Just say fractals. We already knew they appear everywhere in nature.
The Secret of the Fibonacci Sequence in Trees
11–20 of 29 posts
Re: The Secret of the Fibonacci Sequence in Trees
#12I'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 advan…
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
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.
Re: The Secret of the Fibonacci Sequence in Trees
#13> 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…
Good lord, thank you. As a math guy, numerology drives me apeshit.
Re: The Secret of the Fibonacci Sequence in Trees
#14I 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 so…
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.
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Re: The Secret of the Fibonacci Sequence in Trees
#15Earlier quoted context omitted.
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
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 o…
I retract this. Reading deeper, I see that he was comparing equal solar cell areas, and thus your analysis likely correct.
Re: The Secret of the Fibonacci Sequence in Trees
#16I'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 advan…
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
I think it is also related to the angle of sunlight falling on the leaves - not just the shading. The passive arrays may be completely unshaded but they may not receive the optimum sunlight through out the day.
Re: The Secret of the Fibonacci Sequence in Trees
#17> 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…
Good lord, thank you. As a math guy, numerology drives me apeshit.
oh some more things, re-reading that lovely "Fibonacci Flim Flam" essay I linked above, it turns out that:
sunflower seeds actually turn out to grow that way because the organism tries to pack the seeds as close as possible.
from this, if the close-packing manages to occur without disturbance, the golden ratio emerges--but if it is disturbed by anything (disease, damage, etc), the golden ratio becomes less accurate but the organism still continues packing the seeds as closely as possible.
that is how you can tell that the organism "tries" to realize a close packing and just happens to produce the golden ratio and sometimes Fibonacci numbers as a byproduct: if the process would have been based on the golden ratio instead, a disturbance would cause a spiral out of control with many empty patches.
finally, I almost forgot his (and nearly implied otherwise in my previous post), just the fact that the golden ratio occurs in a process or system does not mean that Fibonacci numbers are involved. there are many other number sequences of the same recurrence relationship as Fibonacci numbers that produce the same golden ratio. Lucas numbers, for example. However, the smaller ratios of those other sequences can be very different from the smaller ratios of the Fibonacci sequence (neither sequence approximates phi 0.618.. very closely for small numbers).
Counting seeds in sunflowers shows that some of them follow the Lucas sequence instead of Fibonacci. But again, you don't see those in the design books! (or sometimes you do but nobody bothers to check)
Re: The Secret of the Fibonacci Sequence in Trees
#18Brilliant. Perhaps first time I'm seeing some one using Fibonacci for other than learning programming language ;-)
Fibonacci trees, which are connected to Fibonaccy numbers, are actually useful, not just for learning a language.
Re: The Secret of the Fibonacci Sequence in Trees
#19Here'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... - "A harmonic measure to the human scale, universally applicable to architecture and me…
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.
Re: The Secret of the Fibonacci Sequence in Trees
#20This 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...