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A Fibonacci in Nature Experiment: Count Pinecone Spirals
A Fibonacci in nature experiment with real pinecones: mark the spirals, count both directions, and find out how often the famous numbers actually show up.
Almost everything written about Fibonacci numbers in plants is slightly wrong, and the wrongness is easy to fix with six pinecones and two coloured pens. The popular version says nature follows the sequence. A Fibonacci in nature experiment done properly says something better: the numbers show up most of the time, from a local rule about where the next bud fits, and the exceptions are the interesting part. Your kid will mark spirals, count 8 one way and 13 the other, and then find a cone that gives 9 and 14 and have to decide what to do about it.
Key Takeaways
- You’ll mark the spiral families on six pinecones with coloured pens, count them in both directions, and build a tally table.
- It teaches the Fibonacci sequence, and more importantly that a pattern in nature can be common without being a law.
- Best from 7. The maths is easy; keeping your place while tracing a spiral around a cone is the genuinely hard part.
- Expect pairs like 5 and 8, 8 and 13, or 13 and 21. Expect at least one cone that refuses to cooperate.
- Open, dry cones work. A closed green cone has no visible spiral families and will waste twenty minutes.
What You’ll Need
| Item | How much | Where to get it | If you don’t have it |
|---|---|---|---|
| Open, dry pinecones | 6, as different in size as you can find | Under any pine tree, or a craft shop | A pineapple, a sunflower head, or a Romanesco cauliflower |
| Fine permanent markers | 2 colours, ideally red and blue | Stationery | Small coloured sticker dots, which are easier for small hands |
| Paper and pencil | 2 sheets | Anywhere | Phone notes app |
| A tray or newspaper | 1 | Kitchen | Work outside |
| Toothpick or cocktail stick | 1 per person | Kitchen drawer | A pencil tip, used gently |
| Magnifier | Optional | Toy box | Phone camera zoom works well |
Time: collecting 20 min (or do it on a walk the day before), marking and counting 35 min, cleanup 5 min Cost: free, unless you buy a pineapple Mess level: low, but resin gets on fingers and does not wash off with water
Do the Experiment: A Fibonacci in Nature Experiment
Step 1 – Dry the cones for a day
A closed cone has nothing to count. Leave your cones somewhere warm and dry indoors for 24 hours and they will open on their own. Do not put them in the oven: it works, but it is an unnecessary heat and smoke risk for a step that patience solves.
Step 2 – Find the base and sit the cone down
Hold the cone with the stem end down. Look straight down at the top, or at the flat base, whichever shows clearer rows. You are looking for lines of scales that sweep around the cone, not the scales themselves.
Step 3 – Trace one spiral in red
Pick any scale near the base. Find its neighbour that continues the gentlest, flattest curve to the right, and dot it red. Keep going around the cone, dotting as you climb. You will spiral upward and eventually run off the top. That line of red dots is one spiral of one family.
Step 4 – Count how many red spirals there are
Go back to the base. Start one scale to the left of your first red scale and trace the next spiral in the same direction. Then the next. Keep going until you come back to the first red line. The number of distinct spirals you traced in that direction is your first number. This is the step where everybody loses count, so dot as you go and count dots at the base, not scales in the air.
Step 5 – Do the other direction in blue
Now trace the family of spirals that lean the other way and count those. On most cones the two numbers differ: 8 and 13 is the most common pair on medium cones, 5 and 8 on small ones, 13 and 21 on large ones.
Step 6 – Tally all six cones, then write out Fibonacci
Make a table: cone, size, count one way, count the other way. Only after all six are recorded, write out the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, each number the sum of the two before it. Then compare. Doing it in this order matters, because a child who knows the answer will find it whether or not it is there.
Step 7 – Argue about the odd one out
At least one cone will give something like 9 and 14, or a count you cannot settle. Do not throw it away. Write it down with a note about why it was hard. This is the step that turns a demonstration into data.
What you should see: Four or five of six cones will give two consecutive Fibonacci numbers, usually 8 and 13. One will be ambiguous or off by one, often because the cone is damaged, lopsided, or grew with a kink. Counting one family takes a motivated nine-year-old about four minutes with dots, and roughly forever without them.
What’s Actually Going On
The pattern has a name: phyllotaxis, the arrangement of leaves, scales or seeds around a stem. The spirals you counted are called parastichies, and their counts are the parastichy numbers.
Here is the mechanism, and it is simpler and stranger than the usual story. At the growing tip of a plant, new bumps called primordia form one at a time on a ring of tissue. Each new primordium appears in the largest gap left by the ones already there, because existing primordia inhibit new growth nearby. Run that single local rule repeatedly and the angle between successive primordia converges on roughly 137.5°, the golden angle, which is 360° divided by the square of the golden ratio. Spiral families become visible because the plant keeps placing buds at that angle while the stem grows outward, and the number of visible spirals turns out to be a pair of consecutive Fibonacci numbers. The reason is a fact about the golden ratio: its best rational approximations are exactly the ratios of consecutive Fibonacci numbers.
The important part is that the plant is not doing arithmetic. There is no gene encoding “13”. Douady and Couder demonstrated this in 1992 with a physical model: drops of magnetic fluid falling onto a dish of silicone oil, repelling each other and drifting outward. With no biology at all, the drops arranged themselves into Fibonacci spiral phyllotaxis. The pattern comes from the geometry of packing things that push each other apart, which is why the same numbers show up in cones, sunflowers, pineapples and cacti. Mitchison set out the mathematics of this in Science in 1977.
Two popular claims deserve correcting. The first is that this arrangement is the mathematically optimal way to catch sunlight. It is a good arrangement, and avoiding overlap matters, but the Fibonacci numbers fall out of the local inhibition rule rather than from the plant solving an optimisation problem. The second is that Fibonacci phyllotaxis is universal. It is not. The largest study of this question is a citizen-science project on sunflowers published in Royal Society Open Science in 2016: of 768 reliable spiral counts taken from sunflower heads, 565 were Fibonacci numbers and a further 67 showed a related, predefined kind of Fibonacci structure. That leaves a real remainder, including heads where no spiral number could be assigned at all. Roughly three in four is a common pattern. It is not a law of nature, and telling a child the truth is more interesting than telling them a rule.
How to Explain It to Your Kid
Ages 5–8: find the rows that go round
Don’t say Fibonacci. Say: “There are secret rows on this pinecone. Can you find one?” Help them dot a single spiral with stickers, and then ask whether they can find another one that never touches the first. Count the rows together, out loud, pointing. If they get 8 and you get 8, that is the whole win. Then hand them a pineapple and let them discover the rows go round that too.
Ages 9–12: build the sequence and check it
Write 1, 1, 2, 3, 5, 8, 13, 21 and ask them to find the rule before you say it. Once they have it, go back to the tally table. Ask the sharper question: do the two counts on a single cone sit next to each other in the sequence, or can you get 5 and 21? They will check, and the answer is that they are almost always neighbours. That is a much more specific claim than “pinecones are Fibonacci”, and it is testable.
Ages 13+: the golden angle and the packing rule
Introduce 137.5° and have them construct it: mark points on a spiral on paper, turning 137.5° each time and stepping slightly further out. After twenty points, spiral families appear in their own drawing. Then set the real investigation: repeat the construction at 137.5°, 120°, 90° and 144° and count the visible spiral families at each. Only angles near the golden angle give Fibonacci counts and even spacing; rational angles like 120° give obvious spokes with gaps. That contrast is the actual explanation.
The question to ask: “If a plant put each new leaf exactly halfway round from the last one, every time, what would the plant look like from above? Draw it before you answer.”
Why Teaching This Early Pays Off
Phyllotaxis is one of the few places a child can see a mathematical structure in a thing they picked up off the ground. That matters less for the sequence itself, which they would meet anyway, and more for the idea that a simple repeated rule can generate complicated order. That idea is the foundation of recursion in programming, of fractal geometry, and of most of developmental biology.
The specific payoff is a defence against a bad habit. Fibonacci numbers are the single most over-claimed pattern in popular science: they get attributed to hurricanes, galaxies, stock markets and the Parthenon, usually with no measurement behind it. A child who has counted six cones, found that one did not fit, and written it down anyway has practised the thing that actually separates science from pattern-spotting. The Framework for K-12 Science Education calls that practice analysing and interpreting data.
Smith, diSessa and Roschelle argued that children’s wrong ideas are productive raw material rather than errors to be erased, and this activity is a clean example. “All pinecones are Fibonacci” is a useful first model. The cone that gives 9 and 14 is the thing that upgrades it. Do not smooth that over, and do not promise that one afternoon with cones changes how anyone performs at school. It gives them one solid experience of checking a claim.
Before You Start: What Parents Should Know
| Best age | 7 and up. The counting is easy from about 5, but keeping track of a spiral around a curved object needs a level of planning that usually arrives around 7. A five-year-old can dot one spiral and enjoy it. |
| Supervision | Low, once the cones are dry. Stay close for the first counted spiral, because the method is the whole difficulty. |
| Real hazards | Pine resin is sticky and does not come off with water; use cooking oil then soap. Cone scale tips can be sharp enough to scratch. Check cones for insects before bringing them inside. Cone seeds and small scales are a choking risk for under-3s. |
| Setup | A table with a tray or newspaper. You need both hands free and the cone needs to not roll. |
| Frustration point | Step 4, counting how many spirals are in a family. This is where most attempts collapse. Dots are not optional. |
| Don’t | Don’t dry the cones in the oven to speed things up, and don’t pick the cone that gives a “nice” answer and discard the rest. The discarded cone is the data. |
When It Doesn’t Work
- No spirals are visible. The cone is still closed, or it is a species with very few, very large scales. Dry it another day, or swap for a pineapple, where the rows are unmissable.
- The two counts come out the same. You traced the same family twice. Check the lean: the two families tilt in opposite directions, and if both your lines lean the same way you have one family.
- The count changes every time. The cone is damaged or lopsided, which is common in cones that fell early. Try a different cone and keep the result of the bad one with a note.
- You get 9 and 14, or some other non-Fibonacci pair. This genuinely happens, and the sunflower study above shows it happens in nature at measurable rates. Record it. Then check whether the cone is misshapen on one side.
- The dots smudge or the marker bleeds. Permanent fine markers on dry cones are fine; water-based pens run on resin. Sticker dots solve it completely for younger children.
Take It Further
Test whether size predicts the numbers. Measure each cone’s length and diameter, then plot size against parastichy number. Larger cones tend towards larger Fibonacci pairs, 13 and 21 rather than 5 and 8. With ten cones you can see the trend; with twenty you can argue for it.
Compare species, properly. Collect cones from two different pine species and keep them in separate piles. Count ten of each. Do the species differ in their typical pair? This is a real question with a literature behind it, and a strong science fair project because it has a control, a measurement and a sample size.
Build the spiral on paper at different angles. Use a protractor to place 25 dots, turning a fixed angle each time and moving 2 mm further out. Do it at 137.5°, then 90°, then 120°. Count visible spirals in each drawing. The golden angle version looks like a sunflower; the others look like spokes.
What to Watch For Over the Next 3 Months
- Week 4: They start checking other things. Pineapples, artichokes, the scales on a cactus. Let them count badly and then ask how they would be sure.
- Month 2: The word “pattern” gets used more carefully, often as a challenge: “is that a real pattern or did you just notice it?”
- Month 3: The question worth encouraging is some version of “why that angle?” You can honestly answer that nobody designed it, and that the angle is what you get when each new bud goes in the biggest gap.
Frequently Asked Questions
Which pinecones work best?
Open, dry, undamaged cones of medium size, around 6 to 10 cm. Those usually give 8 and 13, which is the clearest result. Very small cones give 5 and 8 and are fiddly to mark; very large ones give 13 and 21 and take longer to count.
Do we need real pinecones?
No. A pineapple is better for a first attempt because the hexagonal segments make the rows obvious, and it usually gives 8 and 13. A sunflower head gives larger numbers and is harder. A Romanesco cauliflower is the most spectacular and the most confusing.
Why isn’t every count a Fibonacci number?
Because the pattern comes from a growth process that can be disturbed. Damage, uneven growth, crowding and species differences all push counts off. The 2016 sunflower study found that most counts were Fibonacci numbers but a meaningful minority were not, including some heads with no assignable number.
Is the golden ratio really in the Parthenon and in faces?
Mostly no. Those claims usually come from choosing which lines to measure after deciding what answer you want. Phyllotaxis is different, because the angle is a measurable output of a growth mechanism that has been reproduced in a physics experiment with no biology in it.
My kid wants to know if plants can count. Can they?
No, and this is the best answer in the whole activity. Each new bud forms in the largest available gap because the existing buds chemically discourage growth beside them. That one local rule produces the numbers. Nothing in the plant represents 13.
About the author
Ricky Flores is the founder of HiWave Makers and an electrical engineer with 15+ years of experience building consumer technology at Apple, Samsung, and Texas Instruments. He writes about how kids learn to build, think, and create in a tech-saturated world. Read more at hiwavemakers.com.
Sources
- Mitchison, G. J. (1977). “Phyllotaxis and the Fibonacci Series.” Science, 196(4287), 270–275. https://doi.org/10.1126/science.196.4287.270
- Douady, S., & Couder, Y. (1992). “Phyllotaxis as a physical self-organized growth process.” Physical Review Letters, 68(13), 2098–2101. https://doi.org/10.1103/PhysRevLett.68.2098
- Swinton, J., Ochu, E., & The MSI Turing’s Sunflower Consortium. (2016). “Novel Fibonacci and non-Fibonacci structure in the sunflower: results of a citizen science experiment.” Royal Society Open Science, 3(5), 160091. https://doi.org/10.1098/rsos.160091
- National Research Council. (2012). A Framework for K-12 Science Education. National Academies Press. https://doi.org/10.17226/13165
- Smith, J. P., diSessa, A. A., & Roschelle, J. (1994). “Misconceptions Reconceived: A Constructivist Analysis of Knowledge in Transition.” Journal of the Learning Sciences, 3(2), 115–163. https://doi.org/10.1207/s15327809jls0302_1
- NRICH, University of Cambridge. “Tessellating Triangles” and related geometry investigations. https://nrich.maths.org/problems/tessellating-triangles
Related reading: which shapes tile a floor and why, the hidden patterns in Pascal’s triangle, and pattern recognition across maths and music.
