It suggests that Fibonacci spirals emerged separately multiple times throughout plant evolution. ![]() They suggest that non-Fibonacci spirals were ancient in clubmosses, overturning the view that all leafy plants started out growing leaves that followed the Fibonacci pattern.įurthermore, it suggests that leaf evolution and Fibonacci spirals in clubmosses had an evolutionary history distinct from other groups of living plants today, such as ferns, conifers and flowering plants. These findings change our understanding of Fibonacci spirals in land plants. Matt Humpage/Northern Rogue Studios, CC BY-NC-ND Distinct evolutionary history 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? In trees, the Fibonacci begins in the growth of the trunk and then spirals outward as the tree gets larger and taller.Holly-Anne Turner, first author of the study, creating digital 3D models of Asteroxylon mackiei at the University of Edinburgh. Trees Photo from Joel & Jasmin Førestbird/UnsplashĪlthough we all usually see trees everywhere in our day to day, how often do we really look at them for patterns. When analyzing these spirals, the number is almost always Fibonacci. At points, their seed heads get so packed that their number can get exceptionally high, sometimes as much as 144 and more. A perfect example of this is sunflowers with their spiraling patterns. ![]() Most of the time, seeds come from the center and migrate out. Seed Heads Photo from Asgeir Pall Juliusson/UnsplashĪ flower’s head is also where you’ll find the Fibonacci sequence in plants. Of the most visible Fibonacci sequence in plants, lilies, which have three petals, and buttercups, with their five petals, are some of the most easily recognized. The petals of a flower grow in a manner consistent with the Fibonacci. Flower Petals Photo from Alfiano Sutianto/Unsplash ![]() Each cone has its own set of spirals moving outwards in opposing directions. When looking closely at the seed pod of a pinecone, you’ll notice an arranged spiral pattern. Pinecones Photo from Cameron Oxley/Unsplash ![]() The more they grow outward, the higher the Fibonacci sequence is visible. When growing off the branch, Fibonacci can be viewed in their stems as well as their veins. The Fibonacci sequence in plants is quite abundant, and leaves are one of the best examples. Although the Fibonacci sequence (aka Golden Ratio) doesn’t appear in every facet of known structures, it does in many, and this is especially true for plants. The Fibonacci sequence’s ratios and patterns (phi=1.61803…) are evident from micro to macro scales all over our known universe. The Fibonacci sequence was initially developed by Leonardo Fibonacci while he was calculating the expansion of groups of rabbits over a year.
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