The Logarithmic Spiral: Nature being awesome yet again - General

Meet the logarithmic spiral: [IMG]http://upload.wikimedia.org/wikipedia/commons/thumb/4/40/Logarithmic_Spiral_Pylab.svg/540px-Logarithmic_Spiral_Pylab.svg.png[/IMG] The logarithmic spiral is pretty good friends with nature. Nobody's quite sure why they're such good friends. [IMG]http://upload.wikimedia.org/wikipedia/commons/thumb/0/08/NautilusCutawayLogarithmicSpiral.jpg/793px-NautilusCutawayLogarithmicSpiral.jpg[/IMG] [IMG]http://upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Low_pressure_system_over_Iceland.jpg/692px-Low_pressure_system_over_Iceland.jpg[/IMG] [IMG]http://upload.wikimedia.org/wikipedia/commons/thumb/d/db/Messier51_sRGB.jpg/800px-Messier51_sRGB.jpg[/IMG] [IMG]http://sydaby.eget.net/nat/spiral_growth_convallaria/pictures/picture-2.jpg[/IMG] [IMG]http://sydaby.eget.net/nat/spiral_growth_convallaria/pictures/picture-6.jpg[/IMG] [IMG]http://www.educatedearth.net/media/58/1232391765.jpg[/IMG] The approach a hawk takes as it dives, descending upon its prey, is a logarithmic spiral. As an insect, such as a moth, flies toward a stationary source of light, its path as it approaches the light is a logarithmic spiral. The nerves of the eye's cornea are arranged in a logarithmic spiral. [URL="http://en.wikipedia.org/wiki/Logarithmic_spiral_beaches"]Beaches.[/URL] I don't even know how to properly explain this one. Nature's awesome.

woooooah maaaaan

How is it logarithmic?

Fibonacci sequence/spiral. 1,1,2,3,5,8,13,21..... Shit just got Dan Brown in here.

Sexy.

[QUOTE=Pace.;26024169]How is it logarithmic?[/QUOTE] [url=http://www.facepunch.com/threads/1025974-The-Logarithmic-Spiral-Nature-being-awesome-yet-again?p=26024252&viewfull=1#post26024252]because you touch yourself at night[/url]

[QUOTE=Pace.;26024169]How is it logarithmic?[/QUOTE] I'm assuming it has something to do with: [quote=wikipedia]The logarithmic spiral can be determined using the equation (written in polar coordinates): r = eθcotα where: θ = the angle of rotation, is located between two lines drawn from the origin to any two points on the spiral. r = the ratio of the lengths between two lines that extend out from the origin. The two lines are given as RO and R. So r also equals the ratio R/RO. α = the angle between any line R from the origin and the line tangent to the spiral which is at the point where line R intersects the spiral. α is a constant for any given logarithmic spiral.[/quote]

This reminds me of something.... [media]http://kwef.ca/ECO%20Articles_files/image001.jpg[/media]

I don't know why, but this image made me feel excited, then I felt like I was gonna fall over... then my mind started saying I wish I could touch it... [img]http://upload.wikimedia.org/wikipedia/commons/thumb/d/db/Messier51_sRGB.jpg/800px-Messier51_sRGB.jpg[/img] [B]fuckin blew my mind...[/B]

In more layman's terms, if you draw a line through the spiral, the length of the segments between the spiral's sections get [I]exponentially [/I]larger as you move farther from the spiral's origin. Logarithmic. [editline]12th November 2010[/editline] [QUOTE=mr.killa;26024210]This reminds me of something.... [media]http://upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Flag_of_Nazi_Germany_%281933-1945%29.svg/800px-Flag_of_Nazi_Germany_%281933-1945%29.svg.png[/media][/QUOTE] what does this have to do with anything at all

Uzumaki.

Cool stuff. I always thought it was neat how certain patterns seem to be found all over the place in nature.

Nature [i]is[/i] pretty fucking awesome isn't it

[img]http://correlatedcontents.com/wp-content/uploads/2010/06/uzu21.jpg[/img]

I love you, science.

[QUOTE=Furioso;26024252]what does this have to do with anything at all[/QUOTE] mr.killa was expressing how much of a nazi cunt he is :v: I suppose that would "spiral" out of control... :doh:

It seems to me that "exponential spiral" would be a more fitting description. [img]http://www.codecogs.com/gif.latex?r%20=%20e^{\theta}[/img] and [img]http://www.codecogs.com/gif.latex?\theta%20=%20\ln{r}[/img] are both of course correct ways to express the spiral but the former seems more obvious from the appearance of the spiral - the distance of the spiral line increases exponentially, which can be seen with plain eye.

[QUOTE=ThePuska;26024571]It seems to me that "exponential spiral" would be a more fitting description. [img_thumb]http://www.codecogs.com/gif.latex?r%20=%20e^{\theta}[/img_thumb] and [img_thumb]http://www.codecogs.com/gif.latex?\theta%20=%20\ln{r}[/img_thumb] are both of course correct ways to express the spiral but the former seems more obvious from the appearance of the spiral - the distance of the spiral line increases exponentially, which can be seen with plain eye.[/QUOTE] Don't ask me bro I didn't name it

I guess it's naturally a very efficient path to follow for many different purposes, such as growth direction and travel. That's why so many different instances utilize it.

[QUOTE=Canuhearme?;26024495][img_thumb]http://correlatedcontents.com/wp-content/uploads/2010/06/uzu21.jpg[/img_thumb][/QUOTE] this is the first thing it reminded me of

[QUOTE=Badunkadunk;26024962]I guess it's naturally a very efficient path to follow for many different purposes, such as growth direction and travel. That's why so many different instances utilize it.[/QUOTE] That's true, but how does "nature" know that's the most efficient path? How does a hawk know that flying in that path is the most efficient way to fly? How did vegetables end up growing in that manner? More unsolved questions. :saddowns: To me, it's at least somewhat convincing evidence of [I]some[/I] sort of intelligent design in the universe.

[QUOTE=Furioso;26025022]That's true, but how does "nature" know that's the most efficient path? How does a hawk know that flying in that path is the most efficient way to fly? How did vegetables end up growing in that manner?[/QUOTE] They don't, trends like this don't follow any sort of deduction or reasoning. Shit just happens.

[img]http://media.musictoday.com/store/bands/1968/product_large/MUDD562.JPG[/img] Reminded me of this

It's not random, if it was random, then only a fraction or even a single member of the family would exhibit the trait, but every member exhibits it. It's from many many generations having had stumbled upon a very effective action, and passing it down through their genes. I'm not an expert on this stuff, but it's something like that.

They are in nature so much because they are cool. Who doesn't like spirals? You don't like spirals? Wow what is wrong with you, you need to like spirals more.

How incredibly beautiful.

[QUOTE=Badunkadunk;26025179]It's not random, if it was random, then only a fraction or even a single member of the family would exhibit the trait, but every member exhibits it. It's from many many generations having had stumbled upon a very effective action, and passing it down through their genes. I'm not an expert on this stuff, but it's something like that.[/QUOTE] I'm not saying its random, but it's not just one species using the spiral. The amount of species who do use it are countless. Not to mention that it seems to form naturally like in the picture of the hurricane or beaches.

[QUOTE=Furioso;26025022]That's true, but how does "nature" know that's the most efficient path? How does a hawk know that flying in that path is the most efficient way to fly? How did vegetables end up growing in that manner? More unsolved questions. :saddowns: To me, it's at least somewhat convincing evidence of [I]some[/I] sort of intelligent design in the universe.[/QUOTE] Evolution.

I just threw this together. Fucking trippy, man.. [img]http://anyhub.net/file/algorithmic-spiral.png[/img]

[QUOTE=Furioso;26024135] [img_thumb]http://www.educatedearth.net/media/58/1232391765.jpg[/img_thumb] [/QUOTE] I hate fractal broccoli. Looks like something Cthulhu would eat.