, a fractal is a never-ending pattern at different scales. Fractals are complex patterns but they are actually made by repeating a simple process.
What do ferns have to do with fractals?
A fractal is an infinite pattern in mathematics, but we can also find limited fractal patterns in nature!
Head to the kitchen for a fractal-spotting warm up! Broccoli, especially the fancy Romanesco broccoflower, is a great example of a fractal pattern. Do you see repeating patterns and small parts of the broccoli that look like the whole broccoli? You’ve spotted a fractal! Don’t like broccoli? Take a peek at a pineapple—they have fractal patterns too.
Exploring Geometry in Nature
Activity: Go for a “fractal hunt” in the woods!
• Look for similar patterns in natural objects that repeat at different scales.
• Kids’magnifying glasses add extra fun for young nature sleuths.
• Phones/cameras are a great way to capture interesting subjects for reseach later.
• Sketching in nature using a small notebook is another wonderful way to observe mindfully.
1. Trees are great examples of fractals in nature.
• Examine the branches from the trunk to the outer tips. Look for the “Y” repetition at different scales.
• If you come across the exposed roots of a fallen tree look for repeating patterns in the root system.
• Now put on your x-ray glasses and look underground. Look at all the tiny fungi threads growing around the tree roots. Forgot your x-ray goggles? You can check out images of fungi threads (mycelium) online for fun.
2. Plants, leaves and pinecones
Look closely at a fern frond. You’ll see that it’s made up of a series of repeating patterns.
Did you notice that the whole fern has the same shape as one or more of the parts? Fern fractals!
Extra challenge: Use a plant guide to see how many different kinds of ferns you can spot: Sword, Bracken, Maidenhair, Licorice, and Lady Ferns!
Find a leaf. Look at the centre vein, now look at all the separate veins that branch off of it. Look EVEN closer. What’s inside? Even smaller repeating branching veins!
Pick up a pinecone. Follow the repeating spiral pattern from the bottom all the way to the top. You guessed it…the pinecone spirals are similar at different scales.
When we visit a local park it’s the perfect opportunity to remind everyone to tread gently and leave nature the way they found it. Encouraging kids to slow down and observe nature is a super healthy activity. It’s also a great way to nurture their understanding and appreciation of their surroundings.
Frac-tivities and Fun Facts
Draw leaf fractals—trace a leaf outline onto a sheet of paper. Draw the main leaf vein on your paper. Using a different colour draw some of the leaf veins that branch away. Choose another colour and draw some of the even smaller vein patterns inside.
You can look for fractals at the beach too! Seashell spirals, sea urchins and starfish.
Can you think of any other fractal patterns in nature? Hint: river and animal circulatory systems, lightning, clouds, snowflake crystals, lichen and flowers like Queen Anne’s Lace
“Fractal” comes from the Latin word, fractus meaning fragmented or broken.
Benoit Mandelbrot, a famous mathematician came up with the word fractal.
Want to see some amazing patterns—do a deeper dive into the mathematical world of fractals? Check out: The Mandelbrot Set, Koch Snowflake and Sierpinski Triangle.