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Topic: Phi? (Read 1357 times) |
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Peace_Heather
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Phi?
« on: Jan 9th, 2004, 7:37pm » |
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Hello all,
I'm new to the forum. I'm NOT a programmer (unless you really think the BASIC and LOGO I played with about 15 years ago counts). I just really enjoy looking at the things you all have managed to create.
So I'm going to ask a possibly foolish question: Is it possible for you to play with irrational numbers, specifically "phi", in Processing?
(phi = square root of five, divided by two, plus one-half = 5^.5 * .5 + .5 = 1.6180339887...)
I am also not a mathematician; I've only begun studying this number recently, and finding it very cool. (Da Vinci loved it, so I guess I'm in good company.) Phi shows up in nature ALL the freaking TIME, and I thought it might be a useful piece of information for all you artificial-life people to have, if you didn't already.
Basically, if you take two line segments AB and BC, such that the ratio of AB:BC = 1:phi, then you'll also see that the ratio of BC:AC = 1:phi.
You can keep adding the line segments together into infinity, following the pattern of the Fibonnaci sequence, and always, always get a ratio of x:phi*x. Phi is the only number that makes this possible.
Incidentally, if you take the ratios of the Fibonacci numbers themselves (1:1, 1:2, 2:3, 3:5, etc.), you will gradually converge on phi, as well. If you want to skip the inaccurate part of the sequence and just cut to the chase, all you have to do is take the regular Fibonacci sequence (0, 1, 1, 2, 3, 5, 8, etc.) and replace the third number, like this:
(0, 1, phi, phi+1, 2phi+1, 3phi+2, 5phi+3, 8phi+5...)
I saw some Fibonacci representations that a few of you had made that were beautiful, but stuck mostly with the spirals. I was curious to see what a tree structure or other artificial life might look like if it were to branch into segments that matched the 1:phi ratio.
As I said earlier, the ratio of 1:phi shows up in nature a lot. Here are only a few examples from the human body:
The finger bones of your hands -- fingernail = 1, fingertip bone = phi+1, second finger bone = 2phi+1, base finger bone = 3phi+2, bone in hand = 5phi+3.
wrist to fingertip: elbow to fingertip
shoulder to elbow: shoulder to fingertip
knee to floor: hip to floor
navel to floor: crown to floor
chin to tip of nose: chin to crown
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Okay, so all the examples might be overkill. I was just curious, if Processing lets you play with irrational numbers, what you might get if you plugged in phi and played with it.
Cheers, and thanks for letting me ramble.
Heather
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| « Last Edit: Jan 9th, 2004, 7:41pm by Peace_Heather » |
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PeaceHeather
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Re: Phi?
« Reply #2 on: Jan 10th, 2004, 11:25pm » |
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Do you think it would be possible to buils artificial critters or trees or somesuch that segmented along PHI ratios?
Heather, still curious
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PeaceHeather
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Re: Phi?
« Reply #4 on: Jan 12th, 2004, 12:55am » |
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Thanks, Mike... unfortunately, being completely unfamiliar with coding (again, outside of the little LOGO turtle stuff), I'd rather just put in a request as an "audience member", as it were, to see something like a worm or bug with legs or body segments broken down according to some approximation of phi.
Can I get away with that? *grin* Or am I just being horribly pompous and pretentious?
Heather
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| « Last Edit: Jan 12th, 2004, 12:55am by PeaceHeather » |
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