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Fractals

kinjo

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ahh they are beautyful🙂
seems to have a calming effect on me! they look crazy but so diliberate, strange!hmmm:)
 

Luxpyre

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What really amazes me about some fractals is how they mimic natural form at times. The intricacies of nature always amaze me. No matter how big or how small you get, things are always complex and working in such amazing ways.
 

Hoyu

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Fractals are a phenomenon found in nature (snowflakes, ferns, sea shells, etc.). That we have developed software, which enables us to create fractals, is also quite natural in my opinion.
 

Luxpyre

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No, not exactly. Fractals are mathematical formulas that produced forms that are very similar to those in nature. Some mathemetician probably didn't go out and look at a fern and come up with fractals, but rather came up with fractals and realized they mimic nature. There could perhaps be a link in how the natural forms are made and the way fractals are made, but ultimately mathematic fractals are a "purer" form so to speak since natural form will be limited at some level whereas mathematical form is limitless.
 

Hoyu

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Thanks Luxpyre!

Fractals are found everywhere in nature. This is due to the fact that a fractal can be used to describe just about anything. (this is also why fractals are used for image compression) To find an example of a fractal in nature, look anywhere. One example is a leaf. The branching of the veins creates self-similarity and independence of scale. These two things qualify the leaf as a fractal.

Please note that natural objects are not really fractals, but are actually fractal-like. This is because natural processes act over a finite range of scales. In other words, although natural objects can be zoomed in to infinity, they won't look the same at different zooms. For example, the fractal branching of leaf veins ends at the cellular level and new patterns occur.

Source: http://library.thinkquest.org/25810/cgi-bin/fido.cgi?whichtype=0&page=../sitemap.txt#about
 

Twisted

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Take a look at the movie "Pi".
In that movie it's stated that every shape present in nature can be calculated back to a mathematical formula.
 

Hoyu

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Pi

As I remember the guy's migraines get worse and worse the closer he gets to some sort of mathematical enlightenment of God from calculating the Torah. When he finally does come to the truth of the "mind of God" he dies of massive hemorrhaging in his brain. Strange movie, but interesting topics arise.

The Golden Spiral is a mystical shape that is an absolute in both abstract mathematics and chaotic nature. It was first discovered by Phythagoras, a failed Greek messiah and mathematical cult leader in the 5th century B.C.

The spiral is derived via the golden rectangle, a unique rectangle which has the golden ratio. When squared, it leaves a smaller rectangle behind, which has the same golden ratio as the previous rectangle. The squaring can continue indefinitely with the same result. No other rectangle has this trait.

When you connect a curve through the corners of these concentric rectangles, you have formed the golden spiral. The Phythagoreans loved this shape for they found it everywhere in nature: the Nautilus Shell, Ram's horns, milk in coffee, the face of a Sunflower, your fingerprints, our DNA, and the shape of the Milky Way.

"My new Hypothesis: If we're built from Spirals while living in a giant Spiral, then is it possible that everything we put our hands to is infused with the Spiral?"

-- Max Cohen in the motion picture Pi

Source: http://www.pithemovie.com/pithemovie.html
 

Luxpyre

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Its the way that the forms of fractals can be seen in nature that amazes me so much. Its like glimpsing something big and wonderfull through a little hole in a fence and you can only see a little piece of it. You just wonder what else is over there!

I tried to watch pi once, but it was late at night and I fell asleep. I think it was at that point that I realized I don't enjoy black and white movies so much. They just seem to lack something to me. All I really remember about the movie is him having a dream or something with a brain on some steps and he's all wigging out. I thought the premise was interesting though. ;)
 
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