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Shell

 
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Cyclops



Joined: 05 Aug 2006
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Location: North East of England

PostPosted: Sat Sep 06, 2008 6:20 am    Post subject: Shell Reply with quote

this is one of those shells that my 4 year old collected while at the seaside with grandma.
They make great subjects for macro work!




There appears to be a blue cast on the highlishgts but that is the base colour of the shell!
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P_T



Joined: 19 Jul 2008
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Location: Sydney, Australia

PostPosted: Sat Sep 06, 2008 6:49 am    Post subject: Reply with quote

I really like the second shot, I wonder if the circular pattern matches the golden ratio 1.6.
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Cyclops



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PostPosted: Sat Sep 06, 2008 6:50 am    Post subject: Reply with quote

P_T wrote:
I really like the second shot, I wonder if the circular pattern matches the golden ratio 1.6.

The golden what? Never heard that before.
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P_T



Joined: 19 Jul 2008
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Location: Sydney, Australia

PostPosted: Sat Sep 06, 2008 7:21 am    Post subject: Reply with quote

Rik might be able to explain it better.

http://en.wikipedia.org/wiki/Golden_ratio

http://www.astridfitzgerald.com/images/Golden-Mean-1.jpg

http://www.ibm.com/developerworks/rational/library/content/RationalEdge/jan04/lieberman_fig9.jpg

Closely related to the concept of beauty. It's been used by artists since the Renaissance
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rjlittlefield
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Joined: 01 Aug 2006
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PostPosted: Sat Sep 06, 2008 11:54 am    Post subject: Reply with quote

Good links, P_T. I've always thought of the Golden Ratio mostly in terms of the "golden rectangle", also explained in Wikipedia, and summarized there as
Quote:
[a rectangle such that] when a square section is removed, the remainder is another golden rectangle; that is, with the same proportions as the first.

As described in the first Wikipedia article that P_T links to, there is a huge amount of mathematics related to the golden ratio. Most of it is sufficiently arcane that even dedicated mathematicians just say "Cool!", and then move on to other stuff. Wink

--Rik
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Cyclops



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PostPosted: Sat Sep 06, 2008 12:35 pm    Post subject: Reply with quote

Mostly over my head I'm afraid. Mathematics is beautiful but not as beautiful shells.
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Harold Gough



Joined: 09 Mar 2008
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PostPosted: Sat Sep 06, 2008 11:55 pm    Post subject: Reply with quote

Here is another link:

http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/

Harold
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augusthouse



Joined: 16 Sep 2006
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Location: New South Wales Australia

PostPosted: Sun Sep 07, 2008 12:46 am    Post subject: Reply with quote

Larry,
Don't let all the numbers freak you out - all those formulas are beautiful music to those who are able to read them; I can only look at them in awe; but you don't need to be a Mathematician to appreciate the Divine Proportion. This is a beautiful thing.

It is evident in - just about everything, nature, music, architecture anatomy, botany, art, astronomy, microscopy, Hubble... the list goes on; for example, when you have a scene composed in your viewfinder and something inside says "hmmm, that's it", there is a reason why it resonates within you, consciously or subconsciously you recognise a pattern, a balance or signature, in a sense, something familiar.

I have a video called 'Understanding Beauty' that I first saw on The Discovery Channel. I'll have to digitize it and put it on YouTube; if it's not already up there.

You'll come across the term in just about any photography book that deals with composition and every photograph that has a sometimes inexplicable 'rightness'.

Craig
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Last edited by augusthouse on Sun Sep 07, 2008 1:54 am; edited 1 time in total
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rjlittlefield
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PostPosted: Sun Sep 07, 2008 1:06 am    Post subject: Reply with quote

Quote:
Here is another link:

http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/

Wow, now even my eyes are glazing over!

To simplify...

The growth pattern of many shells is that they just get a factor of X bigger on every turn. In the shell that's pictured, X is approximately 1.5 or 1.6, that is, the critter gets 50% or 60% bigger each time it adds another turn.

This sort of growth -- multiplying by a fixed fraction on every turn -- leads to a pattern that mathematicians call a "logarithmic spiral". See the Wikipedia article for details and illustrations.

The growth factor we see here -- 50% or 60% per turn -- is close to the golden ratio. But that's wildly different from the classic "golden spiral", which grows by 62% per quarter turn, about 4 times faster.

And it really doesn't matter -- there's nothing magical about any particular value for the growth factor. You can find spiral worm cases where it's probably more like 10% per turn.

As usual for mathematical modeling of biological stuff, the logarithmic spiral is only a crude approximation to what the animal actually does.

You can see in the picture that the last bit of shell doesn't even come close to following the smooth spiral of earlier growth. Instead, the last bit of shell -- 1/8 turn or so -- has grown substantially toward the sharp tip instead of continuing smoothly toward the blunt end.

I'd speculate that this change in shape indicates the subject had ended its period of rapid growth and was in the process of finalizing its shell into the adult form. But I'm no shell expert, and that could be completely wrong.

--Rik
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Cyclops



Joined: 05 Aug 2006
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PostPosted: Sun Sep 07, 2008 3:22 am    Post subject: Reply with quote

augusthouse wrote:
Larry,
Don't let all the numbers freak you out - all those formulas are beautiful music to those who are able to read them; I can only look at them in awe; but you don't need to be a Mathematician to appreciate the Divine Proportion. This is a beautiful thing.

It is evident in - just about everything, nature, music, architecture anatomy, botany, art, astronomy, microscopy, Hubble... the list goes on; for example, when you have a scene composed in your viewfinder and something inside says "hmmm, that's it", there is a reason why it resonates within you, consciously or subconsciously you recognise a pattern, a balance or signature, in a sense, something familiar.

I have a video called 'Understanding Beauty' that I first saw on The Discovery Channel. I'll have to digitize it and put it on YouTube; if it's not already up there.

You'll come across the term in just about any photography book that deals with composition and every photograph that has a sometimes inexplicable 'rightness'.

Craig

Sounds like the rule of thirds in composition,something that is just intuitive. I look thru the viewfinder and just know if it looks wrong. Its why when I'm photographing bugs and things,if they don't fill the frame without knowing it i put them in the frame so they look aestheticlly pleasing.
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Harold Gough



Joined: 09 Mar 2008
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PostPosted: Sun Sep 07, 2008 6:00 am    Post subject: Reply with quote

Such mathematics gives us fractals, which you may have used in digital image manipulation.

http://en.wikipedia.org/wiki/Fractal

Then there are images themselves:

http://www.fractal-recursions.com/

Harold
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Cyclops



Joined: 05 Aug 2006
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PostPosted: Sun Sep 07, 2008 6:29 am    Post subject: Reply with quote

Harold Gough wrote:
Such mathematics gives us fractals, which you may have used in digital image manipulation.

http://en.wikipedia.org/wiki/Fractal

Then there are images themselves:

http://www.fractal-recursions.com/

Harold

Oh i love fractals,i have James Gleick's book Chaos. Also i have a fractal program and have a few examples up on deviantArt.com
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