![]() ![]() The Fibonacci Sequence and the Golden Ratio These geometric patterns, characterized by intricate details and an infinite border, are derived from a simple mathematical equation. The most famous fractal is perhaps the Mandelbrot set, named after the mathematician Benoit Mandelbrot who pioneered the study of fractals. Fractals can even be observed in the flight patterns of certain birds and insects. The branching patterns seen in rivers, trees, and our blood vessels are examples of fractals. Fractals are not merely mathematical curiosities, but they are everywhere in nature. No matter how much you zoom in, you continue to see the same pattern repeated over and over again. Fractals: Infinite Complexity from Simple Rulesįractals are geometric shapes that are 'self-similar' - they appear identical at every scale. This article aims to explore this fascinating relationship between nature and mathematics, shedding light on how patterns and sequences manifest themselves in our world. From the spirals of galaxies to the branching of trees, the hive structure of bees to the pattern of petals on a flower, mathematics permeates the natural world in surprising and beautiful ways. In trees, the Fibonacci begins in the growth of the trunk and then spirals outward as the tree gets larger and taller.Nature is replete with patterns, sequences, and structures that display an astonishing level of mathematical elegance. 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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