where fibonacci sequence is found in nature

#Where fibonacci sequence is found in nature how to#

Why is the Golden section the 'best' number? Let's now try and show just why phi is the best angle to use in the next few sections ofthis page. The Fibonacci numbers form the best whole number approximations to the golden number, which we examined in greater detail on the first Fibonacci in Nature page.

However, we tend to 'see' the smaller angle which is(1-0♶18034)x360 = 0♳81966x360 = 137♵0776.°.When we look at properties of Phi and phi on a later page, we shall see thatĪnd why do the Fibonacci numbers appear as leaf arrangements and as the number of spirals on seedheads? Why does the Golden Ratio (Phi) appear in plants?The arrangements of leaves is the same as for seeds and petals. You will have already guessed what the fixed angle of turn is - it is Phi cells per turn or phi turns per new cell. The principle that a singleangle produces uniform packings no matter how much growth appears after it was only provedmathematically in 1993 by Douady and Couder, two french mathematicians. Yes! This was suspected by people as early as the last century. Similarly, once a seed is positioned on a seedhead, the seed continues out ina straight line pushed out by other new seeds, but retaining the original angle on the seedhead.No matter how large the seedhead, the seeds will always be packed uniformlyon the seedhead.Īnd all this can be done with a single fixed angle of rotation between new cells? So, once an angle is fixed for a leaf, say,that leaf will least obscure the leaves below and be least obscured by any future leavesabove it. The amazing thing is that a single fixed angle can produce the optimal design nomatter how big the plant grows. These cells may then become a new branch, or perhaps on a flower become petals and stamens. Cells earlier down the stem expand and so thegrowing point rises.Īlso, these cells grow in a spiral fashion, as if the stem turns by an angle and thena new cell appears, turning again and then another new cell is formed and so on. Once formed, they grow in size, but new cells areonly formed at such growing points. So just how do plants grow to maintain this optimality of design? The Meristem and Spiral growth patternsBotanists have shown that plants grow from a single tiny group of cells right atthe tip of any growing plant, called the meristem.There is a separate meristem at the end of each branch or twig where new cells are formed. What is more, ALL of these maintaintheir efficiency as the plant continues to grow and that's a lot to askof a single process! What nature seems to use is the same pattern to place seeds on a seedheadas it used to arrangepetals around the edge of a flower AND to place leaves round a stem.

#Where fibonacci sequence is found in nature how to#

So why doesn't nature use one of these? Seeds are round (mostly), so why don't wesee hexagonal arrangments on seedheads?Īlthough hexagonal symmetry IS the best packing for circular seeds, it doesn't answerthe question of how leaves should be arranged round a stem or how to pack flower-heads(which are circular because that is the shape that encloses maximum area for minimum edge) with seeds that grow in size. Whereas round objects pack better in a hexagonal arrangement. square objects would pack most closely in a square array, PackingsIf you were asked what was the best way to pack objects your answer woulddepend on the shape of the objects since. Why does nature like using Phi in so many plants? The answer lies in packings - the best arrangement of objects to minimise wasted space.