Fractal Patterns In Nature: How to Help Your Outdoorsy Girl Love Math

If you’ve got a tree-hugging kid who adores the great outdoors, she’s gonna LOVE the math of finding fractal patterns in nature.

little girl finding fractal patterns in nature

Fractals are one of the coolest ways to show a connection between math and the real world. Once she knows what to look for, your girl will start looking for math everywhere!

What the heck is a fractal?

Think of fractals as the Russian dolls of nature. A large shape is made of smaller similar shapes, which are made of even smaller similar shapes…and so on.

fractal patterns in nature are like Russian dolls

A fractal is a geometric shape whose parts reflect the whole.

Let’s take a look at some of the most jaw-dropping nature fractals…

A Close-Up Look At Fractal Patterns in Nature

This is Romanesco broccoli. It’s shaped like a cone, with smaller cones that spiral down from the tip. Each one is an identical pattern in miniature.

fractal patterns in nature - Romanesco broccoli

Look closer and you’ll see that the small cones are made of even teenier cones in the exact same spiral shape…

fractal patterns in nature - Romanesco closeup

…and those teeny cones are made of impossibly small, even teensier ones!

It’s like a pinhole glimpse into infinity. How far down does it go??

Ferns are fractals, too. This baby fern frond is a tight spiral, filled with identical-looking mini-spirals…

fractal patterns in nature: unfurling fern

…which are made of even smaller spirals…which are made of even teensier spirals.


It’s not just the fern babies that show this pattern. Mature ferns are some of the most of the coolest fractal patterns in nature.

fractal geometry fern: fractal patterns in nature

Look at the shape of the largest leaf, then look for that shape in smaller and smaller forms.

fractal leaf close-up: fractal patterns in nature

Lightning is an impressive force of nature. How are the parts like the whole?

lightning fractal patterns in nature

Here’s a photo of an oak tree…

oak tree fractal plant: fractal patterns in nature

…and here’s a close-up of one of the branches. What do you notice? What if you zoom in even closer to a smaller branch?

oak tree branch close up: fractal patterns in nature

This is the view of a coastline from an airplane. What do you see?water from above: fractal patterns in nature

This is a river from above. Bodies of water often create repeating patterns.

rivers from above: fractal patterns in nature

Have you ever looked closely at a dandelion?

dandelion fractal patterns in nature

close-up dandelion fractals in nature

What other fractal patterns in nature can you find?


  1. Is a pinecone a fractal?

    1. A pinecone is not a fractal. In a fractal, the smaller parts look like the whole at a smaller scale. The scales of a pinecone do not look like mini-versions of a pinecone, so it is not a fractal. (However, a pinecone IS a great example of Fibonacci numbers in nature!)

  2. I’m an artist but terrible at math, I can’t remember the rules or memorise times tables. I love fractals and geometric patterns. I wanted to be a teacher but could never achieve the maths grades. Can you recommend any good books for me as an adult to learn math, I’m a visual learner. I still want to be a teacher and hope to one day get good at math.


    1. Hi Elle! First off, I highly recommend A Beginner’s Guide to Constructing the Universe by Michael Schneider. It won’t teach you math, but it will take you on a life-changing journey through visual math, and help you see connections to math EVERYWHERE!

      As to a math book for visual adults, that’s trickier. You might try Life of Fred books; they are story based and really good. You might also buy some used textbooks for Singapore Math, just go through them yourself. That method really works for me. Finally, build your confidence and understanding with games and puzzles. https://nrich.maths.org/ and https://youcubed.org have great visual math.

      Let yourself be a beginner, start with whatever feels easy even if that’s fourth grade math, and go from there. Enjoy the journey. I started just like you, and taught myself over time with games, puzzles, pictures, cut paper, whatever worked. You can totally do this!

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