# Complex Systems and Chaos Theory

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• December 13th, 2005, 03:00 AM
Arkimedes
Complex Systems and Chaos Theory
I was browsing through the local University's library, and came upon some books by the Santa Fe Institute on complex Systems. Unfortunately, I don't go to that library, and stuck out like a sore thumb; so I was forced to leave.

My college doesn't really have too much on chaos theory, or complex systems. This is particularly fascinating to me, does anyone know about it?
• December 13th, 2005, 06:26 AM
The Texan
http://en.wikipedia.org/wiki/Chaos_theory try that link... I have drank a 6 pack of coors so im not at full searching potential but i tried :)
• December 13th, 2005, 08:12 AM
omin
Complex systems and chaos theory cover a LOT of different areas so it might be a good idea to narrow down your search. What are your interests? What courses are you taking? These might help you choose a specific area to start with.

Some ideas to get you started....

chaos theory:

I have just one word. FRACTALS :D
If you have not come across fractals before then this is definatly where I would reccommend starting (though chaos theory does cover a LOT more than just fractals). The truest form of computer artwork around, these images are created from a simple mathematical formula but are infinite in complexity. I have been exploring fractals and their variations for many years now and am still fascinated by them.
xaos is a good program to try...
http://xaos.sourceforge.net/english.php
you could also try this link for some nice examples of various types of fractals...
http://sprott.physics.wisc.edu/fractals.htm

complex systems:

This tends to deal with understanding systems that are so complex that prediction of the systems becomes very difficult. ie turbulance in water and clouds, human population interaction and information flow over the internet.
Try a google search for 'john conway' and 'game of life' for some nice descriptions of complex systems - this deals with complex systems emerging from some very simple rules and can be quite astonishing to see in action.
This link offers a nice intro to the game of life...
http://www.math.com/students/wonders/life/life.html

As I said, both these subjects cover WAY more than I have just mentioned. To describe all related subjects would take a LONG time and many, many pages. This is why I reccommend finding areas that you are particularly interested in and staring there.

If you are prepared to do A LOT of reading into these fascinating subjects then you will be highly rewarded. But be warned. This can become addictive. :cool:

omin
• December 13th, 2005, 09:32 AM
Aspman

Try to ignore the film references.
• December 13th, 2005, 09:56 AM
nihil
Hi,

Quote:

My college doesn't really have too much on chaos theory, or complex systems. This is particularly fascinating to me, does anyone know about it?
My first move would be to go to my local librarian and see if you cannot borrow the books through him/her.

They also might be able to arrange "guest reader" rights for you at the other library?

Over here in the UK, this would not be a problem...........a bit like guest membership at a golf/tennis/squash/shooting club?..............except that libraries are free :D

Quote:

I have drank a 6 pack of coors so im not at full searching potential but i tried
Tex~ drink the other six, and I am sure that you will come online? :D

Quote:

The truest form of computer artwork around these images are created from a simple mathematical formula but are infinite in complexity.
Spot on!............/off topic................they make great Christmas presents, for people you do not know what to buy for? \

:)
• December 13th, 2005, 11:00 AM
sec_ware
Hi

As omin has pointed out, the applicability of such theories[1] is
enormous. Myself, I tried to use multi-agent systems[2] to beat
stochastic volatility models of the stock market like Heston-Nandi
or GARCH for option pricing - unfortunately, so far I always was
"over par" (if you want to say so), but who knows... :D

Anyways, when I stare at the Heston-Nandy (or GARCH) process, I
recognise a similarity to chaotic systems: finite difference equations
or differential equations. If the degrees of freedom are coupled
non-linearly, you have a chaotic system - in other words, the
similarity of the above processes indeed is given, but "boring" from a
chaos theoretical point of view.

Hence, my suggestion: Read a paper[3], which theoretically deals
with chaotic behaviour. The reference I have given introduces the
concepts with the Drosophila melanogaster of chaos theory, the
one dimensional logistic map and extends from there.

If you understand the underlying concepts, you will be able to
understand the interdiscplinary applications. Check scholar.google.com

Cheers

[1] http://www.andymeneely.com/Prog/Frac...%20-%20mjd.pdf
[2] http://www.kuenstliche-intelligenz.d...carley-web.pdf
[3] http://ma-yue.net/study/bib/chaos/pr...ntrolchaos.pdf
• December 13th, 2005, 04:31 PM
omin
Very interesting papers sec_ware (got myself a new sig). :)

Just as a side note, xaos does not display 'true' fractals as it only goes through a finite number of iterations (after you have zoomed in for a while it 'runs out') but because of the real-time zooming it is still one of my favourite fractal gererators.
You can even find it in the default download of Knoppix! (at least it was in the most recent Knoppix that I downloaded)

Here are some more links to other fractal generators...

http://www.ultrafractal.com/

http://www.eclectasy.com/Fractal-Explorer/

http://spanky.triumf.ca/www/fractint/fractint.html

...and one of my favourite sites. This has LOTS of resources for anyone interested in exploring fractals further...

http://www.fractalus.com/
• December 13th, 2005, 08:39 PM
Arkimedes: inter college loan. they may be willing to lend you the book through your university. this is esecialy true if the schools aer geographicly close.
• December 13th, 2005, 08:50 PM
JewishIntent
My favorite fractal generator has always been, and may always be, fractal forge. To my knowledge it will never run out by zooming in too much.You can get it here.
http://sourceforge.net/projects/fractalforge/
• December 14th, 2005, 03:21 AM
Arkimedes
Well the problem with interlibrary loan is that my family lives in L.A. (where I am at the moment), and it was at Caltech. I go to Reed in Portland, Oregon.

That too may be a problem with the "guest card" to the library. The requirements are:
Quote:

Users with a legitimate need to use the specialized collections at Caltech may apply for this card. Graduate level status and the recommendation of two members of the Caltech Faculty or administration is required. Application is initiated at the Millikan Library circulation desk between the hours of 8am & 5pm, Monday through Friday. Applicants will be notified by mail following review of their application (approximately two weeks from date of application).
and I qualify for none of these!

If anyone here can get me a lifetime permenant card to the Caltech Library System, I'll give you one hundred dollars cash.

Anyways, I think sec_ware explained it best.

Are complex systems nothing more than a system of chaotic equations? Similiar to the system of equations used in linear algebra and matrices, et al. ?
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