Why do plants have fibonacci

The Fibonacci-ness of Plants. Fibonacci Sequence. Phyllotaxis Leaf Arrangement. For more on phyllotaxis, see the Learn More Section below. Fibonacci and the Golden Ratio. Emerging fern fronds make this same spiral. Putting it all together. Like the first arrangement, the leaves will start to get covered up by other leaves after the first full turn. Perhaps, 1 over an irrational number might do the trick.

This particular example was based on leaves, but this kind of asymmetric growth happens in many other parts of a plant, as well as on the cellular level since plants grow new cells in spirals adding a new cell after a turn. When plants exhibit the golden angle in spiral growth patterns, this results in 2 spirals showing up, one going clockwise and the other going counterclockwise.

Mathematical models and simulations have shown that patterns such as these spirals can emerge if the plant organs are made at regular intervals, but plants are not sentient beings, so how would they know how to grow? Though there is still much research to be done on their biological mechanisms, the answer may lie in the plant hormone auxin, which is responsible for stem elongation and phyllotaxis, the arrangement of leaves on a stem.

Current research shows that when cells detect large amounts of auxin in nearby cells, they transport more auxin towards the cell, creating a hotspot where a new leaf grows. The creation of an auxin hotspot lowers auxin levels in the surrounding area, so new hotspots can only be formed from a certain distance away; causing leaves to be spaced out regularly to form a complex spiral pattern. Some plants display Lucas numbers instead, a sequence similar to the Fibonacci sequence, where the next number is the sum of the two numbers before it 2, 1, 3, 4, 7, 11, 18, etc.

The difference is that the first two terms are 2 and 1, rather than 0 and 1. What role does auxin play in plant growth? Auxins are a class of plant hormones that regulate growth by stimulating the elongation of cells in stems. The concentration of auxin in different parts of a plant is crucial to plant development, as patterns of auxin concentration guide the growth of cells in certain areas. The spiral arrangement and presence of Fibonacci numbers in plants is hypothesized to be due to auxin hotspots that cause leaves to grow as far away from each other as possible, leading to the golden angle.

Why do many plants sprout new leaves at an angle of The part of the flower in the picture is about 2 cm across. It is a member of the daisy family with the scientific name Echinacea purpura and native to the Illinois prairie where he lives. You can have a look at some more of Tim's wonderful photographs on the web.

You can see that the orange "petals" seem to form spirals curving both to the left and to the right. At the edge of the picture, if you count those spiralling to the right as you go outwards, there are 55 spirals. A little further towards the centre and you can count 34 spirals. How many spirals go the other way at these places? You will see that the pair of numbers counting spirals in curing left and curving right are neighbours in the Fibonacci series.

Here is a picture of a seed seedhead with the mathematically closest seeds shown and the closest 3 seeds and a larger seedhead of seeds with the nearest seeds shown. Each clearly reveals the Fibonacci spirals: A larger image appears in the book 50 Visions of Mathematics Sam Parc Editor published by Oxford and also available for the Kindle. Click on the picture on the right to see it in more detail in a separate window. Click on each to enlarge it in a new window. The reason seems to be that this arrangement forms an optimal packing of the seeds so that, no matter how large the seed head, they are uniformly packed at any stage, all the seeds being the same size, no crowding in the centre and not too sparse at the edges.

So the number of spirals we see, in either direction, is different for larger flower heads than for small. On a large flower head, we see more spirals further out than we do near the centre. The numbers of spirals in each direction are almost always neighbouring Fibonacci numbers!

Click on these links for some more diagrams of , and seeds. Click on the image on the right for a Quicktime animation of seeds appearing from a single central growing point. The animation shows that, no matter how big the seed head gets, the seeds are always equally spaced. At all stages the Fibonacci Spirals can be seen.

The same pattern shown by these dots seeds is followed if the dots then develop into leaves or branches or petals. Each dot only moves out directly from the central stem in a straight line.

This process models what happens in nature when the "growing tip" produces seeds in a spiral fashion. The only active area is the growing tip - the seeds only get bigger once they have appeared. A seed which is i frames "old" still keeps its original angle from the exact centre but will have moved out to a distance which is the square-root of i. It also has a page of links to more resources. Note that you will not always find the Fibonacci numbers in the number of petals or spirals on seed heads etc.

Why not grow your own sunflower from seed? I was surprised how easy they are to grow when the one pictured above just appeared in a bowl of bulbs on my patio at home in the North of England. Perhaps it got there from a bird-seed mix I put out last year? Bird-seed mix often has sunflower seeds in it, so you can pick a few out and put them in a pot.

Sow them between April and June and keep them warm. Alternatively, there are now a dazzling array of colours and shapes of sunflowers to try. A good source for your seed is: Nicky's Seeds who supplies the whole range of flower and vegetable seed including sunflower seed in the UK. Have a look at the online catalogue at Nicky's Seeds where there are lots of pictures of each of the flowers. Which plants show Fibonacci spirals on their flowers? Can you find an example of flowers with 5, 8, 13 or 21 petals?

Are there flowers shown with other numbers of petals which are not Fibonacci numbers? Collect some pine cones for yourself and count the spirals in both directions. A tip: Soak the cones in water so that they close up to make counting the spirals easier.

Are all the cones identical in that the steep spiral the one with most spiral arms goes in the same direction? What about a pineapple? Can you spot the same spiral pattern? How many spirals are there in each direction? From St. Mary's College Maryland USA , Professor Susan Goldstine has a page with really good pine cone pictures showing the actual order of the open "petals" of the cone numbered down the cone.

Fibonacci Statistics in Conifers A Brousseau , The Fibonacci Quarterly vol 7 pages - You will occasionally find pine cones that do not have a Fibonacci number of spirals in one or both directions. Sometimes this is due to deformities produced by disease or pests but sometimes the cones look normal too.

This article reports on a study of this question and others in a large collection of Californian pine cones of different kinds. The author also found that there were as many with the steep spiral the one with more arms going to the left as to the right. On the trail of the California pine , A Brousseau, The Fibonacci Quarterly vol 6 pages pine cones from a large variety of different pine trees in California were examined and all exhibited 5,8 or 13 spirals.

Also, many plants show the Fibonacci numbers in the arrangements of the leaves around their stems. If we look down on a plant, the leaves are often arranged so that leaves above do not hide leaves below.

This means that each gets a good share of the sunlight and catches the most rain to channel down to the roots as it runs down the leaf to the stem. Here's a computer-generated image , based on an African violet type of plant, whereas this has lots of leaves.

Leaves per turn The Fibonacci numbers occur when counting both the number of times we go around the stem, going from leaf to leaf, as well as counting the leaves we meet until we encounter a leaf directly above the starting one. If we count in the other direction, we get a different number of turns for the same number of leaves.

The number of turns in each direction and the number of leaves met are three consecutive Fibonacci numbers! For example, in the top plant in the picture above, we have 3 clockwise rotations before we meet a leaf directly above the first, passing 5 leaves on the way. If we go anti-clockwise, we need only 2 turns. Notice that 2, 3 and 5 are consecutive Fibonacci numbers.

For the lower plant in the picture, we have 5 clockwise rotations passing 8 leaves, or just 3 rotations in the anti-clockwise direction. This time 3, 5 and 8 are consecutive numbers in the Fibonacci sequence. One estimate is that 90 percent of all plants exhibit this pattern of leaves involving the Fibonacci numbers.

Each floret is peaked and is an identical but smaller version of the whole thing and this makes the spirals easy to see. These buttons will show the spirals more clearly for you to count lines are drawn between the florets : Here are some investigations to discover the Fibonacci numbers for yourself in vegetables and fruit.

Take a look at a cauliflower next time you're preparing one: First look at it: Count the number of florets in the spirals on your cauliflower. The number in one direction and in the other will be Fibonacci numbers, as we've seen here. Do you get the same numbers as in the picture? Take a closer look at a single floret break one off near the base of your cauliflower. It is a mini cauliflower with its own little florets all arranged in spirals around a centre. If you can, count the spirals in both directions.

How many are there? Then, when cutting off the florets, try this: start at the bottom and take off the largest floret, cutting it off parallel to the main "stem". Find the next on up the stem. Cut it off in the same way. Repeat, as far as you like and.. Now look at the stem. Where the florets are rather like a pine cone or pineapple.

The florets were arranged in spirals up the stem. Counting them again shows the Fibonacci numbers. Try the same thing for broccoli. Chinese leaves and lettuce are similar but there is no proper stem for the leaves.

Instead, carefully take off the leaves, from the outermost first, noticing that they overlap and there is usually only one that is the outermost each time. You should be able to find some Fibonacci number connections. Look for the Fibonacci numbers in fruit. What about a banana? Count how many "flat" surfaces it is made from - is it 3 or perhaps 5? When you've peeled it, cut it in half as if breaking it in half, not lengthwise and look again.

There's a Fibonacci number. What about an apple? Instead of cutting it from the stalk to the opposite end where the flower was , i. Try a Sharon fruit. Where else can you find the Fibonacci numbers in fruit and vegetables? Why not email me with your results and the best ones will be put on the Web here or linked to your own web page. Why not measure your friends' hands and gather some statistics?

NOTE: When this page was first created back in this was meant as a joke and as something to investigate to show that Phi, a precise ratio of 1. The idea of the lengths of finger parts being in phi ratios was posed in but two later articles investigating this both show this is false.