Chromotron t1_jeg2aw4 wrote on March 31, 2023 at 7:21 PM

Reply to comment by CautiousCold8392 in ELI5-What is the fibonacci sequence? by amsdys

> Natural examples include the spiral shapes of shells and galaxies.

No, those are at best just any logarithmic spirals, the factor is not the golden ratio or otherwise Fibonacci-related.

CautiousCold8392 t1_jeg3v46 wrote on March 31, 2023 at 7:31 PM

>No, those are at best just any logarithmic spirals, the factor is not the golden ratio or otherwise Fibonacci-related.

It is true in some cases but not all. Even though there may not always be a connection between math and nature, there are still instances where the golden ratio and the Fibonacci sequence can be seen.

Chromotron t1_jeg5tua wrote on March 31, 2023 at 7:44 PM

There is absolutely no physical process that favours the golden ratio for spirals. The factor for a logarithmic one simply is not too large, and not too small. Like 1.3, 1.5, 1.61, or 1.8, maybe even 2 or 3. Some humans attribute patterns where there are none.

The only exceptions I've ever seen where Fibonacci numbers really (roughly) appear are growth patterns that mimic its recursion. Sunflowers are often mentioned, never checked if even those actually work but they might.

CautiousCold8392 t1_jeg9tsm wrote on March 31, 2023 at 8:11 PM

Even though it may be true that no physical process directly favors them, saying there aren't any in the natural world is inaccurate. Although they might not have been the only factors in the creation of some naturally occurring spirals, the golden ratio and the Fibonacci sequence can be seen in some of them. A nice illustration of the pattern is how seeds are distributed in sunflowers.

Chromotron t1_jegd1bw wrote on March 31, 2023 at 8:32 PM

I did not say there are none, only that almost all of them are random and won't be there in another of the same species of object.

> A nice illustration of the pattern is how seeds are distributed in sunflowers.

That is literally what I mentioned as the only potentially correct occurrence!

CautiousCold8392 t1_jeggbab wrote on March 31, 2023 at 8:54 PM

It's nice to know that we are in agreement. It is true to say that the Fibonacci sequence may not account for the unpredictability of natural processes.

Other examples exist that may resemble the sequence. The spiral pattern on a ram's horns often resembles the golden ratio. As the pinecone grows bigger and you count the spiral in each direction, the ratio gets closer to the golden ratio.

lolcatuser t1_jeghh0t wrote on March 31, 2023 at 9:02 PM

It's inaccurate to call that "the golden ratio" when it's not. If a plant has a logarithmic spiral with a factor of 1.4-1.8 then you shouldn't call it the same as a spiral of (1+sqrt(5))/2, for a lot of reasons - first, there's too much variance; second, there's no way to really prove whether it's the golden ratio or some other number. Suppose there is a slightly different number, say, (2+sqrt(8))/3, which is similar (~1.6 and ~1.6) yet entirely different - is it not just as possible that this is the magic number of life rather than the golden ratio?

Halvus_I t1_jegippy wrote on March 31, 2023 at 9:11 PM

There is no overall systemic use of the sequence in nature. If things match up its a fluke.