It’s found in commonly through nature and often in design (whether intended or by coincidence).
Was wondering if anyone knew exactly why it was so common especially in nature.
In: 30
there is a great book called “The Golden Ratio” that discusses the history of just this. It also looks at a lot of common occurrences of it in art and architecture and (as I recall) concludes that a LOT of them require some fudging to really fit the correct ratio.
Got some cool answers here, all nicely based in metaphors concerned with observable science. A more poetic one is that fundamentally, all of life is the same at it’s root.
Author Mário Livio debunked this. It looks like Fibonacci. But it isn’t most of the time
People just like to find patters.
Phi the golden ratio is a very efficient way to fill space during growth. Check out the flower thing here https://www.mathsisfun.com/numbers/nature-golden-ratio-fibonacci.html
Basically when growing outward, using this spiral optimizes surface area
confirmation bias, partly. also once people got interested in the golden mean/holden spiral, we designed TONS of stuff to fit it. doorways, cameras, art, packaging, etc
phi the golden ratio is an irrational number, in some sense it is the *most* irrational number. Some irrational numbers have a value that is very close to a simple rational number, but phi can only be closely approximated by a ratio of two numbers with a large number of digits (remember, any quotient, or ratio, of two integers is a rational number). So lets say phi is roughly 123591254 / 23412124 (or whatever, lol). A pattern with this ratio, compared to a ratio of say 3/4, will have to iterate many, many more times before there is a “repeat” in the pattern. In other words, the phi pattern is less prone to symmetry.
So for, say, the arrangement of petals around a flower, if the placement pattern corresponds to phi and the Fibonacci sequence, it prevents the petals from overlapping. We tend to view symmetry, patterns, and disorganization as beautiful, but there are many instances in nature, in evolution, in which a ‘perfect disorganization’ is preferred.
The Fibonacci spiral does not actually appear in nature much at all.
Almost all spirals in nature are Archimedean or logarithmic.
The Fibonacci spiral is made of circle segments every quarter turn, which is something that nature is really bad at doing.
That said, numbers from the Fibonacci sequence can sometimes be found in nature, as well as the “Golden Ratio”, a number that is associated with Fibonacci sequence.
Check out [this video](https://youtu.be/ahXIMUkSXX0) and the two after it for a really great explanation about Fibonacci and Fibonacci-like spirals in nature.
Vi Hart is a lovely nerd
It kind of isn’t. There are lots of *logarithmic* spirals in nature, but not all logarithmic spirals are Fibonacci spirals.
EDIT: this isn’t to say that Fibonacci numbers never turn up in nature. They are quite common in botany, for the patterns of seed growth in sunflower heads and pine cones, but it turns out that this is because logarithmic spirals with a rate of turn close to the golden ratio pack very efficiently. Also, the relationship between the Fibonacci numbers and the Golden Ratio is slightly deceptive. While the ratio between consecutive terms of the Fibonacci sequence does tend towards phi, this is not a particular property of that exact sequence, but is also true of all recursive sequences of the form
a, b, (a+b), ((a+b)+b)…
It doesn’t. Not really.
It does appear roughly to systems that tend to compound as they grow but even then it’s not exactly the golden ratio.
People tend to misrepresent any logarithmic spiral as the golden spiral.
You can find the number 1.6 everywhere If you look enough.
Tldr: the movie nymphonaniac made us think that any logarithmic spiral is connected to the golden ratio. It’s not. It’s a myth.
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