![]() The Fibonacci sequence may simply express the most efficient packing of the seeds (or scales) in the space available. As each row of seeds in a sunflower or each row of scales in a pine cone grows radially away from the center, it tries to grow the maximum number of seeds (or scales) in the smallest space. That is, these phenomena may be an expression of nature's efficiency. Why do sunflowers often have precisely 55, 89, or 144 petals, numbers that figure in the famous Fibonacci sequence Nature, it seems, has certain mathematical underpinnings. The same conditions may also apply to the propagation of seeds or petals in flowers. How Common Is The Fibonacci Sequence in Nature The fibonacci appears in the smallest, to the largest objects in nature. Given his time frame and growth cycle, Fibonacci's sequence represented the most efficient rate of breeding that the rabbits could have if other conditions were ideal. The sequence that Fibonacci discovered shows up all over nature. Many publications propose models to explain this phenomenon, eg this one. The Fibonacci sequence is commonly seen in the inside spiral of a flower, this spiral is called a Fibonacci spiral and is also sometimes known as The Golden Angle. Why are Fibonacci numbers in plant growth so common? One clue appears in Fibonacci's original ideas about the rate of increase in rabbit populations. You have many publications claiming that this is true, including very recent ones, eg this one: The phyllotaxis of the model plant Arabidopsis thaliana follows a Fibonacci spiral, the most frequent phyllotactic pattern found in nature. The Fibonacci sequence naturally exists in nature, because it models model physical reality, and it also represents structure and sequences. The number of rows of the scales in the spirals that radiate upwards in opposite directions from the base in a pine cone are almost always the lower numbers in the Fibonacci sequence-3, 5, and 8. The corkscrew spirals of seeds that radiate outward from the center of a sunflower are most often 34 and 55 rows of seeds in opposite directions, or 55 and 89 rows of seeds in opposite directions, or even 89 and 144 rows of seeds in opposite directions. ![]() The arrangement of these terms is set by a definite rule. A sequence is an ordered list of numbers, called terms, that may have repeated values. Similarly, the configurations of seeds in a giant sunflower and the configuration of rigid, spiny scales in pine cones also conform with the Fibonacci series. In this chapter we know about Fibonacci sequence and look at its pattern in the nature and the world around us. ![]() All of these numbers observed in the flower petals-3, 5, 8, 13, 21, 34, 55, 89-appear in the Fibonacci series. There are exceptions and variations in these patterns, but they are comparatively few. Some flowers have 3 petals others have 5 petals still others have 8 petals and others have 13, 21, 34, 55, or 89 petals. For example, although there are thousands of kinds of flowers, there are relatively few consistent sets of numbers of petals on flowers.
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