I started off thinking this post was going to be about the fact that sunflowers make two different kinds of flowers, which I think is really interesting.

When we think of sunflowers, we think of the big showy flowers around a central disk. But the disk is made up of flowers, too!

And actually, the disk flowers are where the seeds are made.

And then, as I was looking at all my sunflower photos, I noticed something really interesting: the disk flowers are arranged in a spiral pattern. I’ve drawn lines to show the pattern. But once you get the hang of looking at the flowers, you can see the pattern without help. Try it looking at the sunflower without swirls, above.

Another sunflower, prairie coneflower, does the same thing.

The patterns develop according to the mathematical sequence of the Fibonacci sequence, after an Italian mathematician in the Renaissance, but the pattern was first noticed in India in the 2nd Century BC. It goes like this: 0, 1, 1, 2, 3, 5, 18, 23, 41 … The sequence results from the product of adding the two numbers before it. So 0 + 1 = 1, 1+1 = 2, 1+2=3, 2+3=5, 3+5=8 …

The Fibonacci sequence shows up in plants, animals, art, architecture, weather, computer science, and probably a few other places I haven’t heard about.

I think a mathematician could tell you why plants order their flowers this way. I think it has something to do with packing the most flowers into an expanding space.

The way the math works out, the swirls go both ways, which I think is amazing!

And it’s not just sunflowers that do it — this teasel is in the honeysuckle family. I’ve written about other plants that I’ve seen the Fibonacci sequence in here.

And then, I noticed that in addition to lining up with swirls that go both directions, the swirling patterns make a spiral out from the center.

Amy Law is a science geek. She feels about science the way some people feel about music, or art, or sports – a total and complete emotional connection. She thinks in science.
For Amy, there’s nothing better than helping people see the beauty of science as she does. She loves to untangle a complicated subject into its parts, explaining it so that anybody can understand what’s happening. Let her show you her world...
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5 thoughts on “Patterns in Nature”

I’ve always found the idea of the Fibonacci sequence fascinating, Amy. Can you tell us more about the origins in India in the 2nd century BCE? Was it first seen in stars, by chance?

I would love to explore the Fibonacci sequence more! I will warn you, though, that it will require a bit of research. And that will take me a little time. But I’m on it!

I know, right? And the craziest part of the whole flower is that those big showy ray flowers around the disk are JUST FOR SHOW! They attract the pollinators to the little disk flowers that actually make the seeds. I love nature. Every time I think I’ve got it figured out, it throws me a curve.

I’ve always found the idea of the Fibonacci sequence fascinating, Amy. Can you tell us more about the origins in India in the 2nd century BCE? Was it first seen in stars, by chance?

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I would love to explore the Fibonacci sequence more! I will warn you, though, that it will require a bit of research. And that will take me a little time. But I’m on it!

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Interesting! I never knew the inner part had flowers too!

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I know, right? And the craziest part of the whole flower is that those big showy ray flowers around the disk are JUST FOR SHOW! They attract the pollinators to the little disk flowers that actually make the seeds. I love nature. Every time I think I’ve got it figured out, it throws me a curve.

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