All are fractions with fibonacci numbers, at least.

Different plants have favored fractions, but they evidently don't read the books because I just computed fractions of 1/3 and 3/8 on a single apple stem, which is supposed to have a fraction of 2/5. So if the stems made three full circles to get a bud back where it started and generated eight buds getting there, the fraction is 3/8, with each bud 3/8 of a turn off its neighbor upstairs or downstairs. You can determine the fraction on your dormant stem by finding a bud directly above another one, then counting the number of full circles the stem went through to get there while generating buds in between. Eureka, the numbers in those fractions are fibonacci numbers! The amount of spiraling varies from plant to plant, with new leaves developing in some fraction-such as 2/5, 3/5, 3/8 or 8/13-of a spiral. The buds range up the stem in a spiral pattern, which kept each leaf out of the shadow of leaves just above it. To confirm this, bring in a leafless stem from some tree or shrub and look at its buds, where leaves were attached. Scales and bracts are modified leaves, and the spiral arrangements in pine cones and pineapples reflect the spiral growth habit of stems. Count the number of spirals and you'll find eight gradual, 13 moderate and 21 steeply rising ones. One set rises gradually, another moderately and the third steeply. Focus on one of the hexagonal scales near the fruit's midriff and you can pick out three spirals, each aligned to a different pair of opposing sides of the hexagon. I just counted 5 parallel spirals going in one direction and 8 parallel spirals going in the opposite direction on a Norway spruce cone. The number of spirals in either direction is a fibonacci number. Actually two spirals, running in opposite directions, with one rising steeply and the other gradually from the cone's base to its tip.Ĭount the number of spirals in each direction-a job made easier by dabbing the bracts along one line of each spiral with a colored marker. Look carefully and you'll notice that the bracts that make up the cone are arranged in a spiral. To see how it works in nature, go outside and find an intact pine cone (or any other cone).

So the sequence, early on, is 1, 2, 3, 5, 8, 13, 21 and so on. More.Better known by his pen name, Fibonacci, he came up with a number sequence that keeps popping up throughout the plant kingdom, and the art world too.Ī fibonacci sequence is simple enough to generate: Starting with the number one, you merely add the previous two numbers in the sequence to generate the next one. He also found that there were as many with the steep spiral (the one with more arms) going to the left as to the right. For instance, a large collection of pine cones of different kinds of Californian pine cones was studied by Brother Alfred Brousseau and reported in The Fibonacci Quarterly vol 7 (1969) pages 525 - 532 in an article entitled Fibonacci Statistics in Conifers. Sometimes this is due to deformities produced by disease or pests. ^^^ You will occasionally find pine cones with do not have a Fibonacci number of spirals in one or both directions. What about a pineapple? Can you spot the same spirala pattern? How many spirals are there in each direction?.Are all the cones identical in that the steep spiral (the one with most spiral arms) goes in the same direction? Does the number of spirals differ for each kind of tree/cone or not?ī. Collect some pine cones for yourself and count the spirals in both directions.Ī tip: Soak the cones in water so that they close up and counting the spirals is easier.Ī.Here is a picture of a pinecone seen from its base (sorry the quality is a bit poor) and another with the spirals emphasised: red in one direction and green in the other. Pine cones show the Fibonacci Spirals clearly.

Fibonacci spiral pine cone