Sonic Youth Gossip - Fractal Geometry: The Basis of the Universe!

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I strongly believe so, yes.

Quote:

Originally Posted by SuchFriendsAreDangerous

Bullshit. while not every fractal is a spiral, every spiral or golden ratio is in fact a fractal. do the math :)

take a line.

divide into thirds.

then draw the three lines, the original line and the two smaller lines, each a third of the original. then do this again. then do it again.

now take the golden ratio 'spiral' and graph it on a number line. take the points and do the math. they are fractal in shape ;)

...

I drew yr lines

Quote:

every spiral or golden ratio is in fact a fractal.

A 'spiral' is not only a logarithmic spiral or a golden spiral. There are many kinds. You could plot a spiral to move inward or outward indefinately without repetition of angle or amount of rotation between angle changes, though my math sucks so I can't write this at all.

Not all fractals need to demonstrate the golden ratio. Yes examples of golden spirals are... fractals.. though a line drawn in such a way is a very very very basic example I would think. There is no detail or recursion, but I am not a mathemetician so it isn't my judgement.

I wish I'd studied a lot more, but the three definitions are completely different ones. Some parts may overlap, but they are three seperate concepts entirely.

you know. the colour blue. a circle. some circles are blue.

for you http://mathdl.maa.org/images/upload_...lMakerDCR.html

Quote:

Originally Posted by phoenix

...

I drew yr lines

I don't need to graph the spiral there are many images available online pre made.

"A mathematical fractal is based on an equation that undergoes iteration, a form of feedback based on recursion.[2]
A fractal often has the following features:[3]
It has a fine structure at arbitrarily small scales.
It is too irregular to be easily described in traditional Euclidean geometric language.
It is self-similar (at least approximately or stochastically).
It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve).[4]
It has a simple and recursive definition.
"

A 'spiral' is not only a logarithmic spiral or a golden spiral. There are many kinds. You could plot a spiral to move inward or outward indefinately without repetition of angle or amount of rotation between angle changes, though my math sucks so I can't write this at all.

Not all fractals need to demonstrate the golden ratio. Yes examples of golden spirals are... fractals.. though a line drawn in such a way is a very very very basic example I would think. There is no detail or recursion, but I am not a mathemetician so it isn't my judgement.

I wish I'd studied a lot more, but the three definitions are completely different ones. Some parts may overlap, but they are three seperate concepts entirely.

you know. the colour blue. a circle. some circles are blue.

for you http://mathdl.maa.org/images/upload_...lMakerDCR.html

thank you ;)

you are one of the first people to actually do their homework on a thread I posted and I truly appreciate the effort!

as well, in doing so you understood my point as posted above, that, "Yes examples of golden spirals are... fractals.. though a line drawn in such a way is a very very very basic example I would think."

peace and love