Life reconstruction of fossil Asteroxylon mackiei. The discovery of non-Fibonacci spirals in such an early fossil is surprising as they are very rare in living plant species today. In fact, non-Fibonacci spirals were the most common arrangement. We took images of thin slices of fossils and then used digital reconstruction techniques to visualise the arrangement of Asteroxylon mackiei’s leaves in 3D and quantify the spirals.īased on this analysis, we discovered that leaf arrangement was highly variable in Asteroxylon mackiei. The fossils we studied are now housed in museum collections in the UK and Germany but were originally collected from the Rhynie chert – a fossil site in northern Scotland. Specifically, we studied plant fossils of the extinct clubmoss species Asteroxylon mackiei. We examined the arrangement of leaves and reproductive structures in the first group of plants known to have developed leaves, called clubmosses. Sandy Hetherington, Author provided Non-Fibonacci spirals in early plants From left to right: spirals in leaves of a monkey puzzle trees, a pine cone and in the flower of a seaside daisy. Now count the number of clockwise and anticlockwise spirals, and in almost every case the number of spirals will be integers in the Fibonacci sequence.Įxamples of living plants with Fibonacci spirals. But look closely and you can see both clockwise and anticlockwise spirals. If you pick up a pinecone and look at the base, you can see the woody scales form spirals that converge towards the point of attachment with the branch.Īt first, you may only spot spirals in one direction. These patterns are particularly widespread in plants and can even be recognised with the naked eye. In most cases, these spirals relate to the Fibonacci sequence – a set of numbers where each is the sum of the two numbers that precede it (1, 1, 2, 3, 5, 8, 13, 21 and so on). Spirals occur frequently in nature and can be seen in plant leaves, animal shells and even in the double helix of our DNA. Luisa-Marie Dickenmann/University of Edinburgh, CC BY-NC-ND What are Fibonacci spirals? All are fractions with fibonacci numbers, at least.Holly-Anne Turner, first author of the study, creating digital 3D models of Asteroxylon mackiei at the University of Edinburgh. 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. 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.
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