

The Secret of the Fibonacci Sequence in Trees - pigbucket
http://www.amnh.org/nationalcenter/youngnaturalistawards/2011/aidan.html

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tripzilch
> Scientists and naturalists have discovered the Fibonacci sequence appearing
> in many forms in nature, such as the shape of nautilus shells, the seeds of
> sunflowers, falcon flight patterns and galaxies flying through space. What's
> more mysterious is that the "divine" number equals your height divided by
> the height of your torso, and even weirder, the ratio of female bees to male
> bees in a typical hive! (Livio)

Except that most of this is simply not true:
<http://www.lhup.edu/~dsimanek/pseudo/fibonacc.htm>

It's a very tasty popular myth that people like to repeat, that there's a
magical sacred golden constant producing all the complexity in nature and
more.

Except that nobody actually bothers to _measure_ anything, they just keep
repeating and reposting the same images of spiral galaxies and nautilus
shells.

Nor is there anything "inherently beautiful" about the golden ratio, research
into perceived aesthetics of ratios simply showed that people prefer fractions
of small numbers. It's imprecise enough that you really can't say whether
people like 1.5 (3/2) or 1.667 (5/3) or 1.618 (phi) best.

The one thing where he _is_ right, is the pattern in sunflower seeds. If you
divide the 360 degrees of a circle in two parts so that their ratio is
1:1.618, and you use that angle (about 137.5 degrees) to rotate outwards as a
spiral, put a big dot at every point, you'll get a pattern that looks pretty
much exactly like sunflower seeds.

The thing about this particular pattern is that the seeds end up being rather
uniformly spaced over the plane, while using other angular ratios creates
swirly patterns and waves of filled and empty regions.

So I can imagine if you apply this to the rotation of tree branches, it'll
result in a more uniformly distributed pattern, that will capture sunlight
more efficiently than a pattern with holes in it.

I kind of wonder, though, if it's not the other way around--because nature
uses golden ratio angles in tree branches, the fibonacci numbers pop up.
Because really it's super easy for fibonacci numbers to pop up anywhere,
especially the small ones, what's _significant_ , however, is when the golden
ratio actually plays a meaningful role.

~~~
taliesinb
(repeating from other thread):
<http://www.wolframscience.com/nksonline/page-410#previous> has something to
say about how the golden ratio can pop out without being encoded directly in
plant phylotaxis.

~~~
tripzilch
Looks interesting--will read later, thanks!

------
extension
I'm not sure how much of this the kid actually discovered on his own. The
Wikipedia page on Phyllotaxis cites plenty of past research on why the
Fibonacci sequence shows up (and the kid oddly hand copied the illustrations
from that page).

It's an emergent pattern from the branches shoving each other around as they
grow. It minimizes the overlap of the leaves _if they are being added
indefinitely_. If you know in advance how many leaves/panels there will be
then obviously you can just space them evenly. If you ran that experiment with
one tree of evenly spaced/angled panels and one tree of golden angle spaced
panels, I think the evenly spaced one would win.

~~~
uvdiv
Crucial difference: the tree-leaf problem is about how to arrange leaves which
are shading each other; but here he compares such a "tree" with a flat array
that has _no overlaps at all_. He claims that the tree generates more energy
than the no-overlaps array, which is impossible. I have a longer comment about
this in the other thread:

<http://news.ycombinator.com/item?id=2902684>

~~~
thyrsus
It's not impossible, because the sun's relative position changes, and the
closer to orthogonal the light, the better the efficiency of the solar cell.
By taking optimal advantage of the height, this design is closer to
orthogonality more of the time, and is thus more efficient per ground area
(though not per solar cell area, as you demonstrate).

Now, if your solar array were mounted such that it actively maintained
orthogonality to the sun (heliotropism), I expect you'd do even better, but
that kind of active system is more subject to failure.

~~~
thyrsus
I retract this. Reading deeper, I see that he was comparing equal solar cell
areas, and thus your analysis likely correct.

------
palish
I wish Aidan had been allowed to write this in his own words, rather than his
parent's / someone else's words.

On the other hand, whoever's taking care of him behind the scenes has done an
incredible job. I'd even say Aidan's "set for life"; that might seem over the
top, but consider... this link will forever be associated with his name. It
demonstrates that even at age 13, he was a very capable real-world problem
solver, while also showing off his ability to perform and present his own
original research in ways that other people can build on.

That's going to impress virtually everyone he ever meets, probably. Admissions
boards, employers, investors, etc. Obviously that assumes he plays his cards
correctly going forward. Still, though... this will always be a future de-
facto "get-his-foot-in-the-door" for him, regardless of whatever it is he's
trying to do. Except maybe pickup chicks.

I just hope he doesn't become a victim of his own success. Hearing "you're
such a genius!" from everyone around him would not be good for his future
self.

~~~
tokenadult
_I'd even say Aidan's "set for life"_

And I would strenuously disagree. No one is set for life at that age. As you
yourself point out, sometimes marking a mark early just makes thing difficult
later on. There are plenty of historical examples.

Best wishes to him. There are still plenty of mountains to climb.

------
nvictor
wow people! slightly off topic but that's how you DELIVER information. no ads
bullshit, straight, references...

now compare that to the first link we got.

------
ColinWright
This is by far and away the better article. Such a shame the discussion is on
the totally crap repackaging of it:

<http://news.ycombinator.com/item?id=2902329>

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thebootstrapper
Brilliant. Perhaps first time I'm seeing some one using Fibonacci for other
than learning programming language ;-)

~~~
eru
Fibonacci trees, which are connected to Fibonaccy numbers, are actually
useful, not just for learning a language.

------
SimHacker
This is a question that fascinated Alan Turing, who wrote a classic paper
called "The Chemical Basis of Morphogenesis" and other unfinished papers about
the subject (some published in a book called "Morphogenesis"). He used lots of
heavy math that came so naturally to him, to model plant growth as a reaction-
diffusion system running in a ring of cells (the stem of the plant). By
computing the reactions by hand on paper, he studied how cells could grow into
"parastichy" with spiral patterns related by Fibbonachi numbers.
<http://botanydictionary.org/parastichy.html>
[http://www.dna.caltech.edu/courses/cs191/paperscs191/turing....](http://www.dna.caltech.edu/courses/cs191/paperscs191/turing.pdf)

------
whileonebegin
This reminded me of the PBS NOVA episode about how the Mandelbrot set can
describe nature, like the spacing of trees in a forest, the spacing of
branches on a tree, the spacing of leaves on a branch, the spacing of veins in
the leaf, etc. It's not just random.

Apparently, the fibonacci sequence can be found within the Mandelbrot set,
which makes sense from the author's discovery.

[http://www.sunflowerblog.ch/2007/06/03/the-fibonacci-
numbers...](http://www.sunflowerblog.ch/2007/06/03/the-fibonacci-numbers-and-
mandelbrots-fractals/)

------
lukesandberg
In wolframs "A new Kind of Science" there is a long discussion of not only the
fact that leaf arrangement tends to use the golden ratio and that it is
optimal for the plant. But also he describes a model (using cellular automata)
that explains why such a pattern might emerge naturally. Unfortunately i don't
remember all the details but it was a compelling use case for why automata
might be a good model for natural phenomenon.

~~~
SimHacker
That was just Stephen Wolfram channeling Alan Turing but not giving him
credit.

------
hackermom
Here's a little something that most people don't know, that I picked up from
my architecturally interested father long ago:

The French architect Le Corbusier
(<http://en.wikipedia.org/wiki/Le_Corbusier>) made use of Fibonacci sequences
to create his famous "Modulor" ([http://www.apprendre-en-
ligne.net/blog/images/architecture/m...](http://www.apprendre-en-
ligne.net/blog/images/architecture/modulor.jpg) \- "A harmonic measure to the
human scale, universally applicable to architecture and mechanics.") which
represents a few fixed points in Fibonacci sequences that have been in use in
architecture, interior decoration, carpentry etc. for more than 50 years, at
least here in Europe - I have no idea if these scales are as rigorously
followed in the Americas or in Asia.

If you look at the picture, and then look at the height of the seat of your
kitchen chairs, your kitchen table, your kitchen sink, your cupboards etc.,
you will find that their tops, bottoms and heights almost always align around
numbers in these scales. These measurements create a strange sense of harmony
in the way the mind processes geometry picked up from eyesight, which is not
perceivable as soon as you move away from these dimensions, in some way quite
similar to how the Golden Ratio pleases the eye.

Just for fun I measured some of the interior in my home. Desk: 69cm. Kitchen
chairs and kitchen table: 43cm and 70cm. Kitchen sink: 88cm. Bottom and top of
wall-mounted kitchen cupboards: 138cm, 225cm (height of 87cm).

Also interesting to note is that similar scales have been found to be used in
ancient times as well - seems we took notice of this particular natural
pattern long ago.

~~~
roel_v
If the height of your desk, chairs, tables, kitchen sink and cupboards are
determined by anything other than the size of resp. your (or at least, 'an
average') torso, calves, torso, legs and total body length, you live in a
weird house. If you look long enough, you can find 'patterns' everywhere.

------
Daniel_Newby
Trees also optimize for shading their competitors and avoiding being shaded,
not just for efficiently gathering raw light. Understanding the shading factor
would require extensive field work and Monte Carlo analysis.

------
ck2
Just say fractals. We already knew they appear everywhere in nature.

~~~
njharman
Why stop there. Just say stuff. We already knew stuff appears everywhere in
nature.

Cause exact words have exact meanings. Fib sequence != fractals

