Fibonacci numbers and nature
What is the Fibonacci sequence?
One of the best and clearest definitions about the Fibonacci sequence can be found on Wikipedia:
In mathematics, the Fibonacci numbers are the numbers in the following integer sequence, called the Fibonacci sequence, and characterized by the fact that every number after the first two is the sum of the two preceding ones:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …
The Fibonacci sequence was name after the Italian mathematician Leonardo di Pisa who was also known as Fibonacci. What makes the Fibonacci sequence so special it is that this sequence is closely related to the golden ratio. The more we advance with the Fibonacci sequence to the infinite dividing the last two numbers will bring us closer to the golden ratio. I want to remind you that the golden ratio’s value is:
If you have the curiosity try to divide 144 with 89. The result will be… 1.617977… But if we calculate the the 66th and 67th numbers from the sequence we will obtain:
- 66th number of Fibonacci sequence: 44945570212853
- 67th number of Fibonacci sequence: 72723460248141
Now let’s do the math: 72723460248141 / 44945570212853 = 1.61803398895. This is very close the above value. But what makes these numbers from the sequence so interesting?
Fibonacci sequence in nature
What makes the Fibonacci sequence so interesting is that you will discover the numbers of the sequence all over nature. In fact this is not only related to the golden ratio, but also to fact that this sequence appears very often in nature. As an illustration, lets see some examples where we will discover the Fibonacci sequence:
- branching trees
- arrangement of leaves on a stem
- the flowering of artichoke
- the arrangement of a pine cone
- the seeds on a sunflower
- the spirals of shells
- the number of petals of daisy flowers
As a matter of fact, seems that this number sequence is an optimum value in nature. Moreover seems to be an efficient way of growing and in the same time using less energy. Moreover, if you want to find out more about the Leonard of Pisa and the Fibonacci sequence you cane read more over here.
Why is Fibonacci important in photography?
This is a legitimate question. I will not give you a scientific answer for that but will rely more on my instinct and experience so far. Nature seems to favor particular numbers like the ones from this sequence. The same way as the golden ratio acts subconsciously, these numbers act the same way. Consequently having the golden ratio and Fibonacci sequence in mind we can generate much pleasing images when the elements in the picture are connected to these numbers. One particular example that comes into my mind is food. I adore food and food photography in general. Not only that they are rich in colors, but placing the elements on the table I consider an art. Below you can find an image that I particularly like and find it catchy.
Let’s analyse the image above and the elements contained within:
- number of spoons: 3
- number of orange slices on the plate: 8
- number of oranges on the plate 1
- number of pumpkin on the plate 1
- number of vanilla on the plate: 5
Therefore you see all the elements in this image is connected with the Fibonacci sequence. Additionally have you notice something interesting? Also the elements in this composition seem to be placed according to the golden ratio, or I see it wrong?
To sum up what we have discovered, the Leonardo di Pisa has worked out the way nature favors one number over the other. We don’t really know exactly the story behind this sequence but one thing is clear. Although we don’t understand why our brain finds the golden ration and Fibonacci sequence pleasant, it is there. In any case I personally consider that will not make any mistake if we take it into account when composing our shot. By the way composing. If you want to find out more about composition rules I have a great article for that.
Leave me a comment below and tell me whether you liked this article or not. There is always room for improvement. Additionally I am curious what do you think about the Fibonacci sequence. Have you used it subconsciously? Have a nice day