Pine Cones and the Fibonacci Sequence

While we’re on the topic of pine cones, have you ever considered their scales and the spirals they form? Nature is replete with spirals, so perhaps it’s no surprise that they are found in pine cones. The more interesting thing is that the number of spirals found on pine cones are almost always Fibonacci numbers. But maybe that’s not that surprising either, as Fibonacci numbers are also pretty common in nature.

Add 1 plus 1 and you get 2. Add 2 plus 1 and you get 3. 3 + 2 = 5, 5 + 3 = 8, and 8 + 5 = 13. One, two, three, five, eight, and thirteen are Fibonacci numbers. Continue adding the sum to the number that came before it, and that’s the Fibonacci Sequence. The ratio of two neighboring Fibonacci numbers is an approximation of the golden ratio (e.g. 8/5 = 1.6). This is commonly represented by drawing a series of squares on graph paper and then drawing a spiral across the squares. Each square drawn is larger than the last in accordance with the Fibonacci sequence, and the spiral drawn through the squares is a logarithmic spiral.

So, what does this have to do with pine cones? Well if you count the number of spirals that are going to the right, then count the number of spirals going to the left, you usually end up with two adjacent numbers in the Fibonacci sequence. Most often it’s either 5 and 8 or 8 and 13. You can find this same pattern in lots of other plant parts, including the aggregate fruits of pineapples, the disc flowers of sunflowers (and other plants in the aster family), the bracts of artichoke flowers, florets on a cauliflower, and leaf arrangements of all sorts of other plants.

The arrangement of leaves is called phyllotaxis, and when the leaves on a stem form a spiral pattern it’s called a phyllotactic spiral. The benefit the plant receives from having its leaves grow in a spiral formation down the length of its stem is actually quite simple – it keeps them from shading each other out and thereby maximizes their exposure to the sun. If you measure the angle between each leaf, the angle should be the same between each adjacent leaf on the stem. In order for the number of spirals to be a Fibonacci number, the leaves have to be oriented at a specific angle from each other. But this isn’t always the case. Depending on the angle, the number of spirals could be part of some other number sequence, like Lucas numbers perhaps.

While the specifics of plant growth can be quite complex, the reason for the patterns that result is actually quite simple. As plants grow new parts, they are put in a spot where there is room for them to grow, which is at some angle from the part that grew before it. Once that angle is “chosen,” it generally doesn’t change, and as more plant parts grow, a spiral forms (or no spiral forms at all, depending on the pattern of growth). If plant parts are oriented at a specific angle (~ 137.5o), the numbers of spirals end up being Fibonacci numbers. For a more thorough and entertaining explanation of all this, check out this three part video series from Khan Academy. It’s well worth the watch.

And now an example:

Count the number of right-hand spirals on this ponderosa pine cone. There are 8. That’s a Fibonacci number!

Count the number of left-hand spirals on this ponderosa pine cone. To make it easier to count, you can start or end with the top left spiral that has alternating red and green scales. There are 13. That’s another Fibonacci number!

And now your mission, should you choose to accept, is to find a pine cone (or some other conifer cone) in which the number of right and left-hand spirals are not Fibonacci numbers. They’re definitely out there, so let me know what you find in the comment section below.

Further Reading:

Out Now! Dispersal Stories #1

Before I started this blog, I had spent 16 years publishing zines at a steady clip and sending them to all corners of the world through the mail. I had never really meant to abandon zines altogether, and in some ways, putting all my writing efforts into a blog felt a little like a betrayal. My intention had always been to one day put together another zine. Now, six and a half years later, I’m happy to report that day has come.

Rather than bring an old zine back from the grave, I decided to make a new zine. Thus, Dispersal Stories #1. It’s quite a bit different from zines I’ve made in the past, which were generally more personal and, I guess, ranty. In fact, Dispersal Stories is very much like this blog, largely because it is mostly made up of writing that originally appeared here, but also because its main focus (for now) is plants. What sets it apart is that, unlike this blog, it zeroes in on a specific aspect of plants. As the title suggests, it’s all about dispersal. For much of their life, plants are essentially sessile. Once they are rooted in place, they rarely go anywhere else. But as seeds, spores, or some other sort of propagule they are actually able to move around quite a bit. The world is their oyster. What’s happening during this period of their lives is the focus of Dispersal Stories.

But why do a zine about this? Apart from just wanting to do another zine after all these years, my hope is that Dispersal Stories will be the start of a much more ambitious project. A book perhaps. My interest in dispersal was born out of my interest in weeds, and there is so much that I would like to learn and share about both of these subjects – so much so that the blog just doesn’t really cut it. So, I’m expanding the Awkward Botany empire. First a zine, then a book, then … who knows? I’m an oyster! (Or something like that.)

Dispersal Stories #1 is available in our etsy shop, or you can contact me here and we can work something out. While you’re at it, check out our new sticker.

If you love looking at plants and learning their names, then you probably enjoy doing it any chance you get. Usually it’s an activity you do while walking, but who says you can’t botanize while riding a bike? This sticker is inspired by a friend who once said that while mountain biking you get to “see three times as many flowers in half the time!” Stick it on your bike or in some other prominent location to remind yourself and others that we can botanize anytime anywhere.

Your purchase of one or both of these items helps support what we do. You can also support us by buying us a ko-fi or putting money in our donorbox. Sharing these posts also helps us out. If you get a copy of the zine, let us know what you think by sending us an email, a message on twitter or facebook, or by leaving a comment below. As always, thanks for reading.

Related Posts:

Pine Cones Are Like Hangars for Pine Tree Seeds

Over the past year I’ve written about the making of pine tar and the drinking of pine needle tea. But why stop there? Pines are a fascinating group of plants, worthy of myriad more posts, and so my exploration into the genus continues with pine cones and the seeds they bear.

Pines are conifers and, more broadly, gymnosperms. They are distinct from angiosperms (i.e. flowering plants), with the most obvious distinction being that they don’t make flowers. Since they are flowerless, they are also fruitless, as fruits are seed-bearing structures formed from the ovary or ovaries of flowering plants. Pines do make seeds though, and, as in angiosperms, pollen is transported from a “male” organ to a “female” organ in order for seeds to form. Rather than being housed in a fruit, the seeds are essentially left out in the open, which is why the term “naked seeds” is frequently used in reference to gymnosperms.

seed cone of Scots pine (Pinus sylvestris ‘Glauca Nana’)

In the case of pines and other conifers, the seeds may be naked, but they’re not necessarily homeless. They have the protection of cones, which is where the female reproductive organs are located. Male, pollen cones are separate structures and are smaller and less persistent than the cones that house the seeds. A cone, also known as a strobilus, is a modified branch. A series of scales grow in a spiral formation along the length of the branch, giving the cone its shape. On the inside of these scales is where the seeds form, two per scale. First they are egg cells, and then, after pollination and a period of maturation, they become seeds. The scales protect them throughout the process and then release them when the time is right.

With more than 120 species in the genus Pinus, there is great diversity in the size, shape, and appearance of pine cones. While at first glance they don’t appear all that different from one another, the cones of each species have unique characteristics that can help one identify the pine they fell from without ever having to see the tree. Pine cones are also distinct from the cones of other conifers. For one, pine cones take at least two or, in some cases, three years to reach maturity, whereas the cones of other conifers develop viable seeds in a single year. Pine cones are also known to remain on the tree for several years even after the seeds are mature – in some species up to 10 years or more – and they don’t always part with their seeds easily. Lodgepole pines (Pinus contorta) require high temperatures to melt the resin that holds their scales closed, the cones of jack pine (P. banksiana) generally only open in the presence of fire, and the seeds of whitebark pine (P. albicaulis) are extracted with the aid of birds (like Clark’s nutcracker) and other animals.

immature seed cone of lodgepole pine (Pinus contorta)

Every pine cone is special in its own right, but some stand out in particular. The largest and heaviest pine cones are found on Coulter pine (P. coulteri), measuring up to 15 inches long and weighing as much as 11 pounds with scales that come to a sharp point. It’s understandable why the falling cones of this species are frequently referred to as widowmakers. Longer cones, but perhaps less dangerous, are found on sugar pine (P. lambertiana). The tallest trees in the genus, the cones of sugar pine consistently reach 10 to 20 inches long and sometimes longer.

Pine tree seeds are a food source for numerous animals, including humans. Most are so small they aren’t worth bothering with, however, several species have seeds that are quite large and worth harvesting. Most commercially grown pine nuts come from stone pine (P. pinea) and Korean pine (P. koraiensis). In North America, a wild source for pine nuts is found in the pinyon pines, which have a long history of being harvested and eaten by humans.

immature seed cone of ponderosa pine (Pinus ponderosa)

The seeds of many pines come equipped with little wings called samaras, which aid them in their dispersal. Upon maturity, pine cone scales open and release the seeds. Like little airplanes leaving the hangar, the seeds take flight. Wind dispersal is not an effective means of dispersal for all pines though. A study published in Oikos found that seeds weighing more than 90 milligrams are not dispersed as well by wind as lighter seeds are. When it comes to long distance dispersal, heavier seeds are more dependent on animals like birds and rodents, and some pines rely exclusively on their services. The author of the study, Craig Benkman, notes that “bird-dispersed pines have proportionately thinner seed coats than wind-dispersed pines,” which he points out in reference to Japanese stone pine (P. pumila) and limber pine (P. flexilis), whose seeds weigh around 90 milligrams yet rely mostly on birds for dispersal. Benkman suspects that the seeds of these two species “would probably weigh over 100 milligrams if they had seed coats of comparable thickness as wind-dispersed seeds.”

Whitebark pine, as mentioned above, holds tightly to its seeds. Hungry animals must pry them out, which they do. Pine seeds are highly nutritious and supplement the diets of a wide range of wildlife. Some of the animals that eat the seeds also cache them for later. Clark’s nutcrackers are particularly diligent hoarders, harvesting thousands more seeds than they can possibly consume and depositing them in small numbers in locations suitable for sprouting.

Even large seeds that naturally fall from their cones have a chance to be dispersed further. As the seeds become concentrated at the base of the tree, ground-foraging rodents gather them up and cache them in another location, which Benkman refers to as secondary seed dispersal.

Particularly in pine species with wind dispersed seeds, what the weather is like helps determine when the hangar door will open to release the flying seeds. When it is wet and rainy, the scales of pine cones close up. The seeds wouldn’t get very far in the rain anyway, so why bother? When warm, dry conditions return, the scales open back up and the seeds are free to fly again. You can even watch this in action in the comfort of your own home by following the instructions layed out in this “seasonal science project.”

immature seed cones of limber pine (Pinus flexilis)

mature seed cones of limber pine (Pinus flexilis)

Further Reading:

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Photos of pine cones were taken at Idaho Botanical Garden in Boise, Idaho