You'll enjoy succulents even more when you see how many have Fibonacci spirals. I show gorgeous examples (all ID'd) in my latest video and in the Gallery below.
What's a Fibonacci spiral?
It’s a pattern often seen in the natural world. You’ve likely seen Fibonacci spirals in the centers of sunflowers, pine cones, artichokes, and even photos of hurricanes and galaxies.
In botany, spiral phyllotaxis is when leaves along a plant’s stem are arranged in the numerical sequence first described by Leonardo Fibonacci, a 12th-century Italian mathematician.
It’s actually pretty simple: Each number in the sequence is the sum of the two numbers that preceded it.
So: 1 and 1 are 2, 1 and 2 are 3, 2 and 3 are 5, 3 and 5 are 8, 5 and 8 are 13, 8 and 13 are 21 and so on. One way to explain it is to draw on graph paper squares each with sides that are successive Fibonacci numbers.
This also illustrates what’s known in art and architecture as the Golden Ratio.
The Golden Ratio
Artists and architects routinely consider the Golden Ratio in their designs. You may be using it yourself without knowing you’re doing so, when composing or cropping a photo; it’s called the Rule of Thirds.
The idea is you can make a photo more pleasing to the eye by placing its subject in the left or right third of an image, leaving the other two thirds more open.
Massachusetts graphic designer Jonathan Cleveland says of the Golden Ratio, “Overall, it’s an interesting way to look at great design through a mathematical lens.”
aesthetic Yet USEFUL
Why do plants have spiral leaf arrangements? What purpose does it serve? It’s certainly practical for succulents. A spiral of leaves enables rain to funnel down to roots, and keeps upper leaves from shading lower ones.
However what’s not so obvious is why Fibonacci spirals strike humans as pleasing to look and fascinating to discover.
It comes down to aesthetics, which is subjective. Perhaps you, like me, gravitate to the unadorned simplicity of spirals. Take echeverias: When I ask people if they like those with bumpy leaves, some do, some don’t.
Personally, I like the weirdness and irregular variations of the bumps, but I also prefer echeverias with tight overlapping leaves. No wonder Echeveria ‘Raindrops’ is so popular. It offers the best of both, having bumps on leaves arranged in a tight pattern.
And who doesn't like agaves with leaves that have a crisp geometry, like the Queen Victoria agave below?
However, I wonder if you feel the same as I do about Agave ‘Cornelius’...
'Cornelius' has yellow-and-green stripes and leaves with wavy edges. It’s colorful, odd and interesting, but those marginal ripples hide the very reason most of us like agaves: their symmetrical leaf arrangements.
Above: Agave americana has leaves arranged in a Fibonacci sequence. This one bloomed and had to be removed (not sure why I'm smiling). Do you see why the core of an agave is called a piña in Mexico? It means pineapple, which also exhibits the sequence. (Photo from my site's tequila post.)
Perhaps the most famous succulent for its Fibonacci sequence is aptly named spiral aloe (Aloe polyphylla). It's tricky to grow, making it the Holy Grail of succulents. If you can grow spiral aloes, you can grow anything.
Other aloes have leaves that follow the Fibonacci sequence, but the longer and narrower the leaf, the less noticeable the spiral.
Succulents with sunflower centers
Medusa euphorbias are known for craggy, snakelike stems that radiate from a spiral that resembles the center of a sunflower.
The spines of spherical cacti follow the Fibonacci sequence. When the pattern is prominent, I prefer the plants out of bloom. The flowers, at least for me, take attention away from the pattern.
Once you realize that plants in your garden and potted collection exhibit Fibonacci spirals, you’ll start seeing them everywhere.
But not 4!
Four is not a Fibonacci number. Very few flowers have four petals. (Don't take my word for it; see if you run across any.) Subliminally, we expect flowers to have 5, 8, 13 or more overlapping petals, and when they don’t, something's not quite right.
So if you draw a flower from imagination, don’t give it four petals; it’ll look more realistic with five.
Do you have a favorite Fibonacci succulent, one you long to have, or a story about one to share? Tell us in the Comments below!
Gallery of Succulents with Fibonacci Spirals
More INFO on this site
Remarkably, the spination of certain cacti suggests snowflakes, something I first noticed years ago at a succulent specialty nursery. I was there to photograph aloes in bloom, but I’d come too early in the season. I thought of leaving, and I’m so glad I didn’t! That afternoon forever changed the way I see certain succulent…
This essential info on medusoid euphorbias (snake-leaved plants) is from “Spiny Succulents: Euphorbias, cacti, and other sculptural succulents,” by renowned nurseryman Jeff Moore, owner of Solana Succulents near San Diego. I highly recommend his brand new book.
How can you tell a spiny euphorbia from a cactus? Observe key characteristics: the type of spines, flowers and leaves (or lack thereof). As I compiled my site’s new Euphorbia page, I happily acquired the ability to tell at a glance which is which. Sure, you can scratch a plant, and if it drips milky sap, it’s