Spirals are everywhere; the fibonacci sequence is not. Take just about any two integers, it doesn't have to be one and one. Add them together, add the result to the larger of the two (or either one if they're the same), repeat, and the ratio will get closer and closer to the golden ratio.

Would it make sense if it was squares instead?

I mean, your answer is basically "drag".

As things spin, elements further away from the center take longer to speed up and be dragged along. Anytime a non-solid, like a pool of water or a galaxy, spins, it takes the form of a spiral because the things at the center speed up faster than the things further away.

HOWEVER, fibonacci is just one very specific spiral. Plenty of spirals are not fibonacci scale spirals.

Because things grow outward

I don’t live near water so don’t see it in spiral shells as much but in plants. Sunflowers: The seed spirals often come in Fibonacci pairs like 34 and 55, or 55 and 89.

Pinecones and pineapples: Their scales spiral in Fibonacci sequences.

Flowers: Petal counts often match Fibonacci numbers—lilies have 3, buttercups 5, marigolds 13, and daisies can have 34, 55, or even 89 petals. It’s nature’s way of optimizing space and efficiency—mathematics hiding in plain sight.

A whole lot of the supposed "fibonacci spirals" that appear in nature, are in fact just general logarithmic spirals, misnamed by people. In fact even your example looks by eye to be a bit too tight to be a true fibonacci spiral. So the answer is that, it doesn't really show up more often than lots of other sequences.

Disagree with the doubters. Since the ancient Greeks called it “the golden mean”, the 1.6:1 replicating ratio has been discovered & documented in nature countless times.
Mankind has applied (or observed) the ratio in many of its own endeavors- from art, to architecture, & even to stock market analysis. It’s an amazing hack of nature.

It doesn't. Perfect example of confirmation bias. There is no proof they are seen more freuqently than any other numbers. Most of the time, non-fib numbers gets "fibbed" by normalizing/changing/playing with numbers.

Nature does not like overlap and perfect alignment. If tree branches grow directly above one another, the top branch blocks light from reaching the branch below it. Cicadas spend years underground before coming up to eat crops - if all cicadas came up to eat crops on the same year there would not be enough crops for all of them.

So nature has evolved to do repetitive things in odd numbers, prime numbers, or other patterns that minimize overlap. The fibonacci sequence is one such pattern. Nature also is rarely exact, so things that are close to the fibonnaci sequence in nature can be approximated so that they match the fibonnaci sequence.

Just do a Google search for it and find the image.  I didn't include that for no reason.  And it wasn't to hype him or support him or anything, it was just a good example of the various and diverse ways the Fibonacci sequence presents itself.  

The Fibonacci sequence is just a mathematical emergent pattern. Nothing about it points to evidence of a creator.

I prefer “creating” than “creator” personally 

Because “creator” implies something that is finished.

But a creating implies an unfoldment…a process that takes shape and continues taking shape….and we play a bit of a role in this co-creating process based on our choices.

Fibonacci might be a pattern within the creating itself…and it keeps unfolding 

Yes i think so, reality is not random. The Fibonacci spiral shows itself in galaxies, waves, and countless natural forms, which to me just proves a shared underlying blueprint. The double-slit experiment also points to hidden coherence rather than chaos. We probably haven't found all the universal patterns of reality butthe Fibonacci sequence is undeniably one of the core frameworks shaping how matter and energy organize and evolve in this universe. I also believe the Fibonacci sequence is much more groundbreaking in terms of explaining realities framework then we have yet realized.

This seems to be the most efficient configuration possible in certain cases. Nature always finds the most efficient option. There are also less efficient options, but because they are less efficient, there are fewer

and i love watching bees follow the spiral from outer to inner! they always look like they’re knitting the spiral as they pollinate 🧶

Plants do all sort of crazy mathatical sequences to maximise spacing and light absorption. I wonder if mathematicians of old got any inspiration from sunflowers?

So every head grows 34 rows, and some varities are larger and some smaller.

This is so cool! Thank you for sharing!

This is the way

STLs if you are interested -> https://www.printables.com/model/334911-fibonacci-spiral-trees

Prints without support

This is amazing. Going on my printer next!

The tool song Lateralus actually has aspects of the Fibonacci sequence throughout it! Worth a listen if you haven't heard it before.

Looks like my favorite form of cauliflower, only orange. :-)

I love it! Thanks for sharing!

Fibonatree

Yes this is why famously the virgo supercluster also looks like a spiral https://supernova.eso.org/exhibition/images/0106F_Virgu_Superlcuster/ Except on no wait of course it fucking doesn't.

Strictly speaking, the Fibonacci sequence is a discrete sequence of numbers. The Ekman spiral can be described as a continuous spiral, not a discrete sequence of numbers.

However, the Fibonacci spiral is an approximatio of the the golden spiral. Both, the golden spiral and an idealized Ekman spiral are examples of "logarithmic spirals" which have the form r = e^(b*θ). The golden spiral is just an example of such a logarithmic spiral for which b takes a special value which depends on the golden ratio φ. b = ln(φ)/90°. The Ekman spiral can also be described as a logarithmic spiral, e.g. by using the depth as the angle θ and the velocity magnitude as the radius r. The growth factor b depends on the Ekman depth, and I suppose in principle if the Ekman depth has the correct value, the Ekman spiral could approach a golden spiral.

Actual mathematician here: the answers so far are all wrong, and so is your presumption. Fibonacci numbers are rare and there is no inherent mechanism in the universe for them.

Multiple answers have claimed it is all over nature, but examples of them appearing at all outside human works are pretty rare. They somewhat happen in sunflowers sometimes, if all the randomness of growth does not almost certainly screw it up. But that's about it. Beyond those rare few examples, it is usually esoteric and/or made up.

All the spiral patterns are not Fibonacci based, either. They are simply what we call logarithmic spirals, which have effectively nothing to do with the numbers. They are based on exponential growth, but that could be the powers of 2, 3, the golden ratio (~ Fibonacci numbers), 5, pi, and most importantly and most common, e.

When you encounter individual Fibonacci numbers, it is random chance. Especially with small numbers like 1,2 and 3, they just as well could be a million other sequences. And it it looks like it might be the golden ratio, it almost always might just as well be 1.5, 1.6, square root of 2 or 3, or a lot of other options. The uncertainty is usually very high, and often we even know that it is definitely not that one number.

Some posts even compared the golden ratio and the Fibonacci numbers to pi. But unlike the former, pi has a lot of reasons to be everywhere in a physical reality. For example, the laws of nature do not change when you rotate things, hence a lot of optimal arrangements are ones that don't change with rotation as well: circles and spheres. Thus pi.

Tl;dr: It is not found everywhere, it describes what is found everywhere.

The way our Universe works is pretty much „Growth“; Atoms „grow“ into Molecules, which grow into Matter, etc. Seeds grow into Trees, Babies grow into Adults, Tribes grow into People.

The way Growth works is always the same: replication. So if you start with 2 of anything and start to grow a population you will first create an offspring of each pair and add it to the total population - 2 becomes 3, now with 3 you can create 2 pairs, so you get 2 offsprings and add them to the population - 3 becomes 5, which can make 3 pairs and so on.

At some point mathematicians observed this and quickly figured out a pattern. This pattern became the fibonacci sequence.

So in the end the sequence isn‘t something that we invented and happens to be found everywhere, but the other way around: we observed something that happens everywhere and found a way to describe it.

Hope this helps, and sorry for any error or bad wording, english isn‘t my first language.

It's not, but what it is, is roughly exponential, and exponential growth (or decay) happens when the rate of change of something is proportional to the amount of that something, and that is something that happens in many different settings.

So it's easy to shoehorn Fibonacci numbers into lots of situations by scaling and rounding.

It doesn’t. Here is a web archive link with more details (original link is dead unfortunately): http://web.archive.org/web/20160309052601/http://www.lhup.edu/~dsimanek/pseudo/fibonacc.htm

It was poorly explained, does not bare scrutiny, and most importantly. wrong