Of course, if you wish to know why some of Earth's most magnificent structures (like grouped mountain ranges--looking at them from over head) many look peculiarly like pieces of fractals, then spend some time looking into the "Golden Number" or the natural number, but as science refers to it: Euler's number (the constant: e). It is related to a great many interesting things.

Beyond seeding fractals, it is used in math a lot, Golden Spirals and the Fibonacci Sequence are part of it. It can be seen in nature in many places: those mountain ranges, trees, our cardiovascular system, and even shells. It's one of the most interesting constants we have and it is related to many structures that occur naturally. Which sometimes makes it appear that natural origins--structurally--may have their beginnings through this number via things like the Golden Spiral and of course fractals.

Just a little information to help make a piece like this seem even more impressive.

I think fibonacci sequences are also to be found in such patterns as the erosion patterns of coastlines, the altitude formation of mountain ranges, the migratory patterns of birds and undulates, the rise and fall of the tides...

4 more comments have been lost in the ether at this killed duplicate.

>> ^dannym3141:

???
This is just showing unrelated numbers and drawing arbitrary boxes around nature.
The bit where it started showing 137.5 degrees and firing circles off which then turned into a sunflower seed, what the hell was that? Why not 132 degrees or 7, there was no correlation to the position or number of the seeds and the angle at which circles were fired off. And every shell adheres to the fibonacci sequence - is that tru? I've never heard that before. A bunch of lines randomly spinning and aligning to show a patch on a wing of a dragonfly? The numbers were completely arbitrary to the pictures shown, don't like the combination of the title to the content of this video.


He's some reading for you: http://library.thinkquest.org/27890/applications5.html

Also he was showing the relationship of "natural" shape patterns. He related them using natural patterns and numbers.

>> ^dannym3141:

???
This is just showing unrelated numbers and drawing arbitrary boxes around nature.
The bit where it started showing 137.5 degrees and firing circles off which then turned into a sunflower seed, what the hell was that? Why not 132 degrees or 7, there was no correlation to the position or number of the seeds and the angle at which circles were fired off. And every shell adheres to the fibonacci sequence - is that tru? I've never heard that before. A bunch of lines randomly spinning and aligning to show a patch on a wing of a dragonfly? The numbers were completely arbitrary to the pictures shown, don't like the combination of the title to the content of this video.


It looks like this was made by an artist with an interest in math, not the reverse. That would explain why the imagery took priority of the mathematical explanations.

???

This is just showing unrelated numbers and drawing arbitrary boxes around nature.

The bit where it started showing 137.5 degrees and firing circles off which then turned into a sunflower seed, what the hell was that? Why not 132 degrees or 7, there was no correlation to the position or number of the seeds and the angle at which circles were fired off. And every shell adheres to the fibonacci sequence - is that tru? I've never heard that before. A bunch of lines randomly spinning and aligning to show a patch on a wing of a dragonfly? The numbers were completely arbitrary to the pictures shown, don't like the combination of the title to the content of this video.

He brings up thermodynamics ( you could add QED into this to make it even stronger, quantum foam and what not...), but entropy would be what he is talking about. Entropy can be seen as something that is the same homogeneous "thing" (quarks, photons, hydrogen; or in the case of QED potential energies) breaking down by "physics" or the physical mechanics and properties of the universe into a less homogeneous "thing". Hence energy then particles then elements, stars, black holes, planets, galaxies, cluster groups, the universe. It never really changed it is merely entropy that distinguishes most of these things.

Time itself may induce entropy, but we still have things to figure out in that area. What QED teaches is that you don't need anything special at all to create the universe, "chance" is more than enough. Throw in time or entropy and wallah, instant mechanical system created with it's own mechanics and in superposition to anything outside to detect it unless they become entangled to us. If they measure anything our "universes" would combine into a hybrid (most likely--impossible for now to begin thinking if this would be possible).

Recently scientists have been able to "tune" cobalt niobate (the magnetic spins) into a quantum critical state (superposition) and more recently they've done the same with electrons. The magnetic "tuning" frequency they used to accomplish this was extremely close to the Euler's number: e. "Euler's number" may be linked to the appearance of entropy merely being a function of mechanics that me be described by physicists later as an algorithm. If e is linked it would explain many observable systems we already have knowledge of. You can see it already at work in multiple situations. It also has a strong correlation with: fractals, golden ratio, golden spiral, Fibonacci sequence, etc... It's also an irrational number which may cause the algorithm to seemingly never stop; you could zoom in and out on the universe and it would continually look the same in correlation with an universal algorithm.

I hoped I made my thoughts clear enough; I dumbed down a lot of the material hopefully I still get the point across. It may be that the universe is merely just potential energies with an algorithm thrown in for spice. Other universes would have their own algorithm and constants like e.

Some articles pertaining to some of this: Here, here, here, here, here, and here.

Fun Fact: During the verse, the rhythm of the lyrics follows the Fibonacci sequence (forwards a little, then backwards, repeat). Gives more significance to the "spiral out" part at the end. I read this on Wikipedia a while ago, it cemented this as my favorite Tool song.

1 black
1 and
2 white are
3 all I see
5 in my infancy
8 red and yellow then came to be
5 reaching out to me
3 lets me see

Enigma is/was the pwn in the 90's.

He should look up "quantum critical states" and the relationship to the natural number e (golden ratio/spiral, Fibonacci sequence); also, e8 symmetry. Physics may get very interesting in the next decade.

You have been awarded 1 Power Point for fixing the embed code for Dead Pool video Pi: Hebrew Torah/Fibonacci Sequence (Darren Aronofsky film). Thank you for helping maintain VideoSift's reliability.

Damn - didn't see this in the queue till now (after I commented this link in my post Pi: Hebrew Torah/Fibonacci Sequence (Darren Aronofsky film) a couple of hours ago!)