# The Naked Scientists Forum

### Author Topic: What is the relationship between Fibonacci and living systems?  (Read 2146 times)

#### annie123

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• Posts: 248
##### What is the relationship between Fibonacci and living systems?
« on: 11/06/2012 02:29:03 »
Does anyone have an idea/knowledge as to why the fibonaci algorithm should be the basis of so much of the structure of living things, plant, marine life etc. Is there any evolutionary advantage to this structure? Why is is so widespread? How far back in time does it go? ARe there fossils that show plants with this structure? (No replies about intelligent design, please.)
« Last Edit: 14/06/2012 08:25:12 by chris »

#### namaan

• Sr. Member
• Posts: 195
##### Re: why Fibonaci?
« Reply #1 on: 11/06/2012 15:58:34 »
As a completely off-the-wall guess, I would say that since they show up in the branching of trees (and likely the branching of anything, including neuronal axons), and trees are 3-dimensional, then first off, the sequence likely depends on the number of dimensions of the system. The optimal sequence for growth/branching in 2D is perhaps, then, a different sequence to that of our fibonacci sequence.

Given that, it likely says something about the rate of growth/branching in 3D such that optimal space is taken up in 3 dimensions. If a tree branched more rapidly, it would at its extreme grow a shell of branches at its boundary, if it branched more slowly, the branches would thin out and leave it bare-looking. It's the "just-right", middle ground that we got where seeming equal amount of empty space exists throughout the space taken up by the tree including all branches, stems and leaves. I have no evidence for anything I just said :P

#### namaan

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• Posts: 195
##### Re: why Fibonaci?
« Reply #2 on: 11/06/2012 16:08:37 »
Ohh, but of course that doesn't explain why the sequence shows up in otherwise "2D" structures like shells/galaxies. Granted, these structures don't involve "branching" as far as I can tell.

#### RD

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##### Re: why Fibonaci?
« Reply #3 on: 11/06/2012 18:31:28 »

Quote
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.
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html#plants

The same optimal packing may apply to embryonic cells, giving rise to close-to-phi proportions in the fully-formed animal.

#### namaan

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• Posts: 195
##### Re: why Fibonaci?
« Reply #4 on: 11/06/2012 19:06:01 »
I'm seeing spirals in that diagram. Do they save my dimensionality hypothesis (in the sense that, yes it is a 2D figure, but it has spirals like those in a sea shell)? Or is dimensionality irrelevant to the sequence I wonder?

#### The Naked Scientists Forum

##### Re: why Fibonaci?
« Reply #4 on: 11/06/2012 19:06:01 »