The omnipresence of these spirals in plants, often referred to as nature’s secret code, has intrigued scientists for centuries. Sunflower heads, pinecones, pineapples, and succulent houseplants all display Fibonacci spirals on their petals, leaves, and seeds. The Fibonacci sequence is particularly prevalent in plants, comprising more than 90 percent of all spirals found among them. The most prolific of these are Fibonacci spirals, which are named after Leonardo Fibonacci, the Italian mathematician who made the sequence famous. Spirals can be found in many forms in nature, ranging from the twist of a DNA helix to the vortex of a hurricane. In a groundbreaking study, researchers have challenged long-standing theories about the origins of Fibonacci spirals, one of nature’s most ubiquitous mathematical patterns.Ĭontrary to the traditional belief that these spirals are a conserved trait originating from Earth’s first land-dwelling plants, the new research indicates that the earliest plants developed an entirely different type of spiral. ![]() The Golden Ratio: The Story of Phi, the World’s Most Astonishing Number. Where We Can Find Equiangular Spirals (or Logarithmic Spirals) The Fibonacci Numbers and the Golden Section in Nature This will be explored in a future article It is another way that Phi and the related Fibonacci numbers are seen in nature. So this is a way also to arrange leaves on a twig or twigs on a branch so that the leaves do not shade each other too much. The reason the packing is optimal is that the amount of overlap is minimized. This same idea works for arranging leaves in a way that they shade each other the least. It is an optimal way to place seeds on a flower head or scales on a pine cone. So this is a way to approximate the theoretical best packing: form 3 seeds every 5 turns, or 5 seeds every 8 turns, or 8 every 13 turns, and so on. You will find that the quotient comes closer and closer to Phi as you use bigger F-numbers. Make fractions that have a Fibonacci number in the numerator and the previous Fibonacci number in the denominator: 5/3, 8/5, 13/8, 21/13, and so on. The Fibonacci Numbers Approximate the Golden Mean Notice that in the last example the “seeds” could be pushed closer and fill the space more efficiently. Notice a decrease in overlap and increased use of space in the last example.Ī diagram showing the progression of 1 to 5 “seeds” per rotation to phi. In the illustration (click to enlarge) the examples progress from 1/2 to 1/6 turn per cell, and then Phi. This will give the least amount of overlap and the best packing. ![]() So the ideal pattern would be to produce a new seed every 137.5 degrees of rotation. If you divide a circle by phi, you get 2 angles, the smaller of which is about 137.5 degrees. One such irrational number is Phi, the golden ratio, 1.61803…. The theoretical best fraction would be an irrational number which cannot be expressed exactly by whole numbers. Any rational fraction (the top and bottom are whole numbers) will give this effect. Most of the space between each line of cells is wasted. If cells grow every ½ turn then they pile up in 2 lines, 1/3 turn would give 3 lines, and so on. How much of a circle should the growth center rotate before growing a new cell? If it rotates a whole turn then the cells still pile up on each other in 1 line. As they form, the center of growth is rotating so that the cells don’t end up on top of each other. Plants grow from active tissue called the meristem, most often at the tip of the branches. This optimal packing means that the plant can build a smaller structure to hold them. The pine scales and seeds are arranged in a way that requires minimum space. The pattern represents an optimization of resources. This gives 1, 1, 2, 3, 5, and so on as above. This series is formed from the starting numbers 1, 1, and then adding together the last 2 numbers to get the next one. The sequence 5, 8, 13, 21, 34, and 55 are members of the Fibonacci series. The numbers occur in these pairs more often than not. ![]() How many in each direction? There can be 5 and 8, 8 and 13, 21 and 34, 34 and 55, and sometimes more. Fibonacci Numbers appear when you count the spirals The spirals can be seen in both clockwise and counterclockwise directions. The scales of the cones and the seeds in the flower trace graceful spirals radiating out from the center. ![]() Pine cones and flower heads of the composite family of flowers both show a similar pattern. Fibonacci numbers can be found in many remarkable patterns in nature.
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