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Q: "Strange Attractors" in chaos theory ( Answered 5 out of 5 stars,   5 Comments )
Question  
Subject: "Strange Attractors" in chaos theory
Category: Science > Physics
Asked by: cats4me-ga
List Price: $15.00
Posted: 31 Mar 2005 11:24 PST
Expires: 30 Apr 2005 12:24 PDT
Question ID: 503260
"Strange attractors."  Can you give me a list of ordinary items in
daily life that mimic (or metaphorically represent) the behavior of
so-called strange attractors / chaotic attractors in chaos theory?
Answer  
Subject: Re: "Strange Attractors" in chaos theory
Answered By: hedgie-ga on 01 Apr 2005 11:40 PST
Rated:5 out of 5 stars
 
Butterfly effect of a Butterfly ballot

 In the essay 

		The Butterfly Effect
	In Global Politics and Commerce
which is here
         http://www.peterussell.com/SP/Butterfly.html
	 
	 Peter Russel, a PhD physicist who studied under S. Hawkins,
	 
	 gives several examples of the effect of the second order events on the
	 first order dynamics,
	
e.g. 1)  Back in the early eighties, IBM decided that there might
after all be a market for personal computers.
	 ...
	 . They decided to hire a small company with some experience in this
area to write the software for them. An owner of the company, a Mr
Bill Gates, met with the IBM executive in charge of the software to
make a deal........ It did take off. Bill Gates became the richest man
on the planet, and Microsoft came to dominate the software industry
worldwide.
The world might be a very different place if the mental butterfly that
flitted through that executive's mind had not caused him to miss the
weakness in the deal...

      2) Sometime back in 2000, Theresa LePore, had the idea to
enlarge the typeface on the ballot paper she was designing for Palm
Beach voters in the US Presidential election, thinking it would make
it easier to read ...
      
      
       Is this really is a chaos theory. Not just a parable. To see
that graphically, you may click on the following link which leads to
an applet which shows a Lorentz attractor. To see this, you need too
have java installed and  enabled.
   If you do, you will see (after a while) a start button which will
start the applet in a new window.
       
 Here is the link to the applet:      
       http://www.cmp.caltech.edu/~mcc/chaos_new/Lorenz.html
        
       Here you can  test if you have java installed and  enabled       
       http://www.bodo.com/javame.htm
         
       Now, assuming that the applet started, you see a point (state
of the system) running along a figure 8 . It may to a right loop, or
left loop.  At the 'decision point' in the middle of the 8, small,
second order effects, will decide if same loop will be repeated, or
other  loop will be started, etc etc
   
 Now, if we recall example 2) we can interpret the small effect
(Theresa LePore's  idea )to cause the the system to swing right
(corresponding to election of republican president). Every four years,
system return to the 'decision point' .
 As long as we have these close elections, we can expect the politics
of a  this system, of any two-party system to be chaotic ....
       
       Hedgie
cats4me-ga rated this answer:5 out of 5 stars and gave an additional tip of: $3.00
Nice links provided to supplement the answer.  And a helpful addendum
in follow up comments.

Comments  
Subject: Re: "Strange Attractors" in chaos theory
From: pinkfreud-ga on 31 Mar 2005 11:31 PST
 
Here's a neat metaphor:

"As a metaphor, think of a point attractor as a rabbit on an elastic
tether?the rabbit moves in all directions but as it tires it is drawn
toward the middle where it lies down to rest. Think of a strange
attractor as a rabbit in a pen with a dog on the outside?the rabbit
keeps running to the side of the pen opposite from the dog but as it
tires it comes to rest in the middle of the pen. The rabbit ends up in
the 'middle' in either case. With the tether the cause is the pull of
the elastic. In the pen the cause is repulsion from the dog
unsystematically attacking from all sides."

http://www.anecdote.com.au/archives/2005/01/a_metaphor_for.html

This website may be of interest:

http://www.strange-attractors.org/
Subject: Re: "Strange Attractors" in chaos theory
From: cats4me-ga on 31 Mar 2005 15:23 PST
 
Thanks!  I love the rabbit metaphor, very interesting.  Kind of you to
send it along.
Michelle
Subject: Re: "Strange Attractors" in chaos theory
From: myoarin-ga on 01 Apr 2005 08:24 PST
 
That's a neat metaphor, but doesn't account for my daughter's rabbit,
that liked to attract/tease the neighbor's dogs on the other side of
an adequately protective chain-link fence.  Hoppel (of course, without
any elastic tether, free-running in our yard) would go near the fence
and the dogs would show interest, without frightening Hoppel. 
Eventually the nice neighbors put up a reed screen to stop the game.
But maybe that is just a turn on pinkfreud's example, Hoppel choosing
to stretch the presumed elastic tether towards the dogs rather going
the other way.
Subject: Re: "Strange Attractors" in chaos theory
From: dmrmv-ga on 05 Apr 2005 13:19 PDT
 
I would suggest water circling a drain. Clearly the water is
"attracted" to the drain, but doesn't take the most direct path. Of
course the water doesn't have the element of randomness that true
chaotic behaviour would have.
Subject: Comment on comments
From: hedgie-ga on 05 Apr 2005 20:26 PDT
 
dm-r-mv,  Watter is not attracted to the sink, but to the Earth - but
that is not relevant. Physical attraction is not required - it is a
mathematical notion. Example fails for diferent reason: The concept
requires some system which moves through a series of states. Why it is
moving is not relevant. What is relevant is that [in some systems] no
matter what the initial point was, system eventually ends up in small
subset of the full space. That subset is
the attractor. Subset can be a single point, (dimensions 0) or part of a line
or curve (dimensions 1) etc. So, Pinkie's parable could describe attractor, if
rabit (originally placed anywhere) would run away from a dog, and then will 
find a fenced area into which dog cannot get. The fenced area would be
an attractor - but it would not be strange. Strange attractors have
fractional dimension, like 1.6 - they are fractals. Example of
fractal, found in nature, is 'the coastline' or 'a snowflake'. But
these are not attractors in any obvious way.
Even parables are not easy to come by, for something this strange.

Turbulent flow, not vortex formed in a sink (which is laminar), could qualify.
Here is a descriptions of different types of attractors:
http://www.answers.com/strange+attractor&r=67

 Of course, chances are that cats4me-ga does not care, which perhaps can 
bring another example: the human attention. Often it wanders and
wanders, from topic to topic, and then when a person worries about
something, it may be comming to the same subject, over and over again.
Or perhaps system which contains cat and catnip ..  (what about some
rating cats4me..? ?? )
Hedgie

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